The remarkable nature of radially symmetric deformation of spherically uniform linear anisotropic elastic solids

Antman and Negron-Marrero [1] have shown the remarkable nature of a sphere of nonlinear elastic material subjected to a uniform pressure at the surfac e of the sphere. When the applied pressure exceeds a critical value the str ess at the center r = 0 of the sphere is infinite. Instead of nonlinear ela stic material, we consider in this paper a spherically uniform linear aniso tropic elastic material. It means that the stress-strain law referred to a spherical coordinate system is the same for any material point. We show tha t the same remarkable nature appears here. What distinguishes the present c ase from that considered in [1] is that the existence of the infinite stres s at r = 0 is independent of the magnitude of the applied traction sigma(0) at the surface of the sphere. It depends only on one nondimensional materi al parameter kappa. For a certain range of kappa a cavitation (if sigma(0) > 0) or a blackhole (if sigma(0) < 0) occurs at the center of the sphere. W hat is more remarkable is that, even though the deformation is radially sym metric, the material at any point need not be transversely isotropic with t he radial direction being the axis of symmetry as assumed in [1]. We show t hat the material can be triclinic, i.e., it need not possess a plane of mat erial symmetry. Triclinic materials that have as few as two independent ela stic constants are presented. Also presented are conditions for the materia ls that are capable of a radially symmetric deformation to possess one or m ore symmetry planes.