The energy in one-dimensional rate-type semilinear viscoelasticity
The existence and properties of a free energy function compatible with the second law of thermodynamics in one-dimensional rate-type semilinear viscoleasticity is analysed. Necessary and sufficient conditions are given such that a free energy as a function of strain and stress exists and is unique, that it is a non-negative function and possesses a monotony property with respect to the equilibrium curve. A bound in energy for the smooth solutions of certain initial and boundary value problems with respect to the input data is established when the equilibrium curve is a non-monotonic curve (i.e. the free energy function is a non-convex one). Thus iron-like behaviour, for instance is also included. An L 2-approach to equilibrium is also discussed. The problem has been presented in a precise and concise manner. A good number of references have been provided at the end of paper to enable the researchers in solid mechanics to continue the work on similar problems or problems of higher quality and merit. The paper from all its aspects is very good. This type of work will be useful for researchers and scientists working in the field of solid mechanics and civil engineering.
scientific article; zbMATH DE number 4066459