Dislocation singularities in layered magneto-electro-elastic plates

A general and unified theory is formulated to investigate static and time-harmonic field solutions induced by dislocation loops and dislocation arrays in three-dimensional multilayered structures. Each homogeneous plate consists of an orthotropic magneto-electro-elastic material including nonlocal effects. While the nonlocal constitutive relations with multi-phase coupling are treated by means of the original Eringen model using a Helmholtz-type operator, the field expressions are based on the mathematically elegant and computationally powerful Stroh formalism in matrix form, consistently combined with double Fourier series expansions and the dual variable and position technique to propagate the extended solutions among the different layers of the multilayered systems. The time-harmonic dislocation loops are represented by a discontinuity in the prescribed elastic displacement, electric potential, and magnetic potential on arbitrarily-located rectangular and elliptical surfaces in the multilayered structures, while the dislocation arrays are composed of infinitely long, straight and uniformly spaced parallel dislocations with the same local Burgers vectors. The new field solutions are first validated against existing frameworks limited to static and local elasticity theory of these two types of extrinsic and intrinsic dislocations, and subsequently applied to analyze several unexplored effects on the dislocation-induced magneto-electro-elastic fields, namely the material anisotropy, interaction with internal heterophase interfaces, multi-phase coupling, nonlocal core-spreading parameter, finite-valued driving forces, vibration frequency, and stacking sequences. The numerical outcomes indicate that each effect is significant and neglecting any one of them leads to an erroneous prediction on the extrinsic and intrinsic dislocation-induced response, thus providing a suitable route for the design of advanced magneto-electro-elastic fabrication devices for energy harvesting applications.