A New Thermodynamical Approach for the Simulation of Thermoforming Process using the Quasi-static Finite Element Method

The problem of modeling and the quasi-static finite element simulation of thermoforming processes for viscoelastic sheet is considered. To take account of the enclosed gas volume, responsible for inflation of the thermoplastic membrane, which contributes significantly to the strength and stiffness of a thermoplastic structure, the expression of external virtual work is expressed by a closed volume integral. The pressure load used in modeling is thus deduced from the thermodynamic law of ideal gases. The viscoelastic behavior of the Lodge model is considered. 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 and free inflation with numerical results. Moreover, the influence of the Lodge constitutive model on the thickness and stress distribution in the thermoforming of containers made of HIPS is presented.