Exact solution for 2D polygonal inclusion problem in anisotropic magnetoelectroelastic full-, half-, and bimaterial-planes

Jiang, Xiaoqian; Pan, Ernian

doi:10.1016/j.ijsolstr.2004.03.017

Cited by 69 publications

(43 citation statements)

References 75 publications

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“…We also show that our solution reduces to the known results of uniform eigenstrains [6,8,13] and of linear eigenstrains [30]. Besides the induced fields listed in the tables and illustrated by the figures, we also analyse the singularity features at the vertex of the polygon and the averages of the induced fields over the inclusion.…”

Section: Introductionmentioning

confidence: 53%

“…Motivation for studying Eshelby's inclusion problem concerning anisotropic magneto-electro-elastic (MEE) materials arises from the wide applications of the composites involving MEE coupling (called multi-ferroics in materials and physics) as well as the many striking features found in these composites [6][7][8]. Furthermore, giant and universal magnetoelectric coupling effects can be designed and induced in many recent advanced soft materials [9].…”

Section: Introductionmentioning

confidence: 99%

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Eshelby's problem of polygonal inclusions with polynomial eigenstrains in an anisotropic magneto-electro-elastic full plane

2015

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This paper presents a closed-form solution for the arbitrary polygonal inclusion problem with polynomial eigenstrains of arbitrary order in an anisotropic magneto-electro-elastic full plane. The additional displacements or eigendisplacements, instead of the eigenstrains, are assumed to be a polynomial with general terms of order M + N. By virtue of the extended Stroh formulism, the induced fields are expressed in terms of a group of basic functions which involve boundary integrals of the inclusion domain. For the special case of polygonal inclusions, the boundary integrals are carried out explicitly, and their averages over the inclusion are also obtained. The induced fields under quadratic eigenstrains are mostly analysed in terms of figures and tables, as well as those under the linear and cubic eigenstrains. The connection between the present solution and the solution via the Green's function method is established and numerically verified. The singularity at the vertices of the arbitrary polygon is further analysed via the basic functions. The general solution and the numerical results for the constant, linear, quadratic and cubic eigenstrains presented in this paper enable us to investigate the features of the inclusion and inhomogeneity problem concerning polynomial eigenstrains in semiconductors and advanced composites, while the results can further serve as benchmarks for future analyses of Eshelby's inclusion problem.

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Section: Introductionmentioning

confidence: 53%

Section: Introductionmentioning

confidence: 99%

Eshelby's problem of polygonal inclusions with polynomial eigenstrains in an anisotropic magneto-electro-elastic full plane

2015

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“…The peak value of B r is for the 0.5 volume fraction of the piezomagnetic fiber and goes on decreasing with the decrease in volume fraction. [Liu et al 2003], barium titanate from [Aboudi 2001] and two phase MEE from [Jiang and Pan 2004]. The response at the middle node, that is, at the center of the layered cylinder, has been studied for a time lapse of 0.005 sec.…”

Section: 2mentioning

confidence: 99%

Untitled

2008

JOMMS

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See inside back cover or http://www.jomms.org for submission guidelines.Regular subscription rate: $500 a year.Subscriptions, requests for back issues, and changes of address should be sent to Mathematical Sciences Publishers, 798 Evans Hall, Department of Mathematics, University of California, Berkeley, CA 94720-3840. ELASTIC CONSTANTS AND THERMAL EXPANSION AVERAGES OF A NONTEXTURED POLYCRYSTAL ROLAND DEWITThis paper gives expressions for the overall average elastic constants and thermal expansion coefficients of a polycrystal in terms of its single crystal components. The polycrystal is assumed to be statistically homogeneous, isotropic, and perfectly disordered. Upper and lower bounds for the averages are easily found by assuming a uniform strain or stress. The upper bound follows from Voigt's assumption that the total strain is uniform within the polycrystal while the lower bound follows from Reuss' original assumption that the stress is uniform. A self-consistent estimate for the averages can be found if it is assumed that the overall response of the polycrystal is the same as the average response of each crystallite. The derivation method is based on Eshelby's theory of inclusions and inhomogeneities. We define an equivalent inclusion, which gives an expression for the strain disturbance of the inhomogeneity when external fields are applied. The equivalent inclusion is then used to represent the crystallites. For the self-consistent model the average response of the grains has to be the same as the overall response of the material, or the average strain disturbance must vanish. The result is an implicit equation for the average polycrystal elastic constants and an explicit equation for the average thermal expansion coefficients. For the particular case of cubic symmetry the results can be reduced to a cubic equation for the selfconsistent shear modulus. For lower symmetry crystals it is best to calculate the self-consistent bulk and shear modulus numerically. IntroductionA polycrystal, whose properties vary in a complicated fashion from point to point over a small microscopic length scale, may appear on average to be uniform or perhaps, more generally, its properties appear to vary smoothly. The determination of such overall properties from the properties and geometrical arrangement of the constituent monocrystal grains is our aim. In the simplest case the polycrystal is assumed to be statistically homogeneous, isotropic, and perfectly disordered. General expressions for averages can then be derived. Many different properties can be averaged, such as dielectric constants, diffusivity, elastic constants, electrical conductivity, magnetic permeability, magnetostriction, piezoelectric constants, thermal conductivity, or thermal expansion. In this paper we treat the elastic constants, which have already received more attention than most other physical properties, and the thermal expansion. Elastic constants are fundamental physical data needed for the characterization of materials. In addition to their fundam...

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“…Liu et al [6] obtained Green's functions for anisotropic magnetoelectroelastic solids containing an elliptical cavity or a crack. Pan and his co-workers presented three dimensional Green's functions in anisotropic magnetoelectroelastic bimaterials [7] and exact solution for 2D polygonal inclusion problem in anisotropic magnetoelectroelastic full-, half-, and bimaterial-planes [8]. Hou and Leung [9] obtained the exact closed-solutions of the coupled field of a spheroidal magnetoelectroelastic inclusion embedded in an infinite magnetoelectroelastic matrix subjected to remote spatially homogeneous mechanical and electromagnetic loadings.…”

Section: Introductionmentioning

confidence: 99%

Integral equation formulations in 2D inhomogeneous magnetoelectroelastic media

Dong¹

2013

Boundary Elements and Other Mesh Reduction Methods XXXVI

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Integral equation formulations for 2D inhomogeneous finite/infinite anisotropic magnetoelectroelastic media are presented. The present formulations only contain the fundamental solutions from the matrix which is taken as a homogeneous anisotropic magnetoelectroelastic medium. Functionally graded linear magnetoelectroelastic inclusions can be considered in which the corresponding fundamental solutions are not needed. In numerical implementation, inclusions are discretized into a series of quadratic quadrilateral or triangular elements, and cracks are meshed into a series of quadratic discontinuous boundary elements. For finite domain, the domain boundaries are discretized into a series of quadratic boundary elements. Finally, the present integral equation method can be used to investigate the interaction between cracks and inclusions in 2D anisotropic magnetoelectroelastic media and to carry out the analysis of effective properties of magnetoelectroelastic media.

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Exact solution for 2D polygonal inclusion problem in anisotropic magnetoelectroelastic full-, half-, and bimaterial-planes

Cited by 69 publications

References 75 publications

Eshelby's problem of polygonal inclusions with polynomial eigenstrains in an anisotropic magneto-electro-elastic full plane

Eshelby's problem of polygonal inclusions with polynomial eigenstrains in an anisotropic magneto-electro-elastic full plane

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Integral equation formulations in 2D inhomogeneous magnetoelectroelastic media

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