Dynamic finite element analysis of nonlinear isotropic hyperelastic and viscoelastic materials for thermoforming applications

In this work, a dynamic finite element method is used in modeling and numerical simulation of the viscoelastic and hyperelastic behavior of a thin, isotropic, and incompressible thermoplastic membrane. The viscoelastic behavior (Lodge, Christensen) and hyperelastic behavior (Ogden and Mooney‐Rivlin), are considered. The thermoforming of the sheet is performed under the action of perfect gas flows. The pressure load used in modeling is thus deduced from the thermodynamic law of perfect gases. 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 obtained results with measured experimental data for the polymeric acrylonitrile‐butadiene‐styrene (ABS) membrane inflation. Moreover, the influence of the Lodge, the Christensen, the Mooney‐Rivlin, and the Ogden constitutive models on the thickness and on the stress distribution in the thermoforming sheet are analyzed. POLYM. ENG. SCI. 45:125–134, 2005. © 2004 Society of Plastics Engineers