Time-harmonic dislocations in a multilayered transversely isotropic magneto-electro-elastic half-space

Abstract

Modeling layered systems with dislocations is very challenging; yet, it is important since most smart structures are made of multilayers to make best use of the combined effective property. As such, during the manufactures, defects, such as dislocations, could be introduced in the multilayers. In this article, we analytically find, for the first time, the response of three-dimensional multilayered magneto-electro-elastic systems due to time-harmonic dislocations. The dislocations are the most general, containing the elastic dislocations and discontinuity of the electric potential and/or magnetic potential over a circular region in any layer in the medium. The fully coupled partial differential equations of motion and the Gauss law for the magneto-electro-elastic materials are solved in terms of cylindrical system of vector functions, and the dual variable and position method is further introduced to treat the multilayers. Numerical examples are carried out based on the derived analytical solution to demonstrate the effects of the time-harmonic dislocations on the induced magneto-electro-elastic fields. This analytical solution is important in both electrodynamics and elastodynamics, with possible applications in material sciences and physics. The numerical results are useful in design process of smart devices made of magneto-electro-elastic solids applicable to other engineering fields like renewable energy.

Dislocation singularities in layered magneto-electro-elastic plates

“…In contrast to the considerable attention paid to the fundamental crack problems , Gao et al, 2003, Wang and Mai, 2003, Rao and Kuna, 2008, Li and Lee et al, 2010, Wan et al, 2013, Hu and Chen, 2015, Bagheri et al, 2015, Mousavi, 2015, Zhao et al, 2015, Bagheri et al, 2017, Zhao et al, 2019, Nourazar and Ayatollahi, 2020, Wu et al, 2021, Hsu and Hwu, 2022 as well the modeling of imperfectly bounded interfaces in MEE solids (Nan et al, 2003, Wang and Pan, 2007, Pan et al, 2009, Huang and Li, 2010, Espinosa et al, 2011, Kuo, 2013, Wang, 2015, Espinosa et al, 2017, Kuo et al, 2018, Jiang et al, 2019, Kuo et al, 2019, Pang et al, 2019, Yang and Li, 2019, the corresponding dislocation boundary-value problem has received little consideration in the literature for MEE bimaterials (Fang et al, 2005, Hao and Liu, 2006, Zheng et al, 2007, Han and Pan, 2013, Chu et al, 2013, and even less for free-standing MEE multilayers until recently (Moshtagh et al, 2019, Vattré and Pan, 2019, Yuan et al, 2019. This circumstance is closely related to the difficulties in determining explicit expressions for the generalized MEE point-source Green's functions in inhomogeneous solids.…”