Submacroscopically Stable Equilibria of Bodies Undergoing Disarrangements and Dissipation

Elasticity is viewed here as a starting point in the description of inelastic behavior. The two-scale geometry provided by structured deformations and a field theory of elastic bodies undergoing disarrangements (non-smooth geometrical changes) and dissipation are used to formulate and illustrate a concept of ”submacroscopically stable configuration.” A body in a submacroscopically stable equilibrium configuration resists additional submacroscopic geometrical changes such as the occurrence of microslips, the formation of microvoids, and the appearance of localized distortions that, together, leave the macroscopic configuration of the body unchanged. Submacroscopically stable configurations represent energetically preferred phases for bodies in equilibrium, and a procedure is described here for determining the submacroscopically stable equilibria of a body. The procedure is carried out in detail here for two classes of bodies that may undergo disarrangements and experience internal dissipation. One class is characterized by its bi-quadratic free energy response function, and the requirement of submacroscopic stability reduces from five to one the number of phases available to a body that is in equilibrium under mixed boundary conditions. For a subclass of these bi-quadratic free energy functions, the distinguished phase determined through this procedure has the same free energy response as one derived for nematic elastomers via statistical calculations. Boundary-value problems for the