Fracture And Adhesion In Soft Materials Subjected To Large Deformation

Abstract

This dissertation studies large deformation elasticity with an aim to understand fracture and adhesion in soft polymeric materials. First, motivated by recent experiments using thin elastic membranes to measure interfacial adhesion, we propose a theory to describe the adhesive contact between an inflated hyperelastic membrane and a rigid substrate based on large deformation elasticity. A key result is the exact expression for the energy release rate in terms of local variables at the contact edge, which links adhesion to the contact angle. In addition, our theory allows two types of friction conditions between the membrane and the substrate: frictionless and no-slip contact. Numerical simulations for a neo-Hookean membrane are carried out to study the relation between applied pressure and contact area. The second part of this dissertation focuses on solving the asymptotic stress and deformation fields near the tip of a Mode I traction free plane stress crack in incompressible hyperelastic solids. We develop a method using hodograph transform to obtain the dominant singularity of the near tip deformation field. This method is particularly useful for severely strain hardening materials and is used to find out the crack tip stress and deformation fields for two types of soft materials: generalized neoHookean solids and an exponentially hardening solid. Our asymptotic solutions are verified using finite element simulations. The limitations of a previous result for the generalized neo-Hookean solids are resolved by our solution. Finally, we study the large deformation of an isolated penny-shaped crack in an infinite block of incompressible hyperelastic solid. The crack is subjected to remote tensile true stresses that are parallel (S) and normal (T) to the undeformed crack faces. We use finite element method to determine the energy release rates for different triaxiality ratios S/T. Our results shows that the energy release rate increases rapidly with S/T at finite strains, while for small deformations, it is independent of S/T. For the special case of pure hydrostatic tension (S/T=1), the energy release rate approaches infinity for the neo-Hookean solid at a finite tension. We also show that strain hardening significantly reduces the energy release rate for the same remote loading.