Stability and breathing motions of pressurized compressible hyperelastic spherical shells

The stability of homogeneous, isotropic, compressible, hyperelastic, thick spherical shells subjected to external dead-load traction are investigated within the context of the finite elasticity theory. The stability of the fi nitely deformed state and small, free, radial vibrations about this state a re investigated using the theory of small deformations superposed on large elastic deformations. The frequencies of small free vibrations about the pr e-stressed state are obtained numerically. The loss of stability occurs whe n the motions cease to be periodic. The critical values of stress and defor mation are given for a foam rubber, slightly compressible rubber and a near ly incompressible rubber. (C) 2001 Academic Press.