Thermodynamical theory of elasticity and plasticity

A theory of elasticity and plasticity is given, which is based on the thermodynamics of irreversible processes. The inelastic strain tensor is defined with the help of the principle of relaxability-in-the-small. In the discussion of this principle the temperature is also taken into account. In the theory the inelastic strain tensor plays the role of an internal degree of freedom. The entropy production, which is due to heat conduction and plastic flow, is derived. The phenomenological equations are given and the Onsager relations for the cross effect between heat conduction and plastic flow, which may exist in anisotropic media, are discussed. Phenomena as, for instance, thermo-elasticity and strain hardening are included in this theory. It is shown that the Von Mises theory of plasticity is an approximation to the theory developed in this paper. The vanishing of the rate of the plastic strain tensor within the yield surface is seen to be due to a property of the phenomenological tensors. It is assumed that the deformations are small