The response of membranes under large strains occurs in several mechanical applications such as biomechanics or forming of hollow plastic parts. The present work deal with the modelling of inflated membranes. First we focus on the development of constitutive equations that take into account the reinforcement of hyperelastic materials with fibres. This approach leads to transversely isotropic formulation in terms of tensorial invariants. A specific model based on this formulation was implemented in a numerical tool to simulates the thermoforming process. Second, we developed a finite element code for the static inflation of membranes under large strains. An object oriented programming language, Fortran 90 was used. Classical membrane finite elements were implemented and validated. With these elements, discretisation problems occur when the curvature of the deformed geometry becomes too large. In order to correct this problems, a new element, with higher continuity property, was developed and the results were significantly improved. Moreover since membrane inflation problems often exhibits unstable behaviours, an algorithm that detects singular points and follows secondary equilibrium branches was developed. For different examples, axisymetric branching diagrams are recovered and some non-axisymetric bifurcation are highlighted. Finally an experimental apparatus for inflation of hollow cylinders is in progress. It is used to produce a biaxial state of strains. Preliminary results are encouraging. The association of these experiments with the numerical methods will be used to characterise rubber-like materials under large strains.
Contribution to the modelling of hyperelastic membranes under large strain