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**Strong discontinuities and continuum plasticity models: the strong discontinuity approach.**
*(English)*
Zbl 1057.74512

This paper aims to clarify the following questions concerning the capture of strong discontinuities using plasticity models: Under what conditions typical elasto-plastic (infinitesimal-strain based) continuum constitutive equations, once inserted in the standard quasi-static solid mechanics problem, induce strong discontinuities having physical meaning and keeping the boundary value problem well-posed? What is the link of the strong discontinuity approach, based on the use of continuum (stress-strain) models, with the discrete discontinuity approach which considers a nonlinear fracture mechanics environment and uses stress vs displacement-jump constitutive equations to model the decohesive behaviour of the discontinuous interface? What is the role of the fracture energy in this context? What are the connections of the strong discontinuity approach to the discontinuous failure theories aiming at the prediction of bifurcations induced by continuum constitutive equations?

Total or partial answers to these questions are given. For the sake of simplicity, two-dimensional problems (plane strain and plane stress) are considered, although the proposed methodology can be easily extended to the general three-dimensional case. The authors deal with the kinematics of the discontinuous problem, and different options are analyzed. The target family of elastoplastic constitutive equations is described, and the corresponding boundary value problem is presented. The bifurcation analysis of general plasticity models is sketched, and some interesting results are kept to be recovered. The strong discontinuity analysis is performed, and crucial concepts as the strong discontinuity equation, the strong discontinuity conditions and the discrete consistent constitutive equation are derived. The authors present a variable bandwidth model as a possible mechanism to link weak to strong discontinuities and to provide a transition between them. The expended power concept in the formulation of a strong discontinuity theory is examined, and conditions for recovering the fracture energy concept as a material property are established. Some details regarding the finite element simulation are then given, and numerical simulations are presented to validate the proposed approach.

Total or partial answers to these questions are given. For the sake of simplicity, two-dimensional problems (plane strain and plane stress) are considered, although the proposed methodology can be easily extended to the general three-dimensional case. The authors deal with the kinematics of the discontinuous problem, and different options are analyzed. The target family of elastoplastic constitutive equations is described, and the corresponding boundary value problem is presented. The bifurcation analysis of general plasticity models is sketched, and some interesting results are kept to be recovered. The strong discontinuity analysis is performed, and crucial concepts as the strong discontinuity equation, the strong discontinuity conditions and the discrete consistent constitutive equation are derived. The authors present a variable bandwidth model as a possible mechanism to link weak to strong discontinuities and to provide a transition between them. The expended power concept in the formulation of a strong discontinuity theory is examined, and conditions for recovering the fracture energy concept as a material property are established. Some details regarding the finite element simulation are then given, and numerical simulations are presented to validate the proposed approach.

Reviewer: Anatoliy S. Semenov (Odessa)