Large deformation analysis of functionally graded visco-hyperelastic materials

Abstract

In this paper, a numerical formulation for the analysis of viscoelastic functionally graded materials under finite strains is presented. The general constitutive modeling is described within the context of Lagrangian and isotropic visco-hyperelasticity. The specific models selected are the compressible neo-Hookean hyperelastic law, the Zener rheological model and the isochoric evolution law described in terms of the rate of the viscous right Cauchy-Green stretch tensor. The material coefficients may vary smooth and continuously along one direction according to the power law. The viscous update is performed via the exponential rule. The main novelty of this paper is the use of gradually variable viscoelastic coefficients in the finite strain regime.Four numerical examples involving functionally graded materials and finite viscoelastic strains are originally analyzed to assess the formulation proposed: a bar under uniaxial extension, a block under simple shear, the Cook’s membrane and an elastomeric bridge bearing. Isoparametric solid tetrahedral finite elements of linear, quadratic and cubic orders are employed. The influence of the material viscoelastic parameters on the mechanical behavior is analyzed in detail. Results confirm that mesh refinement provides more accuracy and the present model can reproduce large levels of viscoelastic strains in functionally graded materials.