ABSTRACT
Fig. 1 An elastic bar prone to damage cess in physical space gives rise to an accompanying reversible process in the Gibbsian state space. An explicit expression for the entropy production is then obtained by eliminating the internal energy term between the classical Gibbs equation and the energy balance equation. In order
to complete the theory, empirical rate equations for the evolution of damage are required. In the absence of such empirical relations, we propose here simple rate equations. These are subjected to the only requirement that the entropy production be nonnegative. The resulting theory predicts, at least qualitatively, many features of real material behavior, such as the dependence of the material response on the loading or straining process (e.g., strain-rate dependency) and on the size and shape of the cross-section of the bar and such as the transition with the rise of temperature from brittle to ductile behavior.
