Hyperelastic behaviour of plates with a centred hole using the asymptotic numerical method

This paper presents a methodological approach to solve nonlinear problems of a membrane plate with a centred hole hyperelastic properties. For this structure, we considered the Mooney-Rivlin and Gent models of strong non-linearity and the Hybrid Integral Approach (HIA) model of very high non-linearity. The finite elements and the asymptotic numerical method are used to handle this nonlinear effects the results of the stress-strain curve are presented, showing the influence of hole size on the structure for the different specified energy models, as well as the influence of structure size when the hole is fixed. We also show from the obtained results a decrease in stress as the size of the hole increases with the parameters of the Dirichlet boundary conditions when the structure has no hole for certain energy models and a decrease for others. The opposite phenomenon is observed regarding the influence of the size of the structure with a hole.