A transformation of the problem of linear elastic structure for application to the inclusion problem and to Green functions

A simple transformation of rite problem of the linear elastic structure is presented. The transformed problem corresponds to a new problem of linear e lastic structure with different behaviour; geometry and prescribed forces a nd displacements. The transformed problem can be easier to study, or can co rrespond to cases with well-known solutions. By means of this transformatio n, the problem of ellipsoidal inclusion is transformed into a problem of sp herical inclusion, the analytical results known far the Eshelby tensor for an isotropic or transversely isotropic matrix are extended to more general cases of matrix behaviour; and finally, close form expressions of the Green function for an infinite medium are derived for some cases of elastic beha viour without transversal isotropy or orthotropy. (C) 2000 Academie des sci ences/Editions scientifiques et medicales Elsevier SAS.