A novel high-performance mixed membrane finite element for the analysis of inelastic structures

A novel high-performance eight-node quadrilateral mixed finite element is presented. Its formulation is based on a Hu-Washizu type functional, suitable to the treatment of material nonlinearities. In order to capture, even for coarse meshes, highly nonlinear spatial distribution of strain field, strain interpolation is assumed to be discontinuous, piecewise-constant over suitable element subdomains. A robust element state determination procedure is proposed to solve compatibility and constitutive equations at element level. The mixed element stability is numerically assessed. Supported by the comparison with compatible quadrilaterals, numerical simulations concerning elastoplastic and shape-memory alloy structures prove accuracy and effectiveness of the proposed formulation.