Load maximum behavior in the inflation of hollow spheres of incompressible material with strain-dependent damage

Carroll has shown three qualitatively different cases of behavior in the load-expansion relation for the inflation of hollow incompressible isotropic elastic spheres. Each of these cases was related to material response in uniaxial compression (or equal biaxial extension). For “type A” materials, load increases monotonically with expansion; for “type B” materials, load increases monotonically and then decreases; for “type C” materials, load increases monotonically, decreases, and again increases. The present work discusses the monotonicity properties of the load-expansion relation when rubbery materials undergo microstructural change or damage. The analysis is carried out using a constitutive equation for materials undergoing continuous scission and reformation of macromolecular junctions. Results are presented for the case when this leads to softening of response. For “type A", sufficient softening can cause loss of monotonicity; for “type B", the softening leads to loss of monotonicity at smaller levels of inflation and lower loads.