Bifurcation of elastoplastic solids to shear band mode at finite strain

This paper formulates and implements a finite deformation theory of bifurcation of elastoplastic solids to planar bands within the framework of multiplicative plasticity. Conditions for the onset of strain localization are based on the requirement of continuity of the nominal traction vector, and are described both in the reference and deformed configurations by the vanishing of the determinant of either the Lagrangian or Eulerian acoustic tensor. The relevant acoustic tensors are derived in closed form to examine the localization properties of a class of elastoplastic constitutive models with smooth yield surfaces appropriate for pressure-sensitive dilatant/frictional materials. A link between the development of regularized strong discontinuity and its unregularized counterpart at the onset of localization is also discussed. The model is implemented numerically to study shear band mode bifurcation of dilatant frictional materials in plane strain compression. Results of the analysis show that finite deformation effects do enhance strain localization, and that with geometric nonlinearities bifurcation to shear band mode is possible even in the hardening regime of an associative elastoplastic constitutive model. (C) 2002 Elsevier Science B.V. All rights reserved.