LARGE DEFORMATION ANALYSIS OF HOMOGENEOUS RUBBER-LIKE MATERIALS VIA SHELL FINITE ELEMENTS

Abstract

IN THIS PAPER, A SHELL FINITE ELEMENT FORMULATION TO PREDICT THE MECHANICAL BEHAVIOR OF HIGHLY DEFORMABLE HOMOGENEOUS ELASTIC MATERIALS IS PRESENTED. THE SHELL KINEMATICS IS BASED ON LAGRANGIAN DESCRIPTION AND ON THE REISSNER-MINDLIN HYPOTHESIS. THE FINITE ELEMENT CAN REPRESENT THICKNESS STRETCH AND, DUE TO THE SEVENTH NODAL PARAMETER, LINEAR STRAIN THROUGH THE THICKNESS DIRECTION, WHICH AVOIDS POISSON LOCKING. OTHER TYPES OF LOCKING ARE ELIMINATED VIA HIGH-ORDER APPROXIMATIONS AND MESH REFINEMENT. FULL INTEGRATION SCHEMES ARE EMPLOYED, WHICH IMPROVE THE ACCURACY AND THE RELIABILITY OF THE FORMULATION. A NUMERICAL STRATEGY IS DEVELOPED TO AUTOMATICALLY GENERATE ANY ORDER ISOPARAMETRIC TRIANGULAR SHELL ELEMENTS. IN THE PRESENT STUDY, THE POSITIONAL VERSION OF THE FINITE ELEMENT METHOD (FEM) IS EMPLOYED. IN THIS CASE, NODAL POSITIONS AND UNCONSTRAINED VECTORS ARE THE CURRENT KINEMATIC VARIABLES, INSTEAD OF DISPLACEMENTS AND ROTATIONS. THE MATERIAL RESPONSE IS DESCRIBED BY MEANS OF NONLINEAR AND ISOTROPIC HYPERELASTIC LAWS, USUALLY ADOPTED TO MODEL ELASTIC MATERIALS UNDER FINITE STRAINS, AS RUBBER-LIKE MATERIALS. IN ORDER TO VALIDATE PROPOSED THE FINITE ELEMENT FORMULATION, SOME BENCHMARK PROBLEMS WITH MATERIALS UNDER LARGE DEFORMATIONS HAVE BEEN ANALYZED, AS THE COOK’S MEMBRANE, THE SPHERICAL SHELL AND THE PINCHED CYLINDER. THE RESULTS SHOW THAT THE MESH REFINEMENT INCREASES THE ACCURACY OF SOLUTIONS, HIGH-ORDER LAGRANGIAN INTERPOLATION FUNCTIONS MITIGATE GENERAL LOCKING PROBLEMS, AND THE SEVENTH NODAL PARAMETER MUST BE USED IN BENDING-DOMINATED PROBLEMS IN ORDER TO AVOID POISSON LOCKING.