Gradient polyconvex material models and their numerical treatment

Abstract

Gradient polyconvex materials are nonsimple materials where we do not assume smoothness of the elastic strain but instead regularity of minors of the strain is required. This allows for a larger class of admissible deformations than in the case of second-grade materials. We describe a possible implementation of gradient polyconvex elastic energies in nonlinear finite strain elastostatics. Besides, a new geometric interpretation of gradient-polyconvexity is given and it is compared with standard second-grade materials. Finally, we demonstrate application of the proposed approach using two different models, namely, a Saint Venant-Kirchhoff material and a double-well stored energy density.