Local Eshelby matrix in eigen-variable boundary integral equations for solids with particles and cracks in full space

In order for the large scale numerical simulation of solids with particles and cracks, the concept of local Eshelby matrix has been introduced into the computational model of the eigen-variable boundary integral equation (BIE) to resolve the problem of interactions among particles and cracks by joining the two concepts of the eigenstrain and eigen COD. The local Eshelby matrix in the present paper is considered as an extension of the concept of Eshelby tensor in numerical form for both equivalent inclusions and cracks, defined on the group of near field particles and cracks in full space. Through some typical numerical examples, the computations of stress intensity factors (SIF) are carried out and compared with the results of the sub-domain method using the dual BIE. With the proposed computational model, it is verified not only the correctness and feasibility but also the high efficiency of the present solution procedure, showing the potential of the proposed method for large scale numerical simulation of solids with particles and cracks.