Section: New Results

Large deformation simulation using adaptive remeshing

Participants : Patrick Laug [correspondant] , Houman Borouchaki.

The object of non-linear solid and structural mechanics is the modeling and the computation of structures with strong non-linearities, both geometrical and physical. The aim is to simulate the behavior of a mechanical part submitted to various mechanical stresses, in order to improve its mechanical strength, or even to optimize its manufacturing process with respect to damage occurrence. Among various theoretical, numerical and geometric tools involved in such a simulation, the interest in adaptive remeshing is really high nowadays. It is generally based on local refinement (governed by error estimation) and vertex smoothing strategies. Let us mention that the main difficulty lies in the fact that, in large strains, the domain geometry is variable and cannot be defined in an explicit way.

New contributions to the strategy using adaptive meshing and a posteriori error estimation in large elasto-plasticity have been developed. We are interested in the problem of remeshing a mechanical structure composed of several parts (which are in contact) subjected to large plastic deformations. A general scheme, constituted by several steps necessary to an almost optimal representation of the evolving domain, is proposed. These steps are divided into two main categories: the definition of the boundary of the deformed parts and the whole remeshing of the parts. The remeshing is governed by a mesh size map representing the conformity with the underlying geometry of the deformed parts, the improvement of the accuracy of the desired mechanical fields, and the convergence of the mechanical process as well. This size map results from an a posteriori estimation of the “interpolation error” independently from the considered mechanical fields. The final deformation after the whole simulation is assumed to be obtained iteratively by “small” deformations (which is the case in the framework of an explicit integration scheme to solve the problem). After such a small deformation, rigid parts are moved and deformable parts are slightly distorted (assuming that each mesh element is still valid). The remeshing is applied to deformable parts after each deformation increment. The proposed technique is used to simulate the impact of a projectile on a confined explosive. We show in particular that the ignition of the explosive appears in two different areas.