Loosening of elastic inclusions

• Published in: International journal of solids and structures Vol. 43; no. 6; pp. 1638 - 1668
• Main Authors: Crouch, S.L., Mogilevskaya, S.G.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-03-2006
• Subjects: Cohesive crack model; Direct boundary integral method; Displacement discontinuities; Gibbs phenomenon; Imperfect interface; Mohr–Coulomb yield condition; Multiple circular inclusions; Somigliana’s formula; Under-relaxation; Displacement discontinuities; Direct boundary integral method; Gibbs phenomenon; Under-relaxation; Somigliana’s formula; Multiple circular inclusions; Mohr–Coulomb yield condition; Cohesive crack model; Imperfect interface
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2005.03.050

A numerical method is presented for simulating the occurrence of localized slip and separation along the interfaces of multiple, randomly distributed, circular elastic inclusions in an infinite elastic plane. The method is an extension of a direct boundary integral approach previously described elsewhere for solving problems involving perfectly bonded circular inclusions. Here, we allow displacement discontinuities to develop along the inclusion/matrix interfaces in accordance with a linear Mohr–Coulomb yield condition combined with a tensile strength cut-off. The displacements, tractions, and displacement discontinuities on the inclusion boundaries are all represented by truncated Fourier series, and an explicit iterative algorithm is adopted to determine zones of slip and separation under the prevailing loading conditions. Several examples are given to demonstrate the accuracy and generality of the approach.