Elastic theory of dislocation loops in three-dimensional isotropic bi-materials

We develop a novel elastic Green's function of point force in three-dimensional isotropic bi-materials that resembles the classical Kelvin solution in the corresponding infinite media. Based upon such a simple bi-material Green's function, we then investigate dislocation loops of arbitrary shape embedded in isotropic bi-materials. The main contribution of this work is an elegant extension of the classical Burgers' formula for displacements, Peach-Koehler's formula for stresses and Blin's formula for the interaction energy from the full-space case to the bi-material case. Most strikingly, our new formulae for bi-materials preserve the same simplicity as the classical expressions in the full space. The correctness of these extended formulae is verified by comparing them with available ones in the literature, and the importance of these formulae is on their direct application in the three-dimensional dislocation dynamics simulation involving interface or surface.