Inflation of elastomeric circular membranes using network constitutive equations

The present paper deals with the use of network-based hyperelastic constitutive equations in the context of thin membranes inflation. The study focus on the inflation of plane circular membranes and the materials are assumed to obey Gaussian and non-Gaussian statistical chains network models. The governing equations of the inflation of axisymmetric thin rubber-like membranes are briefly recalled. The material models are implemented in a numerical tool that incorporates an efficient B-spline interpolation method and a coupled Newton-Raphson/arc-length solving algorithm. Two numerical examples are studied: the homogeneous inflation of spherical balloons and the inflation of initially plane circular membranes. In the second example, the inflation profiles and the distributions of extension ratios along the membrane are extensively analysed during the inflation process. Both examples highlight the need of an accurate modelling of the strain-hardening phenomenon in elastomers.