Finite strain logarithmic hyperelasto-plasticity with softening: a strongly non-local implicit gradient framework

This paper addresses the extension of a Eulerian logarithmic finite strain hyperelasto-plasticity model in order to incorporate an isotropic plastic damage variable that leads to softening and failure of the plastic material. It is shown that a logarithmic elasto-plastic model with a strongly non-local degrading yield stress exactly preserves the structure of its infinitesimal counterpart. The strongly non-local nature of the model makes it an attractive framework for the numerical solution of softening plasticity problems. Consistent constitutive tangent operators are derived for the particular case of hyperelasto-J2-plasticity, which are exactly equal to the corresponding infinitesimal tangent operators. The finite element implementation, along with the geometrically nonlinear contributions and the incremental solution strategy, is outlined. A benchmark example is solved, illustrating the main differences between the purely elasto-plastic case and the case with plastic damage. Finally, the main model characteristics and its practical use are emphasized.