Computational modelling of thermoforming processes in the case of finite viscoelastic materials

In this paper we describe the computational simulation of the inflation phase of a thermoforming process under which a thin polymer sheet is deformed into a mould under the action of applied pressure. It is assumed that the sheet undergoes finite viscoelastic deformation which is treated using a hyperelastic model containing internal variables. The simplification is adopted that the sheet can be treated as a membrane and also that there is a total sticking contact condition when the sheet comes in contact with the mould. The computational model uses finite elements in space and incorporates mesh adaptivity based on a residual estimator in order to simulate the deformation accurately and efficiently. The internal variables satisfy an ordinary differential equation in time which is solved using a predictor–corrector scheme. The constitutive model is a generalisation of that of Le Tallec and Rahier [P. Le Tallec, C. Rahier, Numerical models of steady rolling for non-linear viscoelastic structures in finite deformations, Int. J. Numer. Methods Engrg. 37 (1994) 1159–1186]. In the simulation it is demonstrated how effectively the estimator works in controlling the meshes for some demanding mould shapes.