Semi-analytical model for stretch ratio determination in inflation test for isotropic membranes

Abstract

This article wishes to contribute to the understanding of principal strains distribution in inflation test for circular isotropic soft membranes, combining analytical, numerical, and experimental investigations. The method developed gives a relatively simple and original solution of the deformation and thus of the stresses during an inflating test, provided that the measurement is sufficiently close to the pole. For this purpose, a semi-analytical model (SAM) is proposed and to evaluate that theory, two complementary approaches are used. The first approach is experimental. Inflation and uniaxial tensile tests are set up on medical silicone sheets to identify their hyperelastic constitutive parameters, using Digital Image Correlation. Then these mechanical properties are injected into a 3D finite element model (FEM) of membrane, simulating the inflation test, to compare the strains that had been obtained with those of the SAM. Numerical results show that the strain calculated by the SAM follows the pattern of the circumferential strain obtained by the FEM. Up to a certain distance from the center of the disk (half of the disk for our example), strain calculated by the SAM give a correct approximation of the deformation with respect to radial and circumferential FEM strains.