In this paper, we extend the tangential-displacement normal–normal-stress continuous (TDNNS) method from Pechstein and Schöberl (2011) to nonlinear elasticity. By means of the Hu–Washizu principle, the distributional derivatives of the displacement vector are lifted to a regular strain tensor. We introduce three different methods, where either the deformation gradient, the Cauchy–Green strain tensor, or both of them are used as independent variables. Within the linear sub-problems, all stress and strain variables can be locally eliminated leading to an equation system in displacement variables, only. The good performance and accuracy of the presented methods are demonstrated by means of several numerical examples.

在本文中，我们将Pechstein和Schöberl（2011）的切向位移法向-法向应力连续（TDNNS）方法扩展到非线性弹性。借助Hu–Washizu原理，将位移矢量的分布导数提升为规则应变张量。我们介绍了三种不同的方法，其中将变形梯度，柯西-格林应变张量或两者都用作独立变量。在线性子问题中，所有应力和应变变量都可以局部消除，从而仅产生位移变量方程组。通过几个数值实例证明了所提出方法的良好性能和准确性。