https://hal.archives-ouvertes.fr/hal-00833775Zou, W.-N.W.-N.ZouHe, Qi-ChangQi-ChangHeMSME - Laboratoire de Modélisation et Simulation Multi Echelle - UPEM - Université Paris-Est Marne-la-Vallée - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12 - CNRS - Centre National de la Recherche ScientifiqueZheng, Q.-S.Q.-S.ZhengThermal inclusions inside a bounded mediumHAL CCSD2013[PHYS.MECA.SOLID] Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph][SPI.MECA.SOLID] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph]He, Q. C.2013-06-13 14:58:392022-09-29 14:21:152013-06-13 14:58:39enJournal articles10.1098/rspa.2013.02211In the context of thermal conduction taken as a prototype of numerous transport phenomena, a general method is elaborated to study Eshelby's problem of inclusions inside a bounded homogeneous anisotropic medium. This method consists in: (i) recasting by a linear transformation the initial problem into Eshelby's problem of the transformed inclusion inside the transformed finite isotropic medium and (ii) decomposing Eshelby's problem of a thermal inclusion embedded in a finite isotropic medium into the sub-problem of the same inclusion inside the associated infinite medium and the sub-problem of the finite ambient isotropic medium including no inclusion but undergoing appropriate compensating boundary conditions. The general method is applied in the two-dimensional situation and the corresponding temperature field and Eshelby's conduction tensor are explicitly expressed in terms of some curvilinear complex integrals for the Dirichlet and Neumann boundary conditions. Thus, the difficulties owing to the unavailability or non-existence of Green's function are overcome. The general results in the two- dimensional case are finally specified and illustrated by considering a finite circular medium with circular or polygonal inclusions.