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We consider the energetic description of a visco-plastic evolution and derive an existence result. The energies are convex, but not necessarily quadratic. Our model is a strain gradient model in which the curl of the plastic strain contributes to the energy. Our existence results are based on a time-discretization, the limit procedure relies on Helmholtz decompositions and compensated compactness.

Strain gradient visco-plasticity with dislocation densities contributing to the energy