An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids.

*(English)*Zbl 0924.73084Summary: This paper presents an analysis of strong discontinuities in inelastic solids at finite strains. Solutions exhibiting this type of discontinuities, characterized by a discontinuous displacement field, are shown to make physical and mathematical sense in a classical multiplicative plasticity continuum model if the softening modulus is reinterpreted as a singular distribution. Physically, the strain-softening is localized along the discontinuity. Conditions for the appearance of strong discontinuities in the geometrically nonlinear range are characterized, as it is the response of the material during localization. In addition, these analytical results are exploited in the design of a new class of finite element methods. The proposed methods fall within the class of enhanced strain methods, and lead to solutions independent of the mesh size and insensitive to mesh aligmnent, without requiring any regularization of the solutions by numerical parameters like a characteristic length.