Stress integration scheme for coupled elasto-plastic materials in a hypoelasto-plastic framework

This paper proposes a rigorous additive hypoelasto-plasticity formulation and a corresponding rigorous finite-strain stress integration scheme for coupled elasto-plastic materials. The material model and the integration scheme are required to conform to (1) the principle of material frame indifference, (2) the self-consistency criterion, (3) the yielding-stationarity criterion, and (4) the laws of thermodynamics. An additional requirement imposed on the material response is the prevention of artificial, unphysical oscillatory responses in monotonic simple shear deformation. The role of different forms of the hardening law for large-deformation, large-rotation problems with respect to these oscillations is explored using simple shear deformation analyses for a simple decoupled material following the Mises yield criterion. These simulations show that any tensorial internal variables that do not evolve or that evolve linearly with deformation can result in these oscillatory responses. Finally, the rigor of the proposed stress integration scheme is demonstrated through numerical simulations using a material following a model with a Mises yield function and elastic moduli that are functions of plastic shear strain.