A mixed tetrahedral element with nodal rotations for large-displacement analysis of inelastic structures

A novel mixed four-node tetrahedral finite element, equipped with nodal rotational degrees of freedom, is presented. Its formulation is based on a Hu-Washizu-type functional, suitable to the treatment of material nonlinearities. Rotation and skew-symmetric stress fields are assumed as independent variables, the latter entering the functional to impose rotational compatibility and suppress spurious modes. Exploiting the choice of equal interpolation for strain and symmetric stress fields, a robust element state determination procedure, requiring no element-level iteration, is proposed. The mixed element stability is assessed by means of an original and effective numerical test. The extension of the present formulation to geometric nonlinear problems is achieved through a polar decomposition-based corotational framework. After validation in both material and geometric nonlinear context, the element performances are investigated in demanding simulations involving complex shape memory alloy structures. Supported by the comparison with available linear and quadratic tetrahedrons and hexahedrons, the numerical results prove accuracy, robustness, and effectiveness of the proposed formulation.