Mechanical interaction between spherical inhomogeneities: an assessment ofa method based on the equivalent inclusion

This paper assesses the ability of the Equivalent Inclusion Method (EIM) wi th third order truncated Taylor series (Moschovidis and Mura, 1975) to desc ribe the stress distributions of interacting inhomogeneities. The cases con sidered are two identical spherical voids and glass or rubber inhomogeneiti es in an infinite elastic matrix. Results are compared with those obtained using spherical dipolar coordinates, which are assumed to be exact, and by a Finite Element Analysis. The EIM gives better results for voids than for inhomogeneities stiffer than the matrix. In the case of rubber inhomogeneit ies, while the EIM gives accurate values of the hydrostatic pressure inside the rubber, the stress concentrations are inaccurate at very small neighbo uring distances for all stiffnesses. A parameter based on the residual stre ss discontinuity at the interface is proposed to evaluate the quality of th e solution given by the EIM. Finally, for inhomogeneities stiffer than the matrix, the method is found to diverge for expansions in Taylor series trun cated at the third order. (C) 2001 Editions scientifiques et medicales Else vier SAS.