Cavitation for incompressible anisotropic nonlinearly elastic spheres (Q1330755)

Subject of this research is the formation of a cavity in an incompressible nonlinearly elastic sphere transversely isotropic about the radial direction, which is exposed to a homogeneous tensile load acting on its surface. The authors investigate the critical load and bifurcation for the general strain energy function of a transversely isotropic material and consider then as a special case an anisotropic generalization of the neo-Hookean body, which enables them to obtain explicit results. For small anisotropy, they find a continuous growth of the cavity, whereas for large anisotropy a cavity of finite radius appears at a load which may be smaller than the critical one. Thereafter, the authors study the stability of the different solutions and, finally, the stress distribution for small anisotropy. Outside the immediate neighborhood of the cavity, the homogeneous state of stress agrees with the tensile load. This clearly written paper deserves the interest of researchers in finite elasticity and stability.