Finite element simulation of a two-phase viscoplastic material: calculation of the mechanical behaviour
Résumé
The finite element method is an appropriate numerical tool for solving boundary value problems such as the mechanical response of a heterogeneous material submitted to loading. However the microstructure of the material has to be properly modelled and the mechanical computations need to be accurately performed. For such an analysis, some specific features of the numerical model must be carefully studied: the type of loading i.e., the boundary conditions, the number of elements versus the number of grains and the type of finite elements. In this work, the microstructure is first modelled with Voronoi cells and a method is developed to adapt an existing mesh onto the polyhedrons of the cells. A two-field velocity/pressure formulation is used and it is shown that the pressure field is not continuous at the interface between different incompressible materials. It is also shown that some average values, like the macroscopic viscosity are better described with a continuous interpolation of the pressure but can lead to some problems locally. The influences of boundary conditions and the number of elements in each Voronoi cell on the computed mechanical behaviour are also studied. It is found that the best boundary conditions are periodical ones.