A nonlinear 10-node tetrahedral element based on a Hu-Washizu variational formulation

In this paper a new nonlinear 10–node tetrahedral element is described. A Hu–Washizu functional with independent displacements, stresses and strains is the variational basis of the finite element formulation. The shape functions of the independent quantities are specified. Elimination of the stress and strain parameters on element level leads to a mixed hybrid element. The patch test is fulfilled in the common linear and also in a nonlinear version. The element is characterized by a remarkable robustness with the possibility of very large load steps in nonlinear applications. The total number of iterations is significantly lower than that of the corresponding displacement element. This holds especially for thin structures subjected to bending deformations. The performance of the new element in comparison to existing approaches is illustrated by means of representative numerical simulations.