APPLICATION OF THE THERMODYNAMICAL LAW OF GASES FOR MODELLING OF FREE INFLATION OF THE CLOSED THIN HYPERELASTIC STRUCTURE

F. Erchiqui∗ and A. Bendada∗∗

Keywords

Hyperelastic, quasistatic finite element, gas volume, thermodynamic law, bubble inflation

Abstract

The problem of modelling of the inflation of the hyperelastic thin structure, by quasi-static finite element method is considered. To take account of the enclosed gas volume, responsible for inflation of the structure, which contributes significantly to the strength and stiffness of a structure, the expression of external virtual work is expressed by a closed volume integral. The pressure load used in modelling is thus deduced from the thermodynamic law of ideal gases. The material is assumed hyperelastic and the Mooney–Rivlin form of the strain energy density is adopted. 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 and numerical solution for the free bubble inflation deformation.

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