INFLATION OF A THICK-WALLED SHELL WHICH EXHIBITS STRESS SOFTENING

The Mullins effect (Mullins, 1947), also known as stress softening, is exhibited by certain rubberlike materials and refers to changes of th e mechanical properties, due to prior deformation. Johnson and Beatty (1995) have investigated the Mullins effect in equibiaxial tension by performing cycles of static inflation and deflation experiments on lat ex balloons. These experiments show that stress softening results in a decrease in the pressure necessary to inflate a balloon, and in addit ion, indicate inelastic effects of hysteresis and permanent set. The o bjective of this paper is to investigate the finite deformation static inflation from the virgin state, followed by quasi-static removal of the internal pressure, of a thick-walled homogeneous spherical shell c omposed of an incompressible isotropic rubberlike material which exhib its stress softening and permanent set. Since the initial inflation of the shell, due to application of an internal pressure, does not resul t in a homogeneous deformation, a state of residual stress is present after complete removal of the internal pressure. A procedure is presen ted for the determination of the response of the shell for the first c ycle of inflation and deflation from the virgin sate, and the analysis includes strain softening and th inelastic effects of hysteresis and permanent set. It is assumed that, for the initial static inflation of the shell from the virgin state, the internal pressure and stress dis tribution for a monotonically increasing internal or external radius a re the same as for a hyperelastic shell, and also that the magnitude o f the permanent set of an element of the material is related monotonic ally to the deformation at the end of the inflation.