Solution of the incompatibility problem in linear three-dimensional anisotropic media for an isotropic incompatibility tensor

A solution of the incompatibility problem in three-dimensional anisotropic elasticity is derived for the case that the incompatibility tensor has isotropic symmetry. To that end an infinitely extended linear elastic anisotropic medium is assumed. Under these conditions the internal stresses are obtained by pure differentiations from the corresponding fourth-order stress function tenser. This result is then used to express the internal stress tensor as a convolution of the incompatibility tensor and the elastic Green's function tenser.