An elastic-viscoplastic model exhibiting continuity of solid and fluid states
In this paper specific unified consitutive equations for an elastic- viscoplastic material are developed which in the limit of infinite resistance to plastic flow become those of a general hyperelastic isotropic material; and in the limit of zero resistance to plastic flow become those of a general Reiner-Rivlin fluid. The constitutive equations satisfy the restrictions imposed by continuum thermodynamics and are hyperelastic in the sense that the symmetric Piola-Kirchhoff stress is related to a derivative of the Helmholtz free energy. In this formulation the Helmholtz free energy depends on five scalar invariants: two new scalars which are pure measures of ''elastic'' distortional deformation, a measure of total dilatation, a measure of plastic dilatation, and temperature. Specifically, the stress is not characterized by a hypoelastic equation so no special rates of stress need be considered. Both isotropic hardening and a measure of directional hardening which models the Bauschinger effect are included. Finally, examples of simple shear are considered to examine the solid-like and fluid-like response to large deformations including cycles of loading, unloading and reloading.
scientific article; zbMATH DE number 3999367