Legrain, G.; Moes, N.; Huerta, A. Revue européenne de mécanique numérique = European journal of computational mechanics Vol. 15, num. 1, 2, 3, p. 257-268 DOI: 10.3166/remn.15.257-268 Data de publicació: 2006-06 Article en revista
The treatment of (near-)incompressibility is a major concern for the simulation of rubber-like parts, or forming processes. The use of mixed finite element methods is known to prevent the locking of the F.E. approximation in the incompressible limit. However, the stability of these formulations is conditionned by the fullfilment of the inf-sup condition. Recently, finite elements method has evolved with the introduction of the partition of unity. The X-FEM uses it to remove the need to mesh (and remesh) physical surfaces. In this paper, a strategy is proposed for the treatment of holes within X-FEM in the incompressible setting. Numerical examples show that F.E. convergence rate is preserved and that the inf-sup condition is passed.
Diez, P.; Pares, N.; Huerta, A. Revue européenne de mécanique numérique = European journal of computational mechanics Vol. 13, num. 5- 6- 7, p. 497-507 DOI: 10.3166/reef.13.497-507 Data de publicació: 2004-12 Article en revista
Two implicit residual type estimators yielding upper bounds of the error are presented which do not require flux equilibration. One of them is based on the ideas introduced in [MAC 00, CAR 99, MOR 03, PRU 02]. The new approach introduced here is based on using the estimated error function rather than the estimated error norms. Once the upper bounds are computed, also lower bounds for the error are obtained with little supplementary effort.
Diez, P.; Morata, I.; Huerta, A. Revue européenne de mécanique numérique = European journal of computational mechanics Vol. 12, num. 6, p. 691-715 DOI: 10.3166/reef.12.691-715 Data de publicació: 2003-12 Article en revista
The reliable computation of shell structures requires a tool to assess and control the
quality of the finite element solution. For practical purposes, the quality of the numerical solution
must be measured using a quantity of engineering interest rather than in the standard energy
norm. However, the assessment of the error in an output of interest is based on a standard
energy norm error estimator. The standard error estimator has to be applied to both the original
problem (primal) and a dual problem related with the selected engineering quantity. In shells
with assumed-strain models, the combination of primal and dual error estimation is performed
differently than in the continuum mechanics case. Moreover, a part from the goal-oriented error
estimator, the adaptive process requires a remeshing criterion. This work introduces an specific
remeshing criterion for goal-oriented adaptivity and its particularization to the context of shell
Vidal, Y.; Villon, P.; Huerta, A. Revue européenne de mécanique numérique = European journal of computational mechanics Vol. 11, num. 7-8, p. 869-892 DOI: 10.3166/reef.11.869-892 Data de publicació: 2002-11 Article en revista
Locking in finite elements has been a major concern since its early developments and
has been extensively studied. However, locking in mesh-free methods is still an open topic. Until
now the remedies proposed in the literature are extensions of already developed methods for finite
elements. Here a new approach is explored and an improved formulation that asymptotically suppresses
volumetric locking for the EFG method is proposed. The diffuse divergence converges to
the exact divergence. Since the diffuse divergence-free condition can be imposed a priori, new interpolation
functions are defined that asymptotically verify the incompressibility condition. Modal
analysis and numerical results for classical benchmark tests in solids and fluids corroborate this
Rodriguez-Ferran, A.; Arbós, I.; Huerta, A. Revue européenne de mécanique numérique = European journal of computational mechanics Vol. 10, num. 2,3,4, p. 193-207 Data de publicació: 2001-05 Article en revista
An adaptive finite element strategy for nonlocal damage computations is presented.
The proposed approach is based on the combination of a residual-type error estimator and quadrilateral h-remeshing. A distinctive feature of the error estimator is that it consists in solving simple local problems over elements and so-called patches. The paper focuses on how the
nonlocality of the constitutive model should be accounted for when solving these local problems.
It is shown that the nonlocal damage models must be slightly modified. The resulting
adaptive strategy is illustrated by means of some numerical examples involving the single-edge notched beam test.
The finite element discretization of a shell structure introduces two kinds of errors: the error in the functional approximation and the error in the geometry approximation. The first is associated with the finite dimensional interpolation space and it is present in any finite element computation. The latter is associated with the piecewise polynomial approximation of a curved surface and is much more relevant in shell problems than in any other standard 2D or 3D computation. In the shells framework, formerly the quality control of the finite element solution has been carried out using flux projection a posteriori error estimators. This technique exhibits two main drawbacks: 1) the flux smoothing averages stress components over different elements that may have different physical meaning if the tangent planes are different and 2) the error estimation process uses only the approximate solution and hence, the discretized forces and the computational mesh: the data describing the real geometry and load is therefore not accounted for. In this work, a residual type error estimator introduced for standard 2D finite element analysis is generalized to shell problems. This allows to easily account for the real original geometry of the problem in the error estimation procedure and precludes the necessity of comparing generalized stress components between non coplanar elements. This estimator is based on approximating a reference error associated with a refined reference mesh. In order to build up the residual error equation the computed solution must be represented (projected) on the reference mesh. The use of thin shell finite elements requires a proper formulation in order to preclude shear locking. Following an idea of Donea and Lamain, the interpolation of the rotations is not unique and requires a particular technique to transfer the information from the computational mesh to the reference mesh. This technique is also developed in this work and may be used in any adaptive evolution problem where the solution must be transferred from one mesh to another.