Banding and stability in plastic materials
We have examined the question of material stability. More specifically, we have probed the conditions under which materials become ``unstable'' in the sense that given a homogeneous stress field in a materials domain, their constitutive equation allows the onset of a discontinuous, yet compatible, strain field in a finite subdomain (a ``stress band'') while the state of stress in the entire domain remains unchanged. The central conclusion is that plastic materials are unstable in all inelastic stress states. This is in the light of the fact that our definition of instability is more stringent than that of \textit{T. Y. Thomas} [Plastic flow and fracture in solids (1961; Zbl 0095.389)] and \textit{R. J. Hill} [J. Mech. Phys. Solids 10, 1-16 (1962; Zbl 0111.377)] where the stress state in the band need only satisfy conditions of continuity normal to the band interface. Detailed results of this investigation in so far as plastic (inelastic) solids are concerned, where the plastic strain rate tensor is proportional to the gradient of a plastic potential with respect to the stress tensor, are summarized.
scientific article; zbMATH DE number 4128528