Idea of a device for modeling localization phenomena in domains of arbitrary shape and a generalized localization theory

Abstract

A conceptual diagram of a testing device is proposed where the medium filling a domain of a given (practically arbitrary) shape is subjected to a homogeneous simple shear until the medium becomes unstable. The diagram is based on that of a working prototype. It is proved that the instability occurs immediately after Hadamard’s inequality for the medium plastic response is violated. It is also proved that the onset of instability is necessarily accompanied by a localization of incremental plastic strains; the proof relies on the new theory of generalized localization developed in the present paper. The theoretical results obtained fill in significant logical gaps in the traditional strain localization theory suggested by Rice and his scientific school.