On the structure of the rate equations of materials with internal variables

Abstract

Rate equations for internal variables are not invariant under transformations to other sets of internal variables if such transformations involve the external variables (deformation, temperature), unless the rate equations include the rates of the external variables as well. The simplest invariant rate equations are linear in the external-variable rates; for materials with such rate equations, thermodynamic relations are studied, and conditions are obtained for the reducibility of such rate equations to a form without external-variable rates. Materials with plastic behavior have rate equations that are piecewise linear in the external-variable rates, and thermodynamic relations for such materials are studied as well.