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Anti-plane Circular Nano-inclusion Problem with Electric Field Gradient and Strain Gradient Effects

Shasha Yang, Shengping Shen1

State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, China. Email:

Computers, Materials & Continua 2014, 40(3), 219-239.


As well known, gradient theories can describe size effects that are important in nano-scale problems. In this paper, we analyze the Eshelby-type anti-plane inclusion problem embedded in infinite dielectric body by considering both strain gradient and electric field gradient effects to account for the size effect and high-order electromechanical coupling effect. The size-dependent Eshelby and Eshelby-like tensor, strain, stress, electric field and electric displacement components are derived explicitly by means of Green's function method. Theoretical results indicate that strain and electric field are decoupled for anti-plane inclusion problem while stress field and electric displacement are coupled through strain gradient and electric field gradient. Based on the general form, the expressions for a special case of circular inclusion are obtained analytically. Numerical results reveal that when the inclusion radius becomes small, the gradient effects are significantly important and should not be ignored. The values approach asymptotically to classical solutions as increase of inclusion size. And the high-order electromechanical coupling effect in non-piezoelectric material (centrosymmetric dielectrics) can be equivalent to piezoelectricity of conditional piezoelectric materials when the inclusion size is small.


Cite This Article

S. . Yang and G. . Shen, "Anti-plane circular nano-inclusion problem with electric field gradient and strain gradient effects," Computers, Materials & Continua, vol. 40, no.3, pp. 219–239, 2014.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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