Publications Details

Thermo-visco-inelasticity in large deformations

Herrmann, W.

A formulation is given of constitutive equations valid for large deformations for materials with elastic range and internal state variables intended to describe the internal structure of the material. A material description is used to construct a purely mechanical theory which largely follows that of Carroll. The assumption that the work done in finite closed cycles of homogeneous deformation is non-negative leads to an elastic potential and a dissipation inequality which, in turn, implies a normality condition, by an argument adapted from that of Lin and Naghdi. When the theory is generalized to include temperature dependence, the Clausius-Duhem inequality leads by well-known arguments to an elastic potential and nonnegative dissipation. Rate effects are included by assuming that the inelastic strain rate is a function of the dynamic overstress, but the results of the work assumption or the thermodynamic argument are unchanged. Some remarks regarding implications for stability are made.