We propose to extend the composite tetrahedral finite element first introduced by Thoutireddy et al. (2002) and recently reformulated by Ostien et al. (2016). We generalize the gradient operator and mass matrix to curved domains through analytical expressions weighted by subtetrahedra Jacobians. Optimal integration weights are constructed to increase the accuracy of Gaussian quadrature. We preserve the variational structure of the formulation through a new five-field functional with additional, independent fields for the Jacobian and the pressure. This approach not only obviates volumetric locking but also yields symmetry. A deleterious soft mode, common to both the quadratic and composite tetrahedral element with constant pressure formulations is effectively stabilized through a novel convex energy penalty function. Numerous numerical examples spanning a patch test to the impact of a Taylor bar demonstrate the accuracy, robustness, and convergence of the extended composite tetrahedral element for application to structural metals.

中文翻译：

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扩展用于固体力学的 10 节点复合四面体有限元

我们建议扩展由 Thoutireddy 等人首先引入的复合四面体有限元。(2002) 和最近由 Ostien 等人重新制定。(2016)。我们通过由亚四面体雅可比矩阵加权的解析表达式将梯度算子和质量矩阵推广到弯曲域。构建最佳积分权重以提高高斯正交的精度。我们通过一个新的五域泛函保留了公式的变分结构，其中包含额外的、独立的雅可比和压力场。这种方法不仅避免了体积锁定，而且还产生了对称性。通过新的凸能量惩罚函数有效地稳定了具有恒定压力公式的二次和复合四面体单元所共有的有害软模式。