FUNDAMENTAL SOLUTION OF THE INCOMPATIBILITY PROBLEM IN 3-DIMENSIONAL INFINITE ANISOTROPIC ELASTICITY THEORY

The decomposition of the strain field into its deformation and its inc ompatible parts which is unique in an infinite elastic medium is used to derive a fourth-rank Green's function tensor P-abij (fundamental so lution) of the incompatibility problem of linear anisotropic elasticit y theory. This fundamental solution is homogeneous of degree -1 and no n-unique. For the calculation of internal stresses only one of the pos sible fundamental solutions is needed. In order to solve the integrati on problem, it is convenient to decompose the fundamental solution int o two parts. The one part consists of a particular solution of the inc ompatibility condition (Eq. (3)) and is obtained in a straightforward manner. The other part results from a deformation part of the strain. The integration of this part is worked out by using the theory of resi dues. In the case of hexagonal crystal symmetry an explicit solution i s presented.