Finite deformation analysis of visco-hyperelastic materials via solid tetrahedral finite elements

Abstract

An alternative solid finite element formulation for large deformation analysis of viscoelastic materials is proposed. This new approach is based on positions and makes possible a robust implementation of an isoparametric solid tetrahedral that presents no locking when dealing with complex stress, strain and strain rate for general structural analysis. A consistent way to write internal variables that accounts for finite viscoelastic strains is proposed. In this alternative methodology the neo-Hookean hyperelastic law is taken into account together with the Zener viscoelastic model. The evolution law is described in terms of a rate equation involving the viscous right Cauchy-Green stretch tensor. The study is dedicated to homogeneous materials under isothermal and quasi-static conditions. The nonlinear solution procedure is performed via the Newton-Raphson iterative technique and the backward-Euler method.Four illustrative examples involving large viscoelastic strains are analyzed: uniaxial tension, simple shear, buckling of a clamped column and partially loaded block. The present formulation can reproduce creep, stress relaxation and viscoelastic rate dependent stiffening at large strains, which are usually observed in polymeric materials. Even for very complex stress, strain and strain rates the mesh refinement of the proposed methodology leads to more accurate results, avoiding general locking problems. The effect of the viscosity parameter on the material response and the evolution of viscous stretches over time are also highlighted in the results.