Axisymmetric membrane in adhesive contact with rigid substrates: Analytical solutions under large deformation

The large deformation of an elastic axisymmetric membrane in adhesive contact with a rigid flat punch is studied. Detachment of membrane is analyzed using a critical energy release rate criterion. Two types of incompressible hyperelastic material models are considered: neo-Hookean and a class of materials whose elastic energy density functions are independent of the trace of the Cauchy–Green tensor (I₂-based material). We also include pre-stretch in our formulation and study the stability of detachment process. Closed form analytical solutions for the membrane stresses, deformed profiles and energy release rate are obtained in the regime of large longitudinal stretch. For the I₂-based material, we discover an interesting “pinching” instability where the contact angle suddenly increases in a displacement controlled test. The region of validity of our analytical solutions is determined by comparing them with numerical solutions of the governing equations. We found that the accuracy of our solution improves with pre-stretch; for pre-stretch ratios greater than 1.3, our analytical solution also works well in the small deformation regime.