Assumed stress finite elements are known for their extraordinary good performance in the framework of linear elasticity. In this contribution we propose a mixed variational formulation of the Hellinger–Reissner type for hyperelasticity. A family of hexahedral shaped elements is considered with a classical trilinear interpolation of the displacements and different piecewise discontinuous interpolation schemes for the stresses. The performance and stability of the new elements are investigated and demonstrated by the analysis of several benchmark problems. In addition the results are compared to well known enhanced assumed strain elements.

中文翻译：

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将假定应力有限元扩展到一般超弹性框架

假定应力有限元以其在线性弹性范围内的出色性能而闻名。在这项贡献中，我们提出了用于超弹性的Hellinger-Reissner类型的混合变体公式。考虑了一系列六面体形状的单元，其中包括位移的经典三线性插值和应力的不同分段不连续插值方案。通过分析几个基准问题来研究和证明新元件的性能和稳定性。此外，将结果与众所周知的增强假设应变元素进行了比较。