The remarkable nature of radially symmetric deformation of spherically uniform linear anisotropic elastic solids
The author investigates the stresses state in the interior of a sphere of radius \(r\), subjected to a uniform pressure on its surface. The sphere is made of a spherically uniform linear anisotropic elastic material. It is shown that the existence of infinite stress at \(r=0\) does not depend on the traction \(\sigma_0\) at the surface, but depends only on a non-dimensional material parameter \(k\), a function of elastic constants of the material. For a certain range of \(k\), the author shows that a cavitation (if \(\sigma_0>0)\) or a black hole (for \(\sigma_0<0)\) occurs at the centre of the sphere. Finally, the author studies various particular cases of anisotropy, for instance the triclinic anisotropy, as well as various relations between the elastic constants of the material.
spherically uniform linear anisotropic elastic material
scientific article; zbMATH DE number 1359831