Gradient-enhanced Raviart-Thomas tetrahedron for finite-strain problems. (15th April 2020) - Areias, P.; Silvestre, N.; Rabczuk, T.
Highlights: Hellinger-Reissner principle with full strain and displacement as independent unknowns. Finite strain formulation based on relative measures. Gradient-enhanced formulation based on the Raviart-Thomas formulation and the screened-Poisson equation. Weakly enforced symmetry of the Green-Lagrange strain tensor. Traditional finite-strain benchmarks and a quasi-brittle damage numerical test are performed, with very competitive results. Abstract: A new gradient-enhanced strain-tensor formulation for finite-strain problems is introduced, based on the Raviart-Thomas face-interpolation scheme and the Hellinger-Reissner variational principle. The screened-Poisson equation is employed to relate the kinematic Green-Lagrange strain with the mixed strain. The strain vector obtained from the face normals is now a (vector) degree-of-freedom at each face. In contrast with variational multiscale methods, there are no parameters to fit and stability in compression is verified. When compared with smoothed finite-elements, the formulation is straightforward and sparsity pattern of the classical system retained, albeit with high computational cost. In contrast with traditional gradient-enhanced formulations, a theoretically sound mixed formulation underlies the algorithm. High accuracy is obtained for four-node tetrahedra with incompressibility and bending benchmarks being solved. Traditional finite-strain benchmarks and a quasi-brittle damage numerical test are performed, with very competitive results.