A New Approach to Improve the Numerical Procedure for 2D Anti-Plane Crack Problems in Functionally Graded Magneto-Electro-Elastic Materials

Abstract

Magneto-electro-elastic composite materials have extensive applications in modern smart structures, because they possess good coupling between mechanical, electrical and magnetic fields. This new effect was reported for the first time by Van Suchtelen [1] in 1972. Due to their ceramic structure cracks inevitably exist in these materials. If these cracks extend the material may lose its structural integrity and/or functional properties. In this study we consider functionally graded magneto-electro-elastic materials (MEEM) subjected to anti-plane time-harmonic load. Our purpose is to evaluate the dependence of the stress concentration near the crack tips on the frequency of the applied external load. We use boundary integral equation method (BIEM) for the numerical solution. For materials with complex geometry of cracks the numerical procedure becomes too cumbersome. To increase the speed of the computations we derive new fundamental solutions by the Fourier transform. The more simple form of these fundamental solutions leads to decreasing of the number of the numerical computations. Asymptotic for small arguments of the new solutions will be presented. The results can be used to improve the numerical procedure based on the BIEM for complex crack configurations in MEEM. 2010 Mathematics Subject Classification: 65M38, 65N80, 65Z05.