Original Article Journal of Intelligent Material Systems and Structures 1–12 Ó The Author(s) 2017 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/1045389X17698593 journals.sagepub.com/home/jim Analysis of multiple moving mode-III cracks in a functionally graded magnetoelectroelastic half-plane Mojtaba Ayatollahi 1 , Mojtaba Mahmoudi Monfared 2 and Mahsa Nourazar 1 Abstract This study deals with the interaction of multiple moving mode-III cracks in a functionally graded magnetoelectroelastic half-plane. The cracks are assumed to be either magneto-electrically impermeable or permeable. First, the singular stress, electric displacement, and magnetic induction fields in a half-plane with dislocations are obtained in closed form by the means of complex Fourier transform and then the problem is reduced to a system of singular integral equations in a set of unknown functions representing dislocation densities. These integral equations are Cauchy singular and are solved numerically to determine field intensity factors for multiple moving cracks. The results show that the crack velo- city has great effect on the field intensity factors. Keywords Multiple moving cracks, functionally graded magnetoelectroelastic, singular integral equations, field intensity factors, dis- tributed dislocation technique Introduction In recent years, due to the extensive utilization of adap- tive material systems, there has been a dramatic increase in the number of analytical, numerical, and experimen- tal studies devoted to predicting the elastic-electric- magnetic coupled effects within magnetoelectroelastic composite materials. Composites made of piezoelectric/ piezomagnetic materials exhibit magnetoelectric effect that is not present in single-phase piezoelectric or piezo- magnetic materials, and such magnetoelectric materials have potential applications as transducers, acoustic/ ultrasonic devices, and magnetic and/or electric sensors. Because of the brittleness of magnetoelectroelastic materials, there is a growing interest among the researchers in solving fracture mechanics problems in media possessing coupled piezoelectric, piezomagnetic, and magnetoelectric effects, that is, magnetoelectroelas- tic effects. The dynamic crack problem in smart materi- als has received much attention of researchers in the last few years. The increasing attention to the study of crack problems in smart materials has led to a lot of signifi- cant works. Especially, the effect of the crack moving speed on the crack tip field was a popular subject in classical elastodynamics. The development of functionally graded materials (FGMs) has demonstrated the potential of reducing the stress concentration and increasing the fracture toughness; that is why, the concept has been recently extended to magnetoelectroelastic materials. Yoffe (1951) has addressed the problem of a moving crack with constant velocity through a body under uni- form far-field tensile loading for the first time. The Yoffe crack problem in a piezoelectric material was first studied by Chen and Yu (1997). The dynamic behavior of a finite crack moving with constant velocity in a rec- tangular piezoelectric ceramic block under the com- bined anti-plane shear and in-plane electrical loadings has been stated by Kwon and Lee (2000). The problem of a moving crack in a functionally graded piezoelectric material was solved by Li and Weng (2002). They observed that by increasing the gradient of the material properties, the magnitudes of the stress and electric dis- placement intensity factors reduce. Jin and Zhong (2002) analyzed a moving crack in the functionally graded piezoelectric materials and reported the effects of the velocity of crack propagation and the gradient 1 Faculty of Engineering, University of Zanjan, Zanjan, Iran 2 Department of Mechanical Engineering, Islamic Azad University, Hashtgerd Branch, Alborz, Iran Corresponding author: Mojtaba Ayatollahi, Faculty of Engineering, University of Zanjan, P. O. Box 45195-313, Zanjan, Iran. Email: mo.ayatollahy@gmail.com