Fundamental solutions for two-dimensional anisotropic thermo-magneto-electro-elasticity

In this paper, with the consideration of thermal effects, eight equally important systems of constitutive laws generally used to describe anisotropic magneto-electro-elastic (MEE) materials are all considered. We provide simple mathematical relations to convert any one of the eight equation sets to the other seven sets. The equivalent reduced properties for two-dimensional analysis are obtained for eight possible different plane states of MEE solids. Complex variable Stroh formalism is used to derive the fundamental solution for two-dimensional thermo-MEE analysis. By using the identities of Stroh formalism, the complex form solution can be converted into real form. With the real form fundamental solution, the trouble induced by the multi-valued complex logarithmic function is circumvented and the extra line integral that appears in the thermal analysis of the boundary element method (BEM) can be eliminated. Thus, the temperature information inside the domain required by the extra line integral can be avoided, and a truly BEM for thermo-MEE analysis is achieved for the first time in the literature. The influence of heat source represented by the heat generation rate is also considered in our formulation. Verification of our solution is made by comparison with the analytical solution and the solution obtained by BEM using complex form solution with extra line integral as well as the solution by commercial finite element software ANSYS.

Dynamic analysis of multilayered magnetoelectroelastic plates based on a pseudo-Stroh formalism and Lagrange polynomials

In this article, a semi-analytical three-dimensional modeling of dynamic behavior of the multilayered magnetoelectroelastic plates under simply supported edges boundary conditions is derived. A combination of pseudo-Stroh formalism and the Lagrange polynomials is elaborated for the space and time response. The time domain is subdivided into small intervals that are discretised using the associated Tchybechev points. The layer-time solution is elaborated in time-dependent matrix form. The propagator matrices are used for the laminated multifunctional plates with an arbitrary number of layers. Extended-traction vectors are obtained for mechanical, electrical, and magnetic excitations. To validate the elaborated numerical procedure, the dynamic behavior of the three layered plates made of piezoelectric material [Formula: see text] and piezomagnetic material [Formula: see text] is investigated. The lower surface of the plate is assumed to be traction free, whereas the upper surface is subjected to a dynamic sinusoidal loading. The obtained results are in good agreement with the available ones based on the Layer wise and the state-space approaches. These results demonstrated that a magnetoelectric coupling coefficient is time-independent but depends strongly on the kind of imperfect interfaces and the taking sequences of the multilayered plates. Furthermore, it is established that the imperfect interfaces have a strong influence on the dynamic behavior of the laminated structures.

Uniformly moving non-singular dislocations with elliptical core shape in anisotropic media

To allow for “relativistic”-like core contraction effects, an anisotropic regularization of steadily moving straight dislocations of arbitrary orientation is introduced, with two scale parameters [Formula: see text] and [Formula: see text] along the direction of motion and transverse to it, respectively. The dislocation core shape is an ellipse. When [Formula: see text], the model reduces to the Peierls–Eshelby dislocation, the fields of which are non-differentiable on the slip plane. For finite [Formula: see text] and [Formula: see text], fields are everywhere differentiable. Applying the author’s so-called “causal” Stroh formalism to the model, explicit expressions for the regularized fields in anisotropic elasticity are derived for any velocity. For faster-than-wave velocities, Mach-cone angles are found insensitive to the ratio [Formula: see text], as must be. However, the larger [Formula: see text], the weaker the intensity of the cone branches. An expression is given for the radiative dissipative force opposed to motion. From this expression, it is inferred that the concept of a “radiation-free” intersonic velocity can, when not applicable, be replaced by that of a “least-radiation” velocity.

Modeling and analysis of loaded multilayered magnetoelectroelastic structures composite materials: Applications

This paper presents the detailed analysis of fiber- reinforced magnetoelectroelastic composite plates. The work is divided into two major sections. The first one deals with the homogenization of the properties of each layer based on the Mori-Tanaka mean field approach where all the needed effective coefficients of each layer are determined. Then, in order to perform analysis of the considered, the Stroh formalism is used to provide solutions for multifunctional multilayered magnetoelectroelastic composites, to predict exactly the mechanical and electrical behaviors near or across the interface of material layers.

Electroelastic Green’s function of one-dimensional piezoelectric quasicrystals subjected to multi-physics loads

Green’s functions of infinite and semi-infinite plane problems of one-dimensional quasicrystals with piezoelectric effect are obtained in a closed form by Stroh formalism. Some numerical examples under different loading conditions, such as line forces, line dislocations, and a line charge, are given to explain the mechanical and electric behaviors of the quasicrystals. Various elastic–electric constants of quasicrystals are analyzed and the coupling effects between the phonon and phason fields are studied. The presented solutions will be useful for many boundary value problems of one-dimensional quasicrystals with piezoelectric effect. Moreover, the numerical results can be used to verify the accuracy of the solutions by some numerical methods, such as the finite element and boundary element methods. Furthermore, the Stroh formalism can be generalized to the researches on more complex problems of quasicrystals.