Dialami , N.; Chiumenti, M.; Cervera, M.; Segatori, A.; Osikowicz, W. International journal of mechanical sciences Vol. 133, p. 555-567 DOI: 10.1016/j.ijmecsci.2017.09.022 Data de publicació: 2017-11 Article en revista
Friction is one of the main heat generation mechanisms in Friction Stir Welding (FSW). This phenomenon occurs between the pin and the workpiece as the rotating tool moves along the weld line. An accurate friction model is essential for obtaining realistic results in a FSW simulation in particular temperature, forces and torque. In this work, a modified Norton's friction law is developed. The suggested enhanced friction model aims at providing not only the realistic temperature field but also the forces and torque. This model does not exclusively relate the frictional shear stress to the sliding velocity; conversely it takes into account the effect of non-uniform pressure distribution under the shoulder, as this latter has an important role in the process of heat generation. Longitudinal, transversal and vertical forces and torque are numerically calculated. The effect of the enhanced friction model is reflected in these forces. In particular, it leads to a more realistic estimation of the transversal and longitudinal forces in comparison with the results obtained using former models. The friction model is successfully validated by the experimental measurements provided by the industrial partner (Sapa). The experimental analysis is performed for the material characterization, the calibration of the friction model and, more generally, the assessment of the overall numerical strategy proposed for the FSW simulation.
This work presents the computational strategy adopted for the numerical simulation of the Selective Laser Melting (SLM) technology used in Additive Manufacturing (AM). SLM is used to fabricate industrial components by powder bed technology in a layer-by-layer manner. Hence, firstly the CAD geometry is sliced, and later, the scanning sequence is generated to allow for the selective melting of the different sections of the sliced geometry. The SLM machine makes use of a high power laser beam for the powder melting, while Titanium-64 powder is our reference material. The objective of this work consists of: (i) assessing the inherent shrinkage method to reproduce the manufacturing process in a layer-by-layer manner; (ii) calibrating the model parameters according to the experimental evidence provided by IK4-LORTEK. The transient coupled thermomechanical analysis defined for the high-fidelity simulation of the AM process [1,2] is replaced by a faster sequence of quasi-static mechanical computations according to
the metal deposition in the building sequence. The scanning path is not faithfully reproduced; instead, a layer-by-layer strategy is adopted. This is feasible because, compared to other available AM technologies (e.g. wire-feeding or blown powder), the scanning speed is much faster (almost 10 times) and the power source used for the melting process is much smaller (almost 10 times). Hence, the laser spot and the corresponding Heat Affected Zone (HAZ) is much smaller and the cooling process much faster than for other manufacturing technologies. Avoiding the transient thermal analysis, the thermal stresses are computed by defining an inherent strain field as a function of the material shrinkage and the process parameters that characterise the manufacturing process. The solution strategy proposed is calibrated by the experimental work carried out at IK4-LORTEK, where the distortions and residual stresses induced by the manufacturing process are measured for a number of samples.
Dialamishabankareh, N.; Cervera, M.; Chiumenti, M.; Segatori, A.; Osikowicz, W.; Olsson, B. International Conference on Computational Plasticity p. 1 Data de presentació: 2017-09-07 Presentació treball a congrés
This work presents the results of the numerical simulation and experimental validation of a fast and accurate FEM model for FSW simulation [1,2]. In this model, the fully coupled thermomechanical problem is solved using an apropos kinematic framework, a mixed pressure-velocity formulation and an accurate stabilization procedure with optimal numerical dissipation. The model considers the friction between the tool and the workpiece and the plastic dissipation as the
main sources of heat generation. The friction model proposed is a modified viscoplastic Norton’s law that not only relates the frictional shear stress to the sliding velocity but also accounts for the pressure
distribution. The constitutive model proposed is calibrated by the experimental material characterization provided in terms of stress/strain rate. The study shows that the proposed modelling approach can be used to predict and interpret the FSW behaviour for a given pin geometry. The results obtained in terms of forces, torque and temperature evolution are validated against the measurement provided by the industrial partner (SAPA).
Modelling of cracking in quasi-brittle materials has been the object of intensive study in computational solid mechanics over the last five decades. In most of the studies carried out with standard irreducible elements, the attempts to predict the crack path fail because the obtained solution suffers from spurious bias mesh dependency. The problem is addressed via a mixed strain/displacement finite element formulation [1-4].
In this presentation, a mixed strain/displacement finite element formulation is applied to the solution of nonlinear solid mechanics problems. For this, an enhanced version of the finite element program COMET  has been developed. The proposed mixed formulation is fully general and is applied in 2D and 3D. Also, it is independent of the specific finite element discretization considered; it can be equally used with triangles/tetrahedra, quadrilaterals/hexahedra and prisms.
The feasibility and accuracy of the method is assessed through extensive comparison with experimental evidence. The correlation with the experimental tests shows the capacity of the mixed formulation to reproduce the experimental crack path, failure mechanism and the force-displacement curves with remarkable accuracy. Both 2D and 3D examples produce results consistent with the documented data.
Spurious mesh dependency suffered by both continuous and discontinuous irreducible formulations is avoided by the mixed FE, without the need of auxiliary tracking techniques or other computational schemes that alter the continuum mechanical problem.
This contribution presents a numerical investigation of experimental tests on skew notched beams with the mixed strain-displacement finite element method . Mode III and mixed mode loading conditions are often encountered in tests involving torsion and asymmetrical bending for the mechanical characterization of quasi-brittle materials. Recently, the authors showed that the mixed strain displacement finite elements are capable of delivering very accurate results in the analysis of experimental pull-out tests on unreinforced concrete . This is possible thanks to the enhanced convergence that the mixed formulation provides in a non-linear mechanical problem involving localization and failure, by solving the displacement and strains field as independent variables . In this work, the proposed FE technology is applied to three study cases: firstly, a three point bending test of a Plexiglas beam; secondly, the torsion test of a plain concrete prismatic beam; finally, the torsion test of a cylindrical beam made of plain concrete as well. All three specimens present a notch at the midspan with a 45 degrees inclination. To take into account the complex non-linear mechanical behaviour, Rankine and Drucker-Prager failure criteria are implemented in both plasticity and isotropic continuum damage models. It is shown that the mixed strain displacement formulation is able of overcoming the common issues encountered with the standard irreducible FEM. Indeed, it predicts fracture surfaces, peak loads and
global loss of carrying capability close to the experimental ones. Finally, taking advantage of the compatibility between the displacement-based and the mixed formulations, an enhancement in terms of computational time is presented.
Lafontaine, N.; Cervera, M.; Rossi, R.; Chiumenti, M. Revista internacional de métodos numéricos para cálculo y diseño en ingeniería Vol. 33, num. 3-4, p. 250-261 DOI: 10.1016/j.rimni.2016.06.001 Data de publicació: 2017-07 Article en revista
This paper presents the application of stabilized mixed explicit strain/displacement formulation (MEX-FEM) [23,24] for solving non-linear plasticity problems in solid mechanics with strain localization. In order to use the same linear interpolation order for displacements and strains, the formulation uses the variational subscales method. Compared to the standard irreducible formulation, the proposed formulation yields improved strain and stress fields, and it is capable of addressing nearly incompressible situations. This work investigates the effects of the improved strain and stress fields in problems involving strain softening and localization leading to failure for the Mohr-Coulomb and Drucker Prager plasticity models. Numerical examples validate the ability of the proposed formulation to correctly predict failure mechanisms with localized patterns of strain, virtually free of mesh dependence and without using tracking algorithm.
Dialami , N.; Cervera, M.; Chiumenti, M.; Agelet De Saracibar, C. International Conference on Computacional Methods for Coupled Problems in Science and Engineering p. 1 Data de presentació: 2017-06-13 Presentació treball a congrés
Pin geometry is a fundamental consideration in friction stir welding (FSW). It influences the thermal behaviour, material flow and forces during the weld and reflects on the joint quality.
This work studies four pin tools with circular, triflute, trivex, and triangular profiles adopting a validated model of FSW process developed by the authors [1-3]. The effect of the rotating tool geometry on the flow behaviour and process outcomes is analysed. Additionally, longitudinal and transversal forces and torque are numerically calculated and compared for the different pin shapes. The study is carried out for slip and stick limiting friction cases between pin and workpiece.
The Norton-Hoff constitutive model is adopted to characterize the material behaviour during the weld. The piecewise linear version of the model developed by the authors greatly facilitates the convergence of the numerical solution ensuring both computational efficiency and accuracy. A two-stage computational procedure is applied. In the first stage, a forced transient is carried out; in the second one, the magnitudes of interest are computed.
The study shows that the proposed modelling approach can be used to predict and interpret the FSW behaviour when using specific pin geometry.
This paper aims to address the numerical simulation of additive manufacturing (AM) processes. The numerical results are compared with the experimental campaign carried out at State Key Laboratory of Solidification Processing laboratories, where a laser solid forming machine, also referred to as laser engineered net shaping, is used to fabricate metal parts directly from computer-aided design models. Ti-6Al-4V metal powder is injected into the molten pool created by a focused, high-energy laser beam and a layer of added material is sinterized according to the laser scanning pattern specified by the user.
The numerical model adopts an apropos finite element (FE) activation technology, which reproduces the same scanning pattern set for the numerical control system of the AM machine. This consists of a complex sequence of polylines, used to define the contour of the component, and hatches patterns to fill the inner section. The full sequence is given through the common layer interface format, a standard format for different manufacturing processes such as rapid prototyping, shape metal deposition or machining processes, among others. The result is a layer-by-layer metal deposition which can be used to build-up complex structures for components such as turbine blades, aircraft stiffeners, cooling systems or medical implants, among others.
Ad hoc FE framework for the numerical simulation of the AM process by metal deposition is introduced. Description of the calibration procedure adopted is presented.
The objectives of this paper are twofold: firstly, this work is intended to calibrate the software for the numerical simulation of the AM process, to achieve high accuracy. Secondly, the sensitivity of the numerical model to the process parameters and modeling data is analyzed.
La resolución de problemas de localización de deformaciones y fallos cuasi-frágiles en materiales friccional-cohesivos sigue siendo un tema abierto a discusión. Debido a su complejidad y a las implicaciones en numerosos problemas de ingeniería, se ha dedicado un considerable esfuerzo al desarrollo de teorías y técnicas capaces de manejar el comportamiento inelástico de los sólidos.La introducción de los métodos numéricos en los años '70 proporcionó técnicas rápidas de cálculo que permitían obtener una solución, aunque aproximada, del problema a tratar. El Método de Elementos Finitos (FEM) es capaz de describir de manera eficiente un gran número de geometrías, problemas de ingeniería y condiciones de contorno, por lo que hace de la formulación irreducible la opción mayoritariamente escogida en el análisis de cuerpos sólidos. Asimismo, considerando la regularización del salto por el desplazamiento producido por una grieta a través de una banda de elementos, es posible calcular la aparición y evolución de una fractura.Sin embargo, los elementos finitos estándar se comportan de manera inadecuada en cálculos de localización de deformaciones en materiales con ablandamiento. La formulación irreducible está altamente influenciada por la malla empleada, y frecuentemente la dirección de fractura resultante es incorrecta. Este fenómeno aparece de manera significativa en plasticidad, siendo ortotrópica. De igual manera, con modelos isocóricos, el bloqueo de las deformaciones provoca oscilaciones de presión espurias, que hacen inutilizable la solución numérica obtenida. Es posible demostrar que ambos problemas no están relacionados por la definición continua del problema, sino con su formulación discreta.En este trabajo se presenta una nueva formulación mixta e-u de elementos finitos en desplazamientos y deformaciones para la localización de deformaciones y fallo en plasticidad. Solucionando independientemente deformaciones y desplazamientos, la formulación se caracteriza por la mejora de las capacidades cinemáticas, que da como resultado una mejora crucial en la precisión del cálculo de tensiones y deformaciones. Además, se demuestra que los problemas numéricos de la formulación irreducible se ven mitigados con el uso de la técnica de los elementos finitos mixtos.En los ejemplos, se considera el fallo con carga de Modo I (apertura) a través de un criterio de fallo de Rankine para describir el comportamiento mecánico de materiales, como el hormigón, que fallan por carga de tracción. Luego, se estudia el fallo con carga en Modo II (cizallamiento), empleando los criterios de fallo de J2 von Mises y de Drucker-Prager para la plasticidad incompresible y compresible. Por fin, se discute el fallo en Modo III (rasgado) y en Modo Mixto. Se implementan los criterios de Rankine y Drucker-Prager, tanto en plasticidad como en daño continuo para estudiar el estado de tensión en casos de flexión desviada y de torsión.Entonces, surgen tres conclusiones principales: (i) el método de elementos finitos mixto e-u es capaz de superar los desafíos planteados por la localización de la deformación en sólidos, con soluciones confiables y precisas; (ii) el modelo de fisura distribuida describe la creación y propagación de superficies de fractura por carga en Modo I, Modo II, Modo III y Modo Mixto; (iii) la mejora de la descripción cinemática, con continuidad de desplazamientos y deformaciones, se considera un factor clave para mejorar la solución numérica.El e-u FEM comparte muchos detalles de implementación de leyes constitutivas, conjunto inicial de datos y discretización geométrica con el método estándar. Sin embargo, la formulación mixta propuesta es superior en la predicción de las cargas máximas, patrones de localización de deformación y mecanismos de fallo. Además, demuestra su generalidad y sus posibilidades para un uso favorable en la práctica de la ingeniería.
Strain localization and quasi-brittle failure in frictional-cohesive materials is still an open and challenging problem in computational mechanics. Owing to its complexity and the significant implications on numerous engineering problems, a considerable effort has been devoted to the development of theories and techniques capable of dealing with this topic.
The introduction of numerical methods in the 70's provided a way to compute solutions, even if approximated. The Finite Element Method is able to describe a large number of geometries, engineering problems and various boundary conditions and, for this reason, the displacement-based formulation represents the preferred choice in the mechanical analysis of solids. Moreover, assuming the displacement jump created by a crack to be smeared across an element band, the calculation of the onset and the evolution of a fracture can be performed.
However, standard finite elements are well-known to behave poorly in the case of strain localization of softening materials. Indeed, the irreducible formulation is mesh-biased and the resulting fracture direction is frequently incorrect. Plasticity constitutive models are largely affected by this issue, being directional by their very nature. In addition, when dealing with isochoric conditions, locking of the stresses provokes spurious pressure oscillations, that spoil the numerical solution. Both problems can be shown not to be related to the mathematical statement of the continuous problem but to its discrete (FEM) counterpart.
In this work, a novel mixed e-u strain-displacement finite element method for strain localization and failure in plasticity is presented. Thanks to the independent interpolation of the strain and displacement fields, it is characterized by enhanced kinematic properties which result in an improvement in the accuracy of stresses and deformations. Moreover, it is proved that the numerical quandaries typical of the irreducible formulation are alleviated with the introduction of this FE technology. The e-u FEM is applied to 2D and 3D problems aimed at benchmarking its numerical capabilities as well as proving high-fidelity predictions and simulations of experimental results.
Firstly, failure under Mode I (opening) loading is considered, using a Rankine failure criterion to describe the mechanical behavior of materials, such as concrete, which exhibit cracking under tensile load. Secondly, failure under Mode II (shearing) loading is studied, employing the J2 von Mises and the Drucker-Prager failure criteria for incompressible and compressible plasticity cases. Thirdly, failure under Mode III (tearing) and Mixed Mode loading is discussed. To study the complex stress state arising in torsional and skew-symmetrical bending cases, Rankine and Drucker-Prager failure criteria are developed in both plasticity and isotropic continuum damage models. Finally, the formulation is applied to crack propagation in weak snowpack layers, which is the main cause for the initiation of snow avalanches.
From the results, three main conclusions emerge: (i) the mixed e-u finite element method proposed is capable of overcoming many of the challenges posed by strain localization in solids, providing reliable and accurate solutions; (ii) the smeared crack approach is able to describe effectively the creation and propagation of fracture surfaces in Mode I, Mode II, Mode III and Mixed Mode loading; (iii) the improvement of the kinematic description, with continuity of displacements and strains, is considered a key factor to empower the numerical solution.
The e-u finite elements share numerous aspects with the standard displacement-based ones, in terms of implementation of constitutive laws, initial set of data and geometrical discretization. However, the proposed mixed formulation is superior in predicting peak loads, strain localization patterns and failure mechanisms, demonstrating its generality and its possibilities in the engineering practice.
La resolución de problemas de localización de deformaciones y fallos cuasi-frágiles en materiales friccional-cohesivos sigue siendo un tema abierto a discusión. Debido a su complejidad y a las implicaciones en numerosos problemas de ingeniería, se ha dedicado un considerable esfuerzo al desarrollo de teorías y técnicas capaces de manejar el comportamiento inelástico de los sólidos. La introducción de los métodos numéricos en los años '70 proporcionó técnicas rápidas de cálculo que permitían obtener una solución, aunque aproximada, del problema a tratar. El Método de Elementos Finitos (FEM) es capaz de describir de manera eficiente un gran número de geometrías, problemas de ingeniería y condiciones de contorno, por lo que hace de la formulación irreducible la opción mayoritariamente escogida en el análisis de cuerpos sólidos. Asimismo, considerando la regularización del salto por el desplazamiento producido por una grieta a través de una banda de elementos, es posible calcular la aparición y evolución de una fractura. Sin embargo, los elementos finitos estándar se comportan de manera inadecuada en cálculos de localización de deformaciones en materiales con ablandamiento. La formulación irreducible está altamente influenciada por la malla empleada, y frecuentemente la dirección de fractura resultante es incorrecta. Este fenómeno aparece de manera significativa en plasticidad, siendo ortotrópica. De igual manera, con modelos isocóricos, el bloqueo de las deformaciones provoca oscilaciones de presión espurias, que hacen inutilizable la solución numérica obtenida. Es posible demostrar que ambos problemas no están relacionados por la definición continua del problema, sino con su formulación discreta. En este trabajo se presenta una nueva formulación mixta e-u de elementos finitos en desplazamientos y deformaciones para la localización de deformaciones y fallo en plasticidad. Solucionando independientemente deformaciones y desplazamientos, la formulación se caracteriza por la mejora de las capacidades cinemáticas, que da como resultado una mejora crucial en la precisión del cálculo de tensiones y deformaciones. Además, se demuestra que los problemas numéricos de la formulación irreducible se ven mitigados con el uso de la técnica de los elementos finitos mixtos. En los ejemplos, se considera el fallo con carga de Modo I (apertura) a través de un criterio de fallo de Rankine para describir el comportamiento mecánico de materiales, como el hormigón, que fallan por carga de tracción. Luego, se estudia el fallo con carga en Modo II (cizallamiento), empleando los criterios de fallo de J2 von Mises y de Drucker-Prager para la plasticidad incompresible y compresible. Por fin, se discute el fallo en Modo III (rasgado) y en Modo Mixto. Se implementan los criterios de Rankine y Drucker-Prager, tanto en plasticidad como en daño continuo para estudiar el estado de tensión en casos de flexión desviada y de torsión. Entonces, surgen tres conclusiones principales: (i) el método de elementos finitos mixto e-u es capaz de superar los desafíos planteados por la localización de la deformación en sólidos, con soluciones confiables y precisas; (ii) el modelo de fisura distribuida describe la creación y propagación de superficies de fractura por carga en Modo I, Modo II, Modo III y Modo Mixto; (iii) la mejora de la descripción cinemática, con continuidad de desplazamientos y deformaciones, se considera un factor clave para mejorar la solución numérica. El e-u FEM comparte muchos detalles de implementación de leyes constitutivas, conjunto inicial de datos y discretización geométrica con el método estándar. Sin embargo, la formulación mixta propuesta es superior en la predicción de las cargas máximas, patrones de localización de deformación y mecanismos de fallo. Además, demuestra su generalidad y sus posibilidades para un uso favorable en la práctica de la ingeniería
Finite element macro-modelling approaches are widely used for the analysis of large-scale masonry structures. Despite their efficiency, they still face two important challenges: the realistic representation of damage and a reasonable independency of the numerical results to the used discretization. In this work, the classical smeared crack approach is enhanced with a crack-tracking algorithm, originating from the analysis of localized cracking in quasi-brittle materials. The proposed algorithm is for the first time applied to a large-scale wall exhibiting multiple shear and flexural cracking. Discussion covers structural aspects, as the response of the structure under different assumptions regarding the floor rigidity, but also numerical issues, commonly overlooked in the simulation of large structures, such the mesh-dependency of the numerical results.
The testing of mode III and mixed mode failure is every so often encountered in the dedicated literature of mechanical characterization of brittle and quasi-brittle materials. In this work, the application of the mixed strain displacement e-ue-u finite element formulation to three examples involving skew notched beams is presented. The use of this FE technology is effective in problems involving localization of strains in softening materials.
The objectives of the paper are: (i) to test the mixed formulation in mode III and mixed mode failure and (ii) to present an enhancement in terms of computational time given by the kinematic compatibility between irreducible displacement-based and the mixed strain-displacement elements.
Three tests of skew-notched beams are presented: firstly, a three point bending test of a PolyMethyl MethaAcrylate beam; secondly, a torsion test of a plain concrete prismatic beam with square base; finally, a torsion test of a cylindrical beam made of plain concrete as well. To describe the mechanical behavior of the material in the inelastic range, Rankine and Drucker-Prager failure criteria are used in both plasticity and isotropic continuum damage formats.
The proposed mixed formulation is capable of yielding results close to the experimental ones in terms of fracture surface, peak load and global loss of carrying capability. In addition, the symmetric secant formulation and the compatibility condition between the standard irreducible method and the strain-displacement one is exploited, resulting in a significant speedup of the computational procedure.
Damage-induced strain softening is of vital importance for the modeling of localized failure in frictional-cohesive materials. This paper addresses strain localization of damaging solids and the resulting consistent frictional-cohesive crack models. As a supplement to the framework recently established for stress-based continuum material models in rate form (Wu and Cervera 2015, 2016), several classical strain-based damage models, expressed usually in total and secant format, are considered. Upon strain localization of such damaging solids, Maxwell's kinematics of a strong (or regularized) discontinuity has to be reproduced by the inelastic damage strains, which are defined by a bounded characteristic tensor and an unbounded scalar related to the damage variable. This kinematic constraint yields a set of nonlinear equations from which the discontinuity orientation and damage-type localized cohesive relations can be derived. It is found that for the "Simó and Ju 1987" isotropic damage model, the localization angles and the resulting cohesive model heavily depend on lateral deformations usually ignored in classical crack models for quasi-brittle solids. To remedy this inconsistency, a modified damage model is proposed. Its strain localization analysis naturally results in a consistent frictional-cohesive crack model of damage type, which can be regularized as a classical smeared crack model. The analytical results are numerically verified by the recently-proposed mixed stabilized finite element method, regarding a singly-perforated plate under uniaxial tension. Remarkably, for all of the damage models discussed in this work, the numerically-obtained localization angles agree almost exactly with the closed-form results. This agreement, on the one hand, consolidates the strain localization analysis based on Maxwell's kinematics and, on the other hand, illustrates versatility of the mixed stabilized finite element method.
In this paper, an energy-equivalent orthotropic d+/d- damage model for cohesive-frictional materials is formulated. Two essential mechanical features are addressed, the damage-induced anisotropy and the microcrack closure-reopening (MCR) effects, in order to provide an enhancement of the original d+/d- model proposed by Faria et al. 1998, while keeping its high algorithmic efficiency unaltered. First, in order to ensure the symmetry and positive definiteness of the secant operator, the new formulation is developed in an energy-equivalence framework. This proves thermodynamic consistency and allows one to describe a fundamental feature of the orthotropic damage models, i.e., the reduction of the Poisson’s ratio throughout the damage process. Secondly, a “multidirectional” damage procedure is presented to extend the MCR capabilities of the original model. The fundamental aspects of this approach, devised for generic cyclic conditions, lie in maintaining only two scalar damage variables in the constitutive law, while preserving memory of the degradation directionality. The enhanced unilateral capabilities are explored with reference to the problem of a panel subjected to in-plane cyclic shear, with or without vertical pre-compression; depending on the ratio between shear and pre-compression, an absent, a partial or a complete stiffness recovery is simulated with the new multidirectional procedure
Dialami , N.; Cervera, M.; Chiumenti, M.; Agelet De Saracibar, C. International journal of mechanical sciences Vol. 122, p. 215-227 DOI: 10.1016/j.ijmecsci.2016.12.016 Data de publicació: 2017-03-01 Article en revista
Pin geometry is a fundamental consideration in friction stir welding (FSW). It influences the thermal behaviour, material flow and forces during the weld and reflects on the joint quality.
This work studies four pin tools with circular, triflute, trivex, and triangular profiles adopting a validated model of FSW process developed by the authors. The effect of the rotating tool geometry on the flow behaviour and process outcomes is analysed. Additionally, longitudinal and transversal forces and torque are numerically calculated and compared for the different pin shapes. The study is carried out for slip and stick limiting friction cases between pin and workpiece.
The main novelties of the paper are a “speed-up” two-stage simulation methodology and a piecewise linear version of the constitutive model, both of them conceived for the use in real case industrial applications, where the achievement of accuracy with affordable simulation times is of importance.
The Norton-Hoff constitutive model is adopted to characterize the material behaviour during the weld. The piecewise linear version of the model developed by the authors greatly facilitates the convergence of the numerical solution ensuring both computational efficiency and accuracy. A two-stage computational procedure is applied. In the first stage, a forced transient is carried out; in the second one, the magnitudes of interest are computed.
The study shows that the proposed modelling approach can be used to predict and interpret the FSW behaviour for a specific pin geometry. Moreover, the reduction of the simulation time using the two-stage strategy can be up to 90%, compared to a standard single stage strategy.
Dialami , N.; Cervera, M.; Chiumenti, M.; Agelet De Saracibar, C. International journal of advanced manufacturing technology Vol. 88, num. 9, p. 3099-3111 DOI: 10.1007/s00170-016-9016-3 Data de publicació: 2017-02 Article en revista
This work describes the local–global strategy proposed for the computation of residual stresses in friction stir welding (FSW) processes. A coupling strategy between the analysis of the process zone nearby the pin tool (local level analysis) and the simulation carried out for the entire structure to be welded (global level analysis) is implemented to accurately predict the temperature histories and, thereby, the residual stresses in FSW. As a first step, the local problem solves the material stirring as well as the heat generation induced by the pin and shoulder rotation at the heat affected zone. The Arbitrary Lagrangian Eulerian (ALE) formulation is adopted to deal with the rotation of complex pin shapes. A thermo-rigid-viscoplastic constitutive law is employed to characterize the viscous flow of the material, driven by the high-strain rates induced by the FSW process. A mixed temperature–velocity–pressure finite element technology is used to deal with the isochoric nature of the strains. The output of this local analysis is the heat generated either by plastic dissipation or by friction, and it is used as the power input for the welding analysis at structural (global) level. The global problem is tackled within the Lagrangian framework together with a thermo-elasto-viscoplastic constitutive model. In addition, in this case, the mixed temperature–displacement–pressure format is introduced to deal with the deviatoric nature of the plastic strains. The outcomes of this analysis are the distortions and the residual stresses after welding. The material used in this work is stainless steel 304 L; however, the methodology presented is applicable to a wide range of materials. The proposed numerical strategy is validated by the experimental evidence.
Tracking algorithms constitute an efficient numerical technique for modelling fracture in quasi-brittle materials. They succeed in representing localized cracks in the numerical model without mesh-induced directional bias. Currently available tracking algorithms have an important limitation: cracking originates either from the boundary of the discretized domain or from predefined “crack-root” elements and then propagates along one orientation. This paper aims to circumvent this drawback by proposing a novel tracking algorithm that can simulate cracking starting at any point of the mesh and propagating along one or two orientations. This enhancement allows the simulation of structural case-studies experiencing multiple cracking. The proposed approach is validated through the simulation of a benchmark example and an experimentally tested structural frame under in-plane loading. Mesh-bias independency of the numerical solution, computational cost and predicted collapse mechanisms with and without the tracking algorithm are discussed.
The final publication is available at Springer via http://dx.doi.org/10.1007/s00466-016-1351-6
Lafontaine, N.; Rossi, R.; Cervera, M.; Chiumenti, M. Revista internacional de métodos numéricos para cálculo y diseño en ingeniería Vol. 33, num. 1-2, p. 35-44 DOI: 10.1016/j.rimni.2015.09.003 Data de publicació: 2017-01 Article en revista
This study presents a mixed finite element formulation able to address nearly-incompressible problems explicitly. This formulation is applied to elements with independent and equal interpolation of displacements and strains, stabilized by variational subscales (VMS). As a continuation of the study presented in reference , in which the strains sub-scale was introduced, in this work the effects of sub-scale displacements are included, in order to stabilize the pressure field. The formulation avoids the Ladyzhenskaya-Babuska-Brezzi (LBB) condition and only requires the solution of a diagonal system of equations. The main aspects of implementation are also discussed. Finally, numerical examples validate the behaviour of these elements compared with the irreductible formulation.
Dialami , N.; Chiumenti, M.; Cervera, M.; Agelet De Saracibar, C. Archives of computational methods in engineering Vol. 24, num. 1, p. 189-225 DOI: 10.1007/s11831-015-9163-y Data de publicació: 2017-01 Article en revista
This paper deals with the numerical simulation of friction stir welding (FSW) processes. FSW techniques are used in many industrial applications and particularly in the aeronautic and aerospace industries, where the quality of the joining is of essential importance. The analysis is focused either at global level, considering the full component to be jointed, or locally, studying more in detail the heat affected zone (HAZ). The analysis at global (structural component) level is performed defining the problem in the Lagrangian setting while, at local level, an apropos kinematic framework which makes use of an efficient combination of Lagrangian (pin), Eulerian (metal sheet) and ALE (stirring zone) descriptions for the different computational sub-domains is introduced for the numerical modeling. As a result, the analysis can deal with complex (non-cylindrical) pin-shapes and the extremely large deformation of the material at the HAZ without requiring any remeshing or remapping tools. A fully coupled thermo-mechanical framework is proposed for the computational modeling of the FSW processes proposed both at local and global level. A staggered algorithm based on an isothermal fractional step method is introduced. To account for the isochoric behavior of the material when the temperature range is close to the melting point or due to the predominant deviatoric deformations induced by the visco-plastic response, a mixed finite element technology is introduced. The Variational Multi Scale method is used to circumvent the LBB stability condition allowing the use of linear/linear P1/P1 interpolations for displacement (or velocity, ALE/Eulerian formulation) and pressure fields, respectively. The same stabilization strategy is adopted to tackle the instabilities of the temperature field, inherent characteristic of convective dominated problems (thermal analysis in ALE/Eulerian kinematic framework). At global level, the material behavior is characterized by a thermo–elasto–viscoplastic constitutive model. The analysis at local level is characterized by a rigid thermo–visco-plastic constitutive model. Different thermally coupled (non-Newtonian) fluid-like models as Norton–Hoff, Carreau or Sheppard–Wright, among others are tested. To better understand the material flow pattern in the stirring zone, a (Lagrangian based) particle tracing is carried out while post-processing FSW results. A coupling strategy between the analysis of the process zone nearby the pin-tool (local level analysis) and the simulation carried out for the entire structure to be welded (global level analysis) is implemented to accurately predict the temperature histories and, thereby, the residual stresses in FSW.
Chiumenti, M.; Cervera, M.; Dialami , N.; Wu, B.; Jinwei, L.; Agelet De Saracibar, C. Finite elements in analysis and design Vol. 121, p. 118-133 DOI: 10.1016/j.finel.2016.07.003 Data de publicació: 2016-11 Article en revista
Electron Beam Welding (EBW) is a highly efficient and precise welding method increasingly used within the manufacturing chain and of growing importance in different industrial environments such as the aeronautical and aerospace sectors. This is because, compared to other welding processes, EBW induces lower distortions and residual stresses due to the lower and more focused heat input along the welding line.
This work describes the formulation adopted for the numerical simulation of the EBW process as well as the experimental work carried out to calibrate and validate it.
The numerical simulation of EBW involves the interaction of thermal, mechanical and metallurgical phenomena. For this reason, in this work the numerical framework couples the heat transfer process to the stress analysis to maximize accuracy. An in-house multi-physics FE software is used to deal with the numerical simulation. The definition of an ad hoc moving heat source is proposed to simulate the EB power surface distribution and the corresponding absorption within the work-piece thickness. Both heat conduction and heat radiation models are considered to dissipate the heat through the boundaries of the component. The material behavior is characterized by an apropos thermo-elasto-viscoplastic constitutive model. Titanium-alloy Ti6A14V is the target material of this work.
From the experimental side, the EB welding machine, the vacuum chamber characteristics and the corresponding operative setting are detailed. Finally, the available facilities to record the temperature evolution at different thermo-couple locations as well as to measure both distortions and residual stresses are described. Numerical results are compared with the experimental evidence.
This paper presents an improved computational model for the analysis of masonry structures based on continuum mechanics finite element approaches. The proposed numerical technique uses a cracktracking
algorithm to model the formation of strain localization bands within the discretization domain. This strategy results in two major benefits. First, the representation of the discrete cracks experienced by masonry structural elements is more accurate and consistent with limit analysis, which in turn leads to the realistic prediction of the collapse mechanisms. Second, the numerical solution is mesh-bias independent ensuring the objectivity of the simulation to the direction of the utilized mesh. The efficiency of the proposed algorithm is illustrated through the numerical simulation of a selected experimental test on a masonry pier-spandrel system.
This paper presents an explicit mixed finite element formulation to address compressible and quasi-incompressible problems in elasticity and plasticity. This implies that the numerical solution only involves diagonal systems of equations. The formulation uses independent and equal interpolation of displacements and strains, stabilized by variational subscales. A displacement sub-scale is introduced in order to stabilize the mean-stress field. Compared to the standard irreducible formulation, the proposed mixed formulation yields improved strain and stress fields. The paper investigates the effect of this enhancement on the accuracy in problems involving strain softening and localization leading to failure, using low order finite elements with linear continuous strain and displacement fields (P1P1 triangles in 2D and tetrahedra in 3D) in conjunction with associative frictional Mohr–Coulomb and Drucker–Prager plastic models. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to analytical solutions for plane stress and plane strain situations. Benchmark numerical examples show the capacity of the mixed formulation to predict correctly failure mechanisms with localized patterns of strain, virtually free from any dependence of the mesh directional bias. No auxiliary crack tracking technique is necessary.
The final publication is available at Springer via http://dx.doi.org/ 10.1007/s00466-016-1305-z
This paper presents the 2D and 3D numerical analysis of pullout tests on steel anchorages in concrete blocks using standard and mixed finite elements. A novel (stabilized) mixed formulation in the variables of total strain 8 and displacements u is introduced to overcome the intrinsic deficiencies of the standard displacement-based one in the context of localization of strains, such as mesh dependency. The quasi brittle behavior of concrete is described through an elastoplastic constitutive law with a local Rankine yielding criterion. The proposed formulation is shown to be a reliable and accurate tool, sensitive to the physical parameters of the pullout tests, but objective with respect to the adopted FE mesh. Furthermore, the mixed epsilon/u finite element is able to capture the correct failure mechanism with relatively coarse discretizations. At the same time, the spurious behavior of the standard formulation is not alleviated by mesh-refinement.
In this work the numerical simulation of the Additive Manufacturing (AM) process is addressed. The coupled thermo-mechanical framework used to solve the balance equations, as well as the constitutive laws to describe the material behavior in the entire temperature range are presented. The numerical model has been calibrated through the experimental campaign carried out at the State Key Laboratory of Solidification Processing (SKLSP) where a Laser Solid Forming (LSF) machine is operated. This machine makes use of the blown powder technique to perform the Metal Deposition (MD) process in a layer-by-layer manner. Both the software and the machine read the same scanning sequence given through Common Layer Interface (CLI) format, that is, the sequence of polylines and hatching to cover the entire section of the component for each layer. The power absorption coefficient and the Heat Transfer Coefficients (HTC) for both heat convection and heat radiation laws have been calibrated to capture the temperature evolution at the different locations where the thermocouples have been placed. The response of the thermo-visco-elastic-visco-plastic constitutive model has been calibrated by comparing the distortion of the supporting plate at different locations monitored during the full duration of the manufacturing process.
Remarkable agreement between experimental and numerical results is shown.
This paper presents a numerical study on the effect of the relative geometry between piers and spandrels in the structural response of regular masonry frames against horizontal loading. A sensitivity analysis is carried out for thirty geometrical configurations of piers and spandrels under two different vertical loading conditions. The numerical analyses are performed with the use of a continuum finite
element model enhanced with a crack-tracking technique. This approach is chosen due to its capacity to model accurately cracking phenomena in quasi-brittle materials, yielding realistic collapse mechanisms. The study aims to give an insight on the variation of the capacity and ductility of the structure, as well as the obtained damage pattern, in respect to the relative geometry between piers and spandrels. The results are also useful for the calibration of simplified modelling approaches.
Tracking algorithms constitute a useful tool for the realistic simulation of localized damage using the Finite Element Method. The aim of these algorithms is to identify the correct path of the crack within the discretized domain before damage occurs. Following that, the elements pertaining to it define the damage localization band. Tracking algorithms are used for the enhancement of problems involving the progression of both weak and strong discontinuities. Independently of the chosen approach, the aim of their employment is to obtain numerical results that are mesh-bias independent. Additionally, they provide a realistic representation of tensile cracking in solids, since the localization of damage occurs within a narrow band of the mesh. Despite the aforementioned advantages, the application of tracking algorithms is still narrow, focusing mostly on problems of monotonic loading with a limited number of cracks due to bending or pure traction. This issue is related to inherent assumptions of the tracking algorithms regarding the initiation, propagation and completion of the simulated cracks. This paper presents a tracking algorithm that is able to simulate flexural and shear cracking, as well as intersecting cracks. The work aims to extend the use of tracking algorithms to a wider field of structural applications, including multiple interior and boundary cracks, as well as intersecting cracks due to, for instance, load-reversal. The proposed local crack-tracking algorithm is used in combination with the smeared crack approach. Numerical simulations show that the algorithm is stable and robust and the results are free
of mesh-bias dependency. The methodology is quite inexpensive, making feasible the simulation of 2D large structures, such as building façades, experiencing multiple cracking.
Aiming for the modeling of localized failure in quasi-brittle solids, this paper addresses a thermodynamically consistent plastic-damage framework and the corresponding strain localization analysis. A unified elastoplastic damage model is first presented based on two alternative kinematic decompositions assuming infinitesimal deformations, with the evolution laws of involved internal variables characterized by a dissipative flow tensor. For the strong (or regularized) discontinuity to form in such inelastic quasi-brittle solids and to evolve eventually into a fully softened one, a novel strain localization analysis is then suggested. A kinematic constraint more demanding than the classical discontinuous bifurcation condition is derived by accounting for the traction continuity and the loading/unloading states consistent with the kinematics of a strong (or regularized) discontinuity. More specifically, the strain jumps characterized by Maxwell’s kinematic condition have to be completely inelastic (energy dissipative). Reproduction of this kinematics implies vanishing of the aforesaid dissipative flow tensorial components in the directions orthogonal to the discontinuity orientation. This property allows naturally developing a localized plastic-damage model for the discontinuity (band), with its orientation and the traction-based failure criterion consistently determined a posteriori from the given stress-based counterpart. The general results are then particularized to the 2D conditions of plane stress and plane strain. It is found that in the case of plane stress, strain localization into a strong (or regularized) discontinuity can occur at the onset of strain softening. Contrariwise, owing to an extra kinematic constraint, in the condition of plane strain some continuous inelastic deformations and substantial re-orientation of principal strain directions in general have to take place in the softening regime prior to strain localization. The classical Rankine, Mohr–Coulomb, von Mises (J2) and Drucker–Prager criteria are analyzed as illustrative examples. In particular, both the closed-form solutions for the discontinuity angles validated by numerical simulations and the corresponding traction-based failure criteria are obtained.
Pelà, L.; Bourgeois, J.; Roca, P.; Cervera, M.; Chiumenti, M. International journal of architectural heritage Vol. 10, num. 4, p. 418-437 DOI: 10.1080/15583058.2014.996920 Data de publicació: 2016-04 Article en revista
This paper presents the analysis of the structure of Mallorca Cathedral taking into account the influence on structural behaviour of auxiliary iron ties used during the construction process. Recent studies (Roca et al., 2012, 2013) have presented some hypotheses about the construction process of the cathedral. The present study complements the previous results by considering the use of auxiliary ties as temporary stabilizing device during the construction. Evidence of the use of ties during the construction has been recognized after a comprehensive survey. The study of the role of such ties and the effect of their later removal are studied by a FE analysis carried out on a representative bay of the structure. The study includes a time-dependent FE analysis after the removal of the ties to assess the long-term structural behaviour. The results of the numerical analysis are compared with the deformation trends identified by means of a recent monitoring campaign.
Moreno, E.; Cervera, M. Revista internacional de métodos numéricos para cálculo y diseño en ingeniería Vol. 32, num. 2, p. 100-109 DOI: 10.1016/j.rimni.2015.02.002 Data de publicació: 2016-04 Article en revista
This work presents a methodology for the solution of the Navier-Stokes equations for Bingham and Herschel-Bulkley viscoplastic fluids using stabilized mixed velocity/pressure finite elements. The theoretical formulation is developed and implemented in a computer code.; Viscoplastic fluids are characterized by a minimum shear stress called yield stress. Above this yield stress, the fluid is able to flow. Below this yield stress, the fluid behaves as a quasi-rigid body, with zero strain-rate.; First, the Navier-Stokes equations for incompressible fluid are presented. A review of the viscoplastic rheological models is included, with a detailed description of these models. The regularized viscoplastic models due to Papanastasiou are described. Double viscosity regularized models are proposed as an alternative to the models commonly used.; The discrete model is developed, and the Algebraic SubGrid Scale (ASGS) stabilization method, the Orthogonal Subgrid Scale (OSS) method and the split orthogonal subscales method are introduced.; The methodology proposed in this work provides a computational tool to study confined viscoplastic flows, common in industry.
En els últims anys, l'estudi de l'hemodinàmica computacional en regions vasculars anatòmicament complexes ha generat un gran interès entre els clínics. El progrés obtingut en la dinàmica de fluids computacional, en el processament d'imatges i en la computació d'alt rendiment ha permès identificar regions vasculars on poden aparèixer malalties cardiovasculars, així com predir-ne l'evolució. Actualment, la medicina utilitza un paradigma anomenat diagnòstic. En aquesta tesi s'intenta introduir en la medicina el paradigma predictiu utilitzat des de fa molts anys en l'enginyeria. Per tant, aquesta tesi té com a objectiu desenvolupar models predictius basats en indicadors de diagnòstic de patologies cardiovasculars. Tractem de predir l'evolució de l'aneurisma d'aorta abdominal, la coartació aòrtica i la malaltia coronària de forma personalitzada per a cada pacient. Per entendre com la patologia cardiovascular evolucionarà i quan suposarà un risc per a la salut, cal desenvolupar noves tecnologies mitjançant la combinació de les imatges mèdiques i la ciència computacional. Proposem uns indicadors que poden millorar el diagnòstic i predir l'evolució de la malaltia de manera més eficient que els mètodes utilitzats fins ara. En particular, es proposa una nova metodologia per al càlcul dels indicadors de diagnòstic basada en l'hemodinàmica computacional i les imatges mèdiques. Hem treballat amb dades de pacients anònims per crear una tecnologia predictiva real que ens permetrà seguir avançant en la medicina personalitzada i generar sistemes de salut més sostenibles. Però el nostre objectiu final és aconseguir un impacte en l'àmbit clínic. Diversos grups han tractat de crear models predictius per a les patologies cardiovasculars, però encara no han començat a utilitzar-les en la pràctica clínica. El nostre objectiu és anar més enllà i obtenir variables predictives que es puguin utilitzar de forma pràctica en el camp clínic. Es pot preveure que en el futur tots els metges disposaran de bases de dades molt precises de tota la nostra anatomia i fisiologia. Aquestes dades es poden utilitzar en els models predictius per millorar el diagnòstic o per millorar teràpies o tractaments personalitzats.
In recent years, the study of computational hemodynamics within anatomically complex vascular regions has generated great interest among clinicians.
The progress in computational fluid dynamics, image processing and high-performance computing haveallowed us to identify the candidate vascular regions for the appearance of cardiovascular diseases and to predict how this disease may evolve.
Medicine currently uses a paradigm called diagnosis. In this thesis we attempt to introduce into medicine the predictive paradigm that has been used in engineering for many years. The objective of this thesis is therefore to develop predictive models based on diagnostic indicators for cardiovascular pathologies.
We try to predict the evolution of aortic abdominal aneurysm, aortic coarctation and coronary artery disease in a personalized way for each patient. To understand how the cardiovascular pathology will evolve and when it will become a health risk, it is necessary to develop new technologies by merging medical imaging and computational science. We propose diagnostic indicators that can improve the diagnosis and predict the evolution of the disease more efficiently than the methods used until now. In particular, a new methodology for computing diagnostic indicators based on computational hemodynamics and medical imaging is proposed. We have worked with data of anonymous patients to create real predictive technology that will allow us to continue advancing in personalized medicine and generate more sustainable health systems. However, our final aim is to achieve an impact at a clinical level. Several groups have tried to create predictive models for cardiovascular pathologies, but they have not yet begun to use them in clinical practice. Our objective is to go further and obtain predictive variables to be used practically in the clinical field.
It is to be hoped that in the future extremely precise databases of all of our anatomy and physiology will be available to doctors. These data can be used for predictive models to improve diagnosis or to improve therapies or personalized treatments.
En els últims anys, l'estudi de l'hemodinàmica computacional en regions vasculars anatòmicament complexes ha generat un gran interès entre els clínics. El progrés obtingut en la dinàmica de fluids computacional, en el processament d'imatges i en la computació d'alt rendiment ha permès identificar regions vasculars on poden aparèixer malalties cardiovasculars, així com predir-ne l'evolució. Actualment, la medicina utilitza un paradigma anomenat diagnòstic. En aquesta tesi s'intenta introduir en la medicina el paradigma predictiu utilitzat des de fa molts anys en l'enginyeria. Per tant, aquesta tesi té com a objectiu desenvolupar models predictius basats en indicadors de diagnòstic de patologies cardiovasculars. Tractem de predir l'evolució de l'aneurisma d'aorta abdominal, la coartació aòrtica i la malaltia coronària de forma personalitzada per a cada pacient. Per entendre com la patologia cardiovascular evolucionarà i quan suposarà un risc per a la salut, cal desenvolupar noves tecnologies mitjançant la combinació de les imatges mèdiques i la ciència computacional. Proposem uns indicadors que poden millorar el diagnòstic i predir l'evolució de la malaltia de manera més eficient que els mètodes utilitzats fins ara. En particular, es proposa una nova metodologia per al càlcul dels indicadors de diagnòstic basada en l'hemodinàmica computacional i les imatges mèdiques. Hem treballat amb dades de pacients anònims per crear una tecnologia predictiva real que ens permetrà seguir avançant en la medicina personalitzada i generar sistemes de salut més sostenibles. Però el nostre objectiu final és aconseguir un impacte en l¿àmbit clínic. Diversos grups han tractat de crear models predictius per a les patologies cardiovasculars, però encara no han començat a utilitzar-les en la pràctica clínica. El nostre objectiu és anar més enllà i obtenir variables predictives que es puguin utilitzar de forma pràctica en el camp clínic. Es pot preveure que en el futur tots els metges disposaran de bases de dades molt precises de tota la nostra anatomia i fisiologia. Aquestes dades es poden utilitzar en els models predictius per millorar el diagnòstic o per millorar teràpies o tractaments personalitzats.
This paper presents the application of a stabilized mixed pressure/velocity finite element formulation to the solution of viscoplastic non-Newtonian flows. Both Bingham and Herschel–Bulkley models are considered. The detail of the discretization procedure is presented and the Orthogonal Subgrid Scale (OSS) stabilization technique is introduced to allow for the use of equal order interpolations in a consistent way. The matrix form of the problem is given. A series of examples is presented to assess the accuracy of the method by comparison with the results obtained by other authors. The extrusion in a Bingham fluid and the movement of a moving and rotating cylinder are analyzed in detail. The evolution of the streamlines, the yielded and unyielded regions, the drag and lift forces are presented. These benchmark examples show the capacity of the mixed OSS formulation to reproduce the behavior of a Bingham and Herschel–Bulkley flows with the required accuracy.
Agelet De Saracibar, C.; Boman, R.; Bussetta, P.; Cajas, J.; Cervera, M.; Chiumenti, M.; Coll, A.; Dadvand, P.; Hernandez, J.A.; Houzeaux, G.; Pasenau, M.; Ponthot, J. DOI: 10.1002/9783527693566 Data de publicació: 2016 Capítol de llibre
As one of the results of an ambitious project, this handbook provides a well-structured directory of globally available software tools in the area of Integrated Computational Materials Engineering (ICME). The compilation covers models, software tools, and numerical methods allowing describing electronic, atomistic, and mesoscopic phenomena, which in their combination determine the microstructure and the properties of materials. It reaches out to simulations of component
manufacture comprising primary shaping, forming, joining, coating, heat treatment, and machining processes. Models and tools addressing the in-service behavior like fatigue, corrosion, and eventually recycling complete the compilation. An introductory overview is provided for each of these different modelling areas highlighting the relevant phenomena and also discussing the current state for the different simulation approaches. A must-have for researchers, application engineers, and simulation software providers seeking a holistic overview about the current state of the art in a huge variety of modelling topics. This handbook equally serves as a reference manual for academic and commercial software developers and providers, for industrial users of simulation software, and for decision makers seeking to optimize their production by simulations. In view of its sound introductions into the different fields of materials physics, materials chemistry, materials engineering and materials processing it also serves as a tutorial for students in the emerging discipline of ICME, which requires a broad
view on things and at least a basic education in adjacent fields.
This paper extends the use of crack-tracking techniques within the smeared crack approach for the numerical simulation of cohesive-frictional damage on quasi-brittle materials. The mechanical behaviour is described by an isotropic damage model with a Mohr-Coulomb failure surface. The correct crack propagation among the two alternative fracture planes proposed by the Mohr-Coulomb theory is selected with the use of an energy criterion based on the total elastic strain energy. The simulation of three benchmark problems of mixed-mode fracture in concrete demonstrates that the proposed methodology can reproduce the material's frictional characteristics, showing robustness, as well as mesh-size and mesh-bias independence. (C) 2015 Elsevier Ltd. All rights reserved.
This work shows the development of a numerical technique able to simulate the FSW process in all its complexity together with an ad-hoc material tracing technology. It is a step forward in the field of FSW simulation where a fully thermo-mechanical Finite Element model has been developed. Using the Arbitrary-Lagrangian-Eulerian kinematic framework, the overall computational domain is divided into sub-domains associating an apropos kinematic framework for each one of them. A combination of ALE, Lagrangian and Eulerian formulation for different domain parts is proposed. A sliding mesh, rotating together with the pin is used to handle large deformations and material flow around the pin without necessity of remeshing. The strategy adopted to deal with a generic pin shape (not only cylindrical) together with an accurate definition of the boundary conditions is presented. Special attention for the Heat Affected Zone (HAZ) is taken based on the real process behavior. The sub-domains are joined with direct linking of the degrees of freedom at the contact interface. Heat generation via viscous dissipation (Norton-Hoff and Sheppard-Wright constitutive model) as well as frictional heating due to contact (Norton model) is taken into account (a detailed description can be found in [1, 2]).
The extent of the stir-zone plays a critical role for the quality of the joint-strength. To achieve a high quality and defect-free weld, it is necessary to produce a deep penetrating stir-zone around the pin. The purpose of the current work is to get a better understanding of the material behavior due to the stirring process taking into account the effect of pin shape on the process behavior. The streamlines and trajectories of the stirred material are computed and visualized.
This is an accurate and robust methodology to study the FSW problem allowing for a clear visualization of the material movement at the stir-zone leading to a better understanding of the welding process itself. The results obtained from the proposed numerical method are validated by the experimental evidences.
Chiumenti, M.; Huang, W.; Lin, X.; Cervera, M.; Agelet De Saracibar, C.; Dialami , N.; Ma, L.; Lei, W. International Conference on Computational Plasticity p. 1 Data de presentació: 2015-09-02 Presentació treball a congrés
In this work the numerical simulation of Additive Manufacturing (AM) processes is addressed . Among the different existing technologies, Laser Engineered Net Shaping (LENS) or Laser Powder Forming (LPF) is an additive manufacturing technology developed for fabricating metal parts directly from a CAD model. Metal powder (titanium, Inconel, steel, among others) is injected into a molten pool created by a focused, high-powered laser beam. A layer of added material is created according to the scanning path specified by the user. As a result a layer-by-layer metal deposition can be carried out to build complex shapes for components such as turbine blades, aircraft stiffeners, cooling systems, medical implants, among others. The advantage of this process consists of a rapid cooling of each deposited layer and, consequentially, a finer grain size compared to other metal forming technology such as casting or forming.
The results obtained through the numerical simulation of the LENS technology will be compared with a similar AM technique such as the Selective Laser Melting (SLM) or Selective Laser Sintering (SLS). In this case the process makes use of a metal powder beds prepared for each layer followed by a laser consolidation (sintering) process according to a pre-defined scanning path.
A fully couple thermo-mechanical analysis is carried out following the real laser scanning pattern employed in the laboratory. Those consist of a complex sequence of polylines, which usually define the (smooth) boundaries of the component, and hatches patterns to fill the inner section. The full sequence is given through Common Layer Interface (CLI) format, which is a standard format for layer-by-layer manufacturing processes such as rapid prototyping, SMD or machining, among others. The same input is adopted for the element activation technology used for the high-fidelity, FE-based simulation analysis. A thermo-visco-plastic constitutive law is assumed including strain hardening and thermal softening behaviour. Numerical results are compared with the experimental evidence obtained at SKLSP laboratory.
Fracture can be defined as the onset of a displacement discontinuity in a solid. In the catastrophic failure of slopes, the creation of a slip line in the soil triggers the release of a mass that may develop into a landslide or a rockslide. The determination of the initial detached volume is essential in the stability analysis for safety assessments.
From a computational point of view, this problem poses numerous challenges to be overcome. Within the framework of standard irreducible finite elements, the smeared crack approach  allows treating discontinuity as a band of finite width, where the displacements are continuous and the strains are discontinuous, but bounded. Nevertheless, this hypothesis is well-known to present serious numerical drawbacks. Solving problems that involve strain softening, spurious mesh dependence appears and the fracture line direction is biased. Moreover, when isochoric behaviour is enforced (as in the case of undrained soil), locking of the stresses provokes pressure oscillations, with the consequent pollution of numerical calculations. Both problems can be shown not to be related to the mathematical statement of the continuous problem but, instead, to its discrete (FEM) counterpart.
Recently, the authors proved that strain localization numerical issues can be easily alleviated using a Mixed Finite Element formulation, in terms of strain and displacements . As it was reported by Badia and Codina  and, then, by Cervera et al. , the order of convergence of strains (and stresses) in mixed formulations is one order higher than the displacement-based method, even in case of localized discontinuities. The strain-displacement mixed finite element formulation provides enhanced stress accuracy for a given mesh and allows the determination of localization bands without the introduction of auxiliary tracking techniques. Examples of compressible and incompressible plasticity were presented in , where, in particular, it was shown that the energy dissipation is exactly matched in the case J2 plasticity, confirming the consistency of the method.
From these premises, various problems of geotechnical interest are tackled to demonstrate the capabilities of the formulation. The standard irreducible formulation is compared with the introduced mixed formulation in problems involving stability of slopes and shallow foundations.
This work deals with the FE-based simulation of Friction Stir Welding (FSW) processes. FSW is a solid-state joining technique used in many practical applications where the quality of the resultant joint is of essential importance. This feature decreases the harmful effects of high heat input, including distortion, and avoids solidification defects.
A non-consumable tool, rotating at a constant speed, is inserted into the line between the two plates to be welded. The heat is produced by the friction between the tool shoulder and the work-pieces and the mechanical mixing/stirring process.
In the present paper, a coupled thermo-mechanical analysis using Arbitrary Lagrangian Eulerian (ALE) framework is carried out to accurately predict the temperature histories and material flow around the pin tool. Different constitutive and friction models are presented and discussed and their impact on the final heat generated in the work-piece is studied.
On one side, the material behaviour is characterized by a family of thermo-viscoplastic constitutive laws which consider the material as an incompressible viscous non-Newtonian fluid such as Norton-Hoff, Sheppard-Wright, Bingham or Carreau models.
On the other side, the friction law allows for modeling the frictional contact interface between the pin shoulder and the metal sheet which have a relative sliding movement. Several friction models such as Tresca, Coulomb or Norton laws are used in this work. The final heat generated is studied.
The sensitivity to the constitutive model as well as the frictional law selected is investigated and the final result is compared with the experimental evidence.
This work investigates systematically traction- and stress-based approaches for the modeling of strong and regularized discontinuities induced by localized failure in solids. Two complementary methodologies, i.e., discontinuities localized in an elastic solid and strain localization of an inelastic softening solid, are addressed. In the former it is assumed a priori that the discontinuity forms with a continuous stress field and along the known orientation. A traction-based failure criterion is introduced to characterize the discontinuity and the orientation is determined from Mohr's maximization postulate. If the displacement jumps are retained as independent variables, the strong/regularized discontinuity approaches follow, requiring constitutive models for both the bulk and discontinuity. Elimination of the displacement jumps at the material point level results in the embedded/smeared discontinuity approaches in which an overall inelastic constitutive model fulfilling the static constraint suffices. The second methodology is then adopted to check whether the assumed strain localization can occur and identify its consequences on the resulting approaches. The kinematic constraint guaranteeing stress boundedness and continuity upon strain localization is established for general inelastic softening solids. Application to a unified stress-based elastoplastic damage model naturally yields all the ingredients of a localized model for the discontinuity (band), justifying the first methodology. Two dual but not necessarily equivalent approaches, Le., the traction-based elastoplastic damage model and the stress-based projected discontinuity model, are identified. The former is equivalent to the embedded and smeared discontinuity approaches, whereas in the later the discontinuity orientation and associated failure criterion are determined consistently from the kinematic constraint rather than given a priori. The bidirectional connections and equivalence conditions between the traction- and stress-based approaches are classified. Closed-form results under plane stress condition are also given. A generic failure criterion of either elliptic, parabolic or hyperbolic type is analyzed in a unified manner, with the classical von Mises (J(2)), Drucker-Prager, Mohr-Coulomb and many other frequently employed criteria recovered as its particular cases.
Dialamishabankareh, N.; Chiumenti, M.; Cervera, M.; Agelet De Saracibar, C.; Ponthot, J. International journal of material forming Vol. 8, num. 2, p. 167-181 DOI: 10.1007/s12289-013-1157-4 Data de publicació: 2015-04 Article en revista
This work deals with the modeling of the material flow in Friction Stir Welding (FSW) processes using particle tracing method. For the computation of particle trajectories, three accurate and computationally efficient integration methods are implemented within a FE model for FSW process: the Backward Euler with Sub-stepping (BES), the 4-th order Runge-Kutta (RK4) and the Back and Forth Error Compensation and Correction (BFECC) methods. Firstly, their performance is compared by solving the Zalesak's disk benchmark. Later, the developed methodology is applied to some FSW problems providing a quantitative 2D and 3D view of the material transport in the process area. The material flow pattern is compared to the experimental evidence.
Cervera, M.; Chiumenti, M.; Benedetti, L.; Codina, R. Computer methods in applied mechanics and engineering Vol. 285, p. 752-775 DOI: 10.1016/j.cma.2014.11.040 Data de publicació: 2015-03 Article en revista
This paper presents the application of a stabilized mixed strain/displacement finite element formulation for the solution of nonlinear solid mechanics problems involving compressible and incompressible plasticity. The variational multiscale stabilization introduced allows the use of equal order interpolations in a consistent way. Such formulation presents two advantages when compared to the standard, displacement based, irreducible formulation: (a) it provides enhanced rate of convergence for the strain (and stress) field and (b) it is able to deal with incompressible situations. The first advantage also applies to the comparison with the mixed pressure/displacement formulation. The paper investigates the effect of the improved strain and stress fields in problems involving strain softening and localization leading to failure, using low order finite elements with continuous strain and displacement fields (P1P1 triangles or tetrahedra and Q1Q1 quadrilaterals, hexahedra, and triangular prisms) in conjunction with an associative frictional Drucker-Prager plastic model. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to a previously proposed pressure/displacement formulation. Benchmark numerical examples show the capacity of the mixed formulation to predict correctly failure mechanisms with localized patterns of strain, virtually free from any dependence of the mesh directional bias. No auxiliary crack tracking technique is necessary.
Low-order finite elements face inherent limitations related to their poor convergence properties. Such difficulties typically manifest as mesh-dependent or excessively stiff behaviour when dealing with complex problems. A recent proposal to address such limitations is the adoption of mixed displacement-strain technologies which were shown to satisfactorily address both problems. Unfortunately, although appealing, the use of such element technology puts a large burden on the linear algebra, as the solution of larger linear systems is needed. In this paper, the use of an explicit time integration scheme for the solution of the mixed strain-displacement problem is explored as an alternative. An algorithm is devised to allow the effective time integration of the mixed problem. The developed method retains second order accuracy in time and is competitive in terms of computational cost with the standard irreducible formulation.
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The development of slip lines, due to strain localization, is a common cause for failure of soil in many circumstances investigated in geotechnical engineering. Through the use of numerical methods - like finite elements - many practitioners are able to take into account complex geometrical and physical conditions in their analyses. However, when dealing with shear bands, standard finite elements display lack of precision, mesh dependency and locking. This paper introduces a (stabilized) mixed finite element formulation with continuous linear strain and displacement interpolations. Von Mises and Drucker-Prager local plasticity models with strain softening are considered as constitutive law. This innovative formulation succeeds in overcoming the limitations of the standard formulation and provides accurate results within the vicinity of the shear bands, specifically without suffering from mesh dependency. Finally, 2D and 3D numerical examples demonstrate the accuracy and robustness in the computation of localization bands, without the introduction of additional tracking techniques as usually required by other methods. (C) 2014 Elsevier Ltd. All rights reserved.
In previous works, the authors have presented the stabilized mixed displacement/pressure formulation to deal with the incompressibility constraint. More recently, the authors have derived stable mixed stress/displacement formulations using linear/linear interpolations to enhance stress accuracy in both linear and non-linear problems. In both cases, the Variational Multi Scale (VMS) stabilization technique and, in particular, the Orthogonal Subgrid Scale (OSS) method allows the use of linear/linear interpolations for triangular and tetrahedral elements bypassing the strictness of the inf-sup condition on the choice of the interpolation spaces. These stabilization procedures lead to discrete problems which are fully stable, free of volumetric locking or stress oscillations.; This work exploits the concept of mixed finite element methods to formulate stable displacement/stress/pressure finite elements aimed for the solution of nonlinear problems for both solid and fluid finite element (FE) analyses. The final goal is to design a finite element technology able to tackle simultaneously problems which may involve isochoric behavior (preserve the original volume) of the strain field together with high degree of accuracy of the stress field. These two features are crucial in nonlinear solid and fluid mechanics, as used in most numerical simulations of industrial manufacturing processes.; Numerical benchmarks show that the results obtained compare very favorably with those obtained with the corresponding mixed displacement/pressure formulation. (C) 2014 Elsevier B.V. All rights reserved.
Bussetta, P.; Dialamishabankareh, N.; Boman, R.; Chiumenti, M.; Agelet De Saracibar, C.; Cervera, M.; Ponthot, J. Steel research international Vol. 85, num. 6, p. 968-979 DOI: 10.1002/srin.201300182 Data de publicació: 2014-06 Article en revista
Friction stir welding (FSW) process is a solid-state joining process during which materials to be joined are not melted. As a consequence, the heat-affected zone is smaller and the quality of the weld is better with respect to more classical welding processes. Because of extremely high strains in the neighborhood of the tool, classical numerical simulation techniques have to be extended in order to track the correct material deformations. The Arbitrary Lagrangian-Eulerian (ALE) formulation is used to preserve a good mesh quality throughout the computation. With this formulation, the mesh displacement is independent from the material displacement. Moreover, some advanced numerical techniques such as remeshing or a special computation of transition interface is needed to take into account non-cylindrical tools. During the FSW process, the behavior of the material in the neighborhood of the tool is at the interface between solid mechanics and fluid mechanics. Consequently, a numerical model of the FSW process based on a solid formulation is compared to another one based on a fluid formulation. It is shown that these two formulations essentially deliver the same results in terms of pressures and temperatures.
This paper presents an implicit orthotropic model based on the Continuum Damage Mechanics isotropic models. A mapping relationship is established between the behaviour of the anisotropic material and that of an isotropic one. The proposed model is used to simulate the failure loci of common orthotropic materials, such as masonry, fibre-reinforced composites and wood. The damage model is combined with a crack-tracking technique to reproduce the propagation of localized cracks in the discrete FE problem. The proposed numerical model is used to simulate the mixed mode fracture in masonry members with different orientations of the brick layers.