A thermodynamic framework for rate-type fluid models.

*(English)*Zbl 0960.76005From the summary: We develop a thermodynamic approach for modeling a class of viscoelastic fluids based on the notion of an ‘evolving natural configuration’. The material has a family of elastic (or non-dissipative) responses governed by a stored energy function that is parametrized by the ‘natural configurations’. Changes in the current natural configuration result in dissipative behavior that is determined by a rate of dissipation function. By choosing different forms for the stored energy function and the rate of dissipation function, a whole plethora of energetically consistent rate-type models can be developed. We show that the choice of a neo-Hookean type stored energy function and a rate of dissipation function that is quadratic, leads to a Maxwell-like fluid response. By using this procedure with a different choice for the rate of dissipation, we also derive a model that is similar to the Oldroyd-B model. We also discuss several limiting cases, including the limit of small elastic strains, but arbitrarily large total strains, which leads to the classical upper convected Maxwell model as well as to the Oldroyd-B model.