Finite element analysis of rubber‐like materials by a mixed model

Abstract

AbstractA Reissner type variational principle is utilized to formulate a mixed finite element model for a finite‐strain analysis of Mooney‐Rivlin rubber‐like materials. An incremental and stationary Lagrangian formulation is adopted. The functional consists of incremental displacements and incremental hydrostatic and distortional stresses as variables. In the finite element formulation the displacements are interpolated in terms of nodal displacements while the two different strss components are approximated independently. The stress parameters for the distortional stresses are eliminated at the element level and the resulting matrix equations for each incremental solution involve the incremental nodal displacements and the average hydrostatic pressure in each element as unknowns. Four‐node quadrilateral plane stain elements were used to analyze the inflation of an infinitely long thick‐walled cylinder subjected to internal pressure. Both resulting displacements and stresses are found to converge to exact values as the magnitude of the loading increments is decreasing.