Time-harmonic Green’s functions for anisotropic magnetoelectroelasticity

Abstract

Two-dimensional (2-D) and three-dimensional (3-D) time-harmonic Green's functions for linear magnetoelectroelastic solids are derived in this paper by means of Radon-transform. Displacement field and electric and magnetic potentials in a fully anisotropic magnetoelectroelastic infinite solid due to a time-harmonic point force, point charge and magnetic monopole are obtained in form of line integrals over a unit circle in 2-D case and surface integrals over a unit sphere in 3-D case. This dynamic fundamental solution is then split into the sum of regular dynamic plus singular terms. The singular terms coincide with the Green's functions for the static problem and may be further reduced to closed form expressions. The proposed Green's functions can be used in the corresponding boundary element method (BEM) formulation.

Analysis of cracked magnetoelectroelastic composites under time-harmonic loading

“…u à IJ and p à IJ denote the fundamental solution or Green's functions displacements and tractions at boundary point x due to a unit harmonic load placed at point n (Rojas-Diaz et al, 2008), with the expressions summarized in the previous section; and c IJ (n) results from the Cauchy principal value integration of the singular p à IJ kernels and thus depends on the geometry variation at the point n. The tractions BIE follows from differentiation of Eq. (32) with respect to n k and application of Hooke's law, to yield c IJ ðnÞp J ðn; xÞ þ N q Z C s à qIJ ðx; n; xÞu J ðx; xÞdCðxÞ…”

“…The approach presented herein is a generalization to magnetoelectroelastic materials of our previous works for dynamic fracture of anisotropic and piezoelectric media Sáez et al, 2006). The timeharmonic fundamental solution derived by Rojas-Diaz et al (2008) using the Radon transform is split into singular plus regular parts. The singular part is independent of the frequency and it coincides with the static fundamental solution.…”

“…A traction boundary integral equation formulation is applied to solve the problem in combination with recently obtained time-harmonic Green's functions (Rojas-Diaz et al, 2008). The hypersingular boundary integral equations appearing in the formulation are first regularized via a simple change of variables that permits to isolate the singularities.…”

Wave band gaps in two-dimensional piezoelectric/piezomagnetic phononic crystals

“…The constitutive equations of a composite material with piezoelectric and piezomagnetic phases are given by (Liu et al, 2001;Tian and Gabbert, 2005;Rojas-Dí az et al, 2008) r ij ¼ c ijmn e mn À e nij E n À q nij H n ;…”

Application of the extended traction boundary element-free method to the fracture of two-dimensional infinite magnetoelectroelastic solid

“…Hou et al [14] obtained the Green's functions for infinite and semi-infinite magnetoelectroelastic media, which are expressed in terms of elementary functions. Rojas-Diaz et al [15] derived two-dimensional (2D) and three-dimensional (3D) time harmonic Green's functions for anisotropic magnetoelectroelasticity by means of Radon-transformation. Based on the extended Stroh formalism, Pan [16] derived 3D Green's functions in anisotropic magnetoelectroelastic full space, half space, and bi-materials.…”