×

Fracture analysis of magnetoelectroelastic solids by using path-independent integrals. (English) Zbl 1196.74217

Summary: A solution scheme based on the fundamental solution for a generalized edge dislocation in an infinite magnetoelectroelastic solid is presented to analyze problems involving single, multiple and slowly growing impermeable cracks. The fundamental solution for a generalized dislocation is obtained by extending the complex potential function formulation used for anisotropic elasticity. The solution for a continuously distributed dislocation is derived by integrating the solution for an edge dislocation. The problem of a system of cracks subjected to remote mechanical, electric and magnetic loading is formulated in terms of set of singular integral equations by applying the principle of superposition and the solution for a continuously distributed dislocation. The singular integral equation system is solved by using a numerical integration technique based on Chebyshev polynomials. The \(J_i\) and \(M\)-integrals for single crack and multi-cracks problems are derived and their dependence on the coordinate system is investigated. Selected numerical results for the \(M\)-integral, total energy release rate and mechanical energy release rate are presented for single, double and multiple crack problems. The case of a slowly growing crack interacting with a stationary crack is also considered. It is found that \(M\)-integral presents a reliable and physically acceptable measure for assessment of fracture behaviour and damage of magnetoelectroelastic materials.

MSC:

74R10 Brittle fracture
74F15 Electromagnetic effects in solid mechanics
PDF BibTeX XML Cite
Full Text: DOI

References:

[5] Erdogan, F. (1978). Mixed boundary-value problem in mechanics. In Mechanics today (Edited by S. Nemat-Nasser), vol. 4, pp. 1-86, Pergamon Press. · Zbl 0369.45004
[28] Singh, R.N. and Wang, H. (1995). Adaptive materials systems. (Edited by G.P. Carman, C. Lynch, N.R. Scottos), Proceedings of AMD-vol. 206/MD-vol. 58, ASME, pp. 85-95.
[33] Ting, T.C.T. (1996). Anisotropic Elasticity: Theory and Application. Oxford Science, New York. · Zbl 0883.73001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.