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.

中文翻译：

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梯度多凸材料模型及其数值处理

梯度多凸材料是非简单材料，我们不假设弹性应变的平滑性，而是需要应变的次要规律。与二级材料的情况相比，这允许更大类别的允许变形。我们描述了梯度多凸弹性能的可能实现。此外，给出了梯度-多凸性的新几何解释，并将其与标准二级材料进行了比较。最后，我们使用两种不同的模型展示了所提出的方法的应用，即 St.-Venant Kirchhoff 材料和双阱存储能量密度。