Numerical Simulation of the Effect of Damaged Induced Softening on the Inflation of a Circular Rubber Membrane

Rubbery materials can undergo deformation induced microstructural changes leading to softening of response and permanent set. In this work, these materials are modeled by a constitutive equation that incorporates the following micromechanism : when the deformation becomes large enough, network junctions break during further increments of deformation and then heal. New networks are formed by this conversion process, each unstressed in the local configuration at which it is formed. The constitutive equation is used to describe the response of the particles of an initially flat circular membrane which is inflated by lateral pressure. The original material and each newly formed network are assumed to respond as neo-Hookean elastic materials. Results of a numerical simulation show the influence of this conversion process on the distribution of stretch ratios, inflated shapes and the relation between the pressure and the crown stretch ratio.