A theory of mechanical behavior of elastic media with growing damage and other changes in structure

Abstract

Strain energy-like potentials are used to model the mechanical behavior of linear and nonlinear elastic media with changing structure, such as micro- and macrocrack growth in monolithic and composite materials. Theory and experiment show that the applied work for processes in which changes in structure occur is in certain cases independent of some of the deformation history. Consequences of this limited path-independence are investigated, and various relationships for stable mechanical response are derived. For example, it is shown that work is at a minimum during stable changes in structure, which should be useful for developing approximate solutions by variational methods. Some final remarks indicate how the theory may be extended to include thermal, viscoelastic and fatigue effects.