## Abstract

This paper describes a novel formulation for the solution of problems involving shear band localization using a local isotropic J${\textstyle _{2}}$ continuum damage model and mixed linear simplex (triangles and tetrahedra). Stabilization methods are used to ensure existence and uniqueness of the solution, attaining global and local stability of the corresponding discrete finite element formulation. Consistent residual viscosity is used to enhance robustness and convergence of the formulation. Implementation and computational aspects are also discussed. A simple isotropic local J${\textstyle _{2}}$ damage constitutive model is considered, either with linear or exponential softening. The softening modulus is regularized according to the material mode II fracture energy and the element size. Numerical examples show that the formulation derived is fully stable and remarkably robust, totally free of volumetric locking and spurious oscillations of the pressure. As a consequence, the results obtained do not suffer from spurious mesh-size or mesh-bias dependence, comparing very favourably with those obtained with the ill-posed standard approaches.

### Document information

Published on 01/01/2004

DOI: 10.1016/j.cma.2003.11.009