Abstract

This paper exploits the concept of stabilized finite element methods to formulate stable mixed stress/displacement and strain/displacement finite elements for the solution of nonlinear solid mechanics problems. The different assumptions and approximations used to derive the methods are exposed. The proposed procedure is very general, applicable to 2D and 3D problems. Implementation and computational aspects are also discussed, showing that a robust application of the proposed formulation is feasible. Numerical examples show that the results obtained compare favorably with those obtained with the corresponding irreducible formulation.

Abstract

In this paper, a new strategy for the simulation of quasi-static cold compaction processes of powders is presented. A material model formulated within the framework of isotropic finite strain multiplicative hyperelastoplasticity is used. An elliptic plastic model expressed in terms of the Kirchhoff stresses and the relative density models the transition between the loose powder and the compacted sample. The Coulomb dry friction model is used to capture friction effects at powder-die contact. Excessive distortion of Lagrangian meshes due to large mass fluxes is usual in powder compaction problems. Moreover, Lagrangian approaches cannot deal properly with mass fluxes around sharp corners. For these reasons, an Arbitrary Lagrangian-Eulerian (ALE) formulation is used here. The present results illustrate that this approach allows simulating highly demanding powder compaction processes without mesh distortion and spurious oscillations in the results. Moreover, it is shown that the mass conservation principle is verified with a low relative error.