A new efficient explicit formulation for linear tetrahedral elements non-sensitive to volumetric locking for infinitesimal elasticity and inelasticity
Résumé
We introduce an innovative formulation for simple linear tetrahedral elements non-sensitive to volumetric locking. Tetrahedral meshes enable to deal with high deformation by using efficient and robust adaptive meshers - while standard explicit formulations based on linear hexahedral elements with reduced integration and hourglassing stabilization cannot be coupled with efficient remeshing procedures. The principle of this anti-locking modification is to impose the volumetric constraints at each node instead of at each integration point, as been done in the averaged nodal pressure formulation proposed by Bonet in 1998. However, the modification made here is material independent: the strain tensor is directly modified before any stress or pressure calculus. The formulation is extended to incompressible elasticity and von Mises incompressible isotropic inelasticity (elastic-visco-plasticity). An infinitesimal strain formulation has been chosen in order to obtain a very simple and thus computational time saving algorithm. This choice can be easily justified taking into account the value of the critical time step in explicit simulations, especially for metal-forming processes. Standard elastic and inelastic benchmarks issued from the literature validate qualitatively and quantitatively this promising formulation for quasi-incompressible deformations cases.