A viscohyperelastic finite element model for rubber Original Research Article

A recently developed finite deformation internal solid theory for viscoelastic deformations of rubber is reviewed and an axisymmetric finite element implementation of the theory is presented. The theoretical model is a three-dimensional, total Lagrangian, finite deformation generalization of the Maxwell internal solid theory for viscoelasticity. It utilizes time dependent reference shapes for internal hyperelastic solids to approximate the viscous effects found in rubber and is called a viscohyperelastic model. The material constants for the sum of the internal solidsʹ hyperelastic energy functions can be found by performing the classical tensile, biaxial and shear tests as step-strain tests. A nearly incompressible finite element version of the theory is presented. The viscous equations of motion are solved with a predictor-corrector integration scheme. Time dependent pressure loads are applied to the interior of both a thick walled rubber cylinder and sphere to numerically demonstrate the viscohyperelastic finite element algorithm.