A finite strain Raviart-Thomas tetrahedron

Abstract

A finite-strain stress-displacement mixed formulation of the classical low-order tetrahedron element is introduced. The stress vector obtained from the face normals is now a (vector) degree-of-freedom at each face. Stresses conjugate to the relative Green-Lagrange strains are used within the framework of the Hellinger-Reissner variational principle. Symmetry of the stress tensor is weakly enforced. In contrast with variational multiscale methods, there are no additional parameters to fit. When compared with smoothed finite-elements, the formulation is straightforward and sparsity pattern of the classical system retained. High accuracy is obtained for fournode tetrahedra with incompressibility and bending benchmarks being solved. Accuracy similar to the F hexahedron are obtained. Although the ad-hoc factor is removed and performance is highly competitive, computational cost is comparatively high, with each tetrahedron containing 24 degrees-of-freedom. We introduce a finite strain version of the Raviart-Thomas element within a common hyperelastic/elasto-plastic framework. Three benchmark examples are shown, with good results in bending, tension and compression with finite strains.