The unrestrainable growth of a shear band in a prestressed material

A weak line inclusion model in a nonlinear elastic solid is proposed to analytically quantify and investigate, for the first time, the stress state and growth conditions of a finite-length shear band in a ductile prestressed metallic material. The deformation is shown to become highly focused and aligned coaxial to the shear band—a finding that provides justification for the experimentally observed strong tendency towards rectilinear propagation—and the energy release rate to blow up to infinity, for incremental loading occurring when the prestress approaches the elliptic boundary. It is concluded that the propagation becomes ‘unrestrainable’, a result substantiating the experimental observation that shear bands are the preferential near-failure deformation modes.