In this paper, we extend the tangential-displacement normal-normal-stress continuous (TDNNS) method from [26] to nonlinear elasticity. By means of the Hu-Washizu principle, the distibutional 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 (available via www.gitlab.com/mneunteufel/nonlinear_elasticity).

翻译：在本文中,我们将异位变异正常压力连续法(TDNNS)从[26]推广到非线性弹性(TDNNS),根据Hu-Washizu原则,迁移矢量的异相衍生物被提升到正常的菌株强度。我们引入了三种不同方法,即变形梯度、Cauchy-Green菌株强或两者都作为独立变量使用。在线性子问题中,所有压力和菌株变量都可以在当地消除,最终在变位变量中形成等式系统。通过几个数字实例(见www.gitlab.com/mneunteufel/nonlinear_弹性),可以证明所述方法的良好性能和准确性。