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

Carroll has shown three qualitatively different cases of behavior in the lo ad-expansion relation for the inflation of hollow incompressible isotropic elastic spheres. Each of these cases wits related to material response in u niaxial compression (or equal biaxial extension). For "type A" materials, l oad increases monotonically with expansion, for "type B" materials, load in creases monotonically and then decreases; for "type C" materials, load incr eases monotonically, decreases, and again increases. The present work discu sses the monotonicity properties of the load-expansion relation when rubber y materials undergo microstructural change or damage. The analysis is carri ed out using a constitutive equation for materials undergoing continuous sc ission and reformation of macromolecular junctions. Results are presented f or the case when this leads to softening of response. For "type A", suffici ent. softening can cause loss of monotonicity; for "type B", the softening leads to loss of monotonicity at smaller levels of inflation and lower load s.