Multiscale Analysis of the Multiple Interacting Inclusions Problem: Finite Number of Interacting Inc
Elastic analysis of local fields in heterogeneous solids containing multiple inclusions subjected to remote loading is of considerable interest in many engineering disciplines. Several techniques have been proposed for computing multi-particle interactions in an infinite medium. In the two-dimensional case the method of Kolosov-Muskhelishvili’s complex potentials is highly efficient. Combining the body force method with complex stress function theory, a complex integral equation method was proposed in ,  to study interaction problems between holes and other defects in an infinite or semiinfinite elastic plane. The conformal mapping technique was generalized in  for the analysis of elastic fields in two joined half-planes with an inclusion of an arbitrary shape. Sherman  constructed an elegant complex variable method based on the Kolosov- Muskhelishvili potentials leading to a singular integral equation for a complexvalued density. An effective numerical algorithm utilizing this method  was developed, and Greengard and Helsing  combined Sherman’s method with the fast multipole method and adaptive quadrature technique; the methods mentioned can be implemented in two-dimensional piecewise inhomogeneous media with isotropic constituents.
KeywordsSingular Integral Equation Boundary Integral Equation Stress Concentration Factor Multiscale Analysis Small Inclusion
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