Finite Element Analysis of Transversely Isotropic Viscoelastic Material for Thermoforming Process

Abstract

In this work, a dynamic finite element method is used in the modeling and numerical simulation of the transversely viscoelastic behavior of a thin, isotropic, and incompressible thermoplastic membrane. The transversely isotropic viscoelastic functional based on the kinetic theory of rubber elasticity is presented. The model is expressed in terms of four material parameters and equations relating these parameters. The thermoforming of the sheet is performed under the action of perfect gas flows. The Lagrangian formulation, together with the assumption of the membrane theory, is used in the finite element implementation. The numerical validation is performed by comparing the theoretical solution for the uniaxial and equibiaxial Hencky deformation with numerical results. Moreover, the influence of fiber direction in the transversely viscoelastic material on the thickness and on the stress distribution in the thermoforming sheet are analyzed.