A note on overstress and over-thermodynamic forces derivation for elasto-viscoplastic media: Thermodynamic analysis of an isothermal relaxation process. (August 2015) - dos Santos, Tiago; Ramos, Gustavo Roberto; Rossi, Rodrigo
Abstract: In this work, we perform a thermodynamical analysis of an isothermal relaxation process inside the context of elasto-viscoplasticity under the assumption of small deformations. Departing from the one-dimensional Bingham rheological model and assuming that some key decompositions on stress, free energy, and dissipation are possible we demonstrate that, among all equilibrium states satisfying the yield criterion, the actual equilibrium state, given a prescribed total deformation, is the one which minimizes the viscous energy dissipated during the relaxation process. From the one-dimensional motivation we extend the formulation to the multidimensional hardening case. Therefore, based on concepts of thermodynamics with internal variables (TIV) and some results of convex analysis, we arrive at a constrained minimization problem whose solution are state equations for the "over quantities", or for the equilibrium state, which are identical to those obtained from the minimum complementary free energy principle. This result brings some physical aspects which can aid the understanding of relaxation processes in elasto-viscoplastic media, providing physical foundations which can help the understanding of well established viscoplastic models, as well as the proposing of constitutive formulations and solution algorithms for this class of materials.