Three-field mixed finite element methods for nonlinear elasticity

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 Hu–Washizu principle, distributional derivatives displacement vector are lifted a regular strain tensor. We introduce three different methods, where either deformation gradient, Cauchy–Green tensor, or both them used as independent variables. Within linear sub-problems, all stress variables can be locally eliminated leading an equation system in variables, only. The good performance accuracy presented methods demonstrated by several numerical examples.