Open Access

ARTICLE

BIE Method for 3D Problems of Rigid Disk-Inclusion and Crack Interaction in Elastic Matrix

V.V. Mykhas’kiv¹, O.I. Stepanyuk²

1 Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, 79060 Lviv, Ukraine
2 Lviv National Academy of Veterinary Medicine, 79010 Lviv, Ukraine

Computer Modeling in Engineering & Sciences 2005, 10(1), 45-64. https://doi.org/10.3970/cmes.2005.010.045

Abstract

The 3D elastostatic problem for an infinite remotely loaded matrix containing a finite number of arbitrarily located rigid disk-inclusions and plane cracks is solved by the boundary integral equation (BIE) method. Its boundary integral formulation is achieved by the superposition principle with the subsequent integral representations of superposition terms through surface integrals, which should satisfy the displacement linearity conditions in the inclusion domains and load-free conditions in the crack domains. The subtraction technique in the conjunction with mapping technique under taking into account the structure of the solution at the edges of inhomogeneities is applied for the regularization of BIE obtained. The discrete analogue of equations is constructed by using the collocation scheme. The mixed mode stress intensity factors as functions of angular coordinates of front points for the interacting pairs of circular inclusions and cracks, which have different mutual orientations, distances and sizes, are calculated. The reinforcing properties of dispersed phase are estimated for involved models.

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