Regularization of softening plasticity with the cumulative plastic strain-rate gradient

We propose a novel variational framework to regularize softening plasticity problems. Specifically, we modify the plastic dissipation potential term by adding a contribution depending on the cumulative plastic strain-rate gradient. We formulate the evolution of the so-obtained strain-rate gradient plasticity model with an incremental variational principle. The time-discretized evolution equations are deduced from the corresponding first-order optimality conditions. To investigate the model, the problem of a bar in traction is studied. Analytical solutions are explicitly derived, and characterized by exponential localization profiles. Contrary to other regularization strategies, no spurious spreading of the plastic localization band is observed. A first numerical implementation in 1D and 2D plane strain conditions is proposed based on conic programming solvers and validated against the analytical predictions. Numerical results on plane strain von Mises plasticity show that the proposed framework leads to mesh-independent results and efficient control of plastic localization bands.