  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. 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 St.-Venant Kirchhoff material
and a double well stored energy density.
