On the Stability of Shear Bands

Abstract

Prediction of the onset of localization of the deformation in solids under stress, and, in particular, the initiation of shear bands, is a problem of considerable importance in the context of metal plasticity (see, for example, the review by Rice [1]). There is growing interest also in geophysical applications, as highlighted in the recent work of Leroy and Molinari [2]. Shear bands are usually treated as surfaces of discontinuity of the deformation gradient (or its incrernental counterpart), and the formation of shear bands has been predicted for a variety of models describing either plastic or nonlinearly elastic response. In the case of elasticity the phenomenon is associated with loss of ellipticity of the governing partial differential equations of equilibrium and involves the use of non-convex stored-energy functions, as exemplified in the work of Knowles and Sternberg [3] and Abeyaratne [4].