Toro, S.; Sánchez, P.; Blanco, P.; de Souza, E.; Huespe, A.; Feijóo, R. International journal of plasticity Vol. 76, p. 75-110 DOI: 10.1016/j.ijplas.2015.07.001 Data de publicació: 2016-01 Article en revista
This contribution presents a two-scale formulation devised to simulate failure in materials with heterogeneous micro-structure. The mechanical model accounts for the nucleation of cohesive cracks in the micro-scale domain. The evolution and propagation of cohesive micro-cracks can induce material instability at the macro-scale level. Then, a cohesive crack is nucleated in the macro-scale model which considers, in a homogenized sense, the constitutive response of the intricate failure mode taking place at the smaller length scale. The two-scale semi-concurrent model is based on the concept of Representative Volume Element (RVE). It is developed following an axiomatic variational structure. Two hypotheses are introduced in order to build the foundations of the entire theory, namely: (i) a mechanism for transferring kinematical information from macro-to-micro scale along with the concept of “Kinematical Admissibility”, and (ii) a Multiscale Variational Principle of internal virtual power equivalence between the involved scales of analysis. The homogenization formulae for the generalized stresses, as well as the equilibrium equations at the micro-scale, are consequences of the variational statement of the problem. The present multiscale technique is a generalization of a previous model proposed by the authors (Sánchez et al., 2013; Toro et al., 2014) and could be viewed as an application of a recent contribution (Blanco et al., 2014). The main novelty in this article lies on the fact that failure modes in the micro-structure involve a set of multiple cohesive cracks, connected or disconnected, with arbitrary orientation, conforming a complex tortuous failure path. Following the present multiscale modeling approach, the tortuosity effect is introduced as a kinematical concept and has a direct consequence in the homogenized mechanical response. Numerical examples are presented showing the potentialities of the model to simulate complex and realistic fracture problems in heterogeneous materials. In order to validate the multiscale technique in a rigorous manner, comparisons with the so-called DNS (Direct Numerical Solution) approach are also presented.
The formulation of a phase-field continuum theory for brittle fracture in elastic-plastic solids and its computational implementation are presented in this contribution. The theory is based on a virtual-power formulation in which two additional and independent kinematical descriptors are introduced, namely the phase-field and the accumulated plastic strain. Further, it incorporates irreversibility of both phase-field and plastic strain evolutions by introducing suitable constraints and by carefully heeding the influence of those constraints on the kinetics underlying microstructural changes associated with plasticity and fracture. The numerical implementation employs the finite-element method for spatial discretization and a splitting scheme with sub-stepping for the time integration. To illustrate its potential utility,
we apply the model to a number of well known linear, as well as non-linear, fracture mechanics problems. The described phase-field model, coupled with plasticity, provides a feasible technique to analyzing crack initiation and the subsequent crack growth resistance only if the length scale parameter included in the phase-field model is finite and treated as a material parameter which should be properly characterized.
We present a finite element method with a finite thickness embedded weak discontinuity to analyze ductile fracture problems. The formulation is restricted to small geometry changes. The material response is characterized by a constitutive relation for a progressively cavitating elastic–plastic solid. As voids nucleate, grow and coalesce, the stiffness of the material degrades. An embedded weak discontinuity is introduced when the condition for loss of ellipticity is met. The resulting localized deformation band is given a specified thickness which introduces a length scale thus providing a regularization of the post-localization response. Also since the constitutive relation for a progressively cavitation solid is used inside the band in the post-localization regime, the traction-opening relation across the band depends on the stress triaxiality. The methodology is illustrated through several example problems including mode I crack growth and localization and failure in notched bars. Various finite element meshes and values of the thickness of the localization band are used in the calculations to illustrate the convergence with mesh refinement and the dependence on the value chosen for the localization band thickness.
Chiumenti, M.; Valverde, Q.; Agelet De Saracibar, C.; Cervera, M. International journal of plasticity Vol. 20, num. 8-9, p. 1487-1504 DOI: 10.1016/j.ijplas.2003.11.009 Data de publicació: 2004-08 Article en revista
In this paper, a stabilized finite element method to deal with incompressibility in solid mechanics is presented. Both elastic and J2-plastic constitutive behavior have been considered. A mixed formulation involving pressure and displacement fields is used and a continuous linear interpolation is considered for both fields. To circumvent the Babuška–Brezzi condition a stabilization technique based on the orthogonal sub-scale method is introduced. The main advantage of the method is the possibility of using linear triangular or tetrahedral finite elements, which are easy to generate for real industrial applications. Results are compared with standard Galerkin and Q1P0 mixed formulations in either elastic or elasto-plastic incompressible problems.