A novel internal dissipation inequality by isotropy and its implication for inelastic constitutive characterization. (Q1405213)

A new dissipation inequality is derived for the finite inelastic deformation of an isotropic material. This inequality is \(r: (r- h_e)\geq 0,\) where \(r= q_{in}\) is the inelastic branch stresses, \(d\) is the rate-of-deformation tensor, and \(h_e\) is the ``principal rate'' of spatial elastic logarithmic strain. The inequality has the most concise form among a variety of internal dissipation inequalities, including the one widely used in constitutive characterization of isotropic finite strain elastoplasticity and viscoplasticity. The inequality makes evident the dependence of the evolution of elastic logarithmic strain \(h_e\) on the current branch stress \(r\) and on the rate-of-deformation tensor \(d\). The authors postulate the specific evolution law of the internal variable \(h_e\) of the form \(d- h_e= g(r)\), where \(g\) is a symmetric isotropic tensor mapping of order two; \(g\) and \(r\) have the same eigenspace.