Linearization and computation for large-strain visco-elasticity

Time-discrete numerical minimization schemes for simple visco-elastic materials in the Kelvin-Voigt rheology at high strains are not well posed because of the non-quasi-convexity of the dissipation functional. A possible solution is to resort to non-simple material models with higher-order gradients of deformations. However, this makes numerical computations much more involved. Here, we propose another approach that relies on local minimizers of the simple material model. Computational tests are provided that show a very good agreement between our model and the original.