Stress, strain and dissipation accurate 3-field formulation for inelastic isochoric deformation

Abstract

This work exploits the high accuracy of the mixed 3-field u/e/p formulation to address materially non-linear inelastic problems including isochoric deformations. Motivated by the strain-driven format of several constitutive equations used in FEA, the mixed u/s/p formulation is reinterpreted, selecting the deviatoric strains as primary variables, together with the displacements and the pressure field. The mixed formulation is complemented with several constitutive equations suitable for Solid and Fluid Mechanics. The convergence rate upon mesh refinement, as well as the enhanced accuracy of the stress and strain fields is proven in several non-linear problems with isochoric deformation in both the elastic and the inelastic ranges. 2D and 3D problems involving different FE discretizations are solved with J2-plasticity, J2-damage and Bingham models, all of them including strain localization. Numerical results show that perfectly convergent and mesh-independent results are achieved in terms of peak load, failure mechanism, stress release and energy dissipation. Revealing comparison with the u/p formulation is also addressed.