A Thermodynamic Approach to Rate-Type Models of Elastic-Plastic Materials

Within the framework of continuum thermodynamics, a tensor-valued rate-type model of elastic-plastic materials is established. The evolution of the stress-strain relation is governed by a free-energy function and a hysteretic function proportional to the entropy production density. It is a key point of the present approach that the entropy production is given by a constitutive function consistent with the second-law inequality. The free energy depends on both stress and strain, as well as temperature. In the absence of hysteretic loops the evolution of the stress depends on the values of stress and strain and is affected by the time derivative of the strain. The hysteretic behaviour is modelled in detail in the one-dimensional case. Simple examples are established by a hysteretic function proportional to the absolute value of the strain rate. While the entropy production is formally similar to the widely used dissipation potentials the corresponding approaches are qualitatively different. The entropy production and the free energy potential are functions of the same set of physical variables and no internal variable is involved. The analysis of the second-law inequality leads to the sought constitutive relation, here in the rate-type form, for stress and strain.