General solution for transversely isotropic magneto-electro-thermo-elasticity and the potential theory method

Chen, W.Q; Lee, Kang Yong; Ding, Hu

doi:10.1016/j.ijengsci.2004.04.002

Cited by 168 publications

(127 citation statements)

References 38 publications

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“…The fracture behavior of two 3D rectangular cracks has not yet been studied in an orthotropic elastic media in the open literature. The process and method in the present paper are quite different from those literatures as mentioned above [6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 83%

Basic solution of two 3D rectangular cracks in an orthotropic elastic media

Liu

Zhou

2014

Z Angew Math Mech

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Key words Mechanics of solids, orthotropic elastic media, two rectangular cracks, the stress intensity factors.By using the generalized Almansi's theorem and the Schmidt method, the solution of two 3D rectangular cracks in an orthotropic elastic media is investigated. The problems are solved through 2D Fourier transform as three pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. To solve the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. The effects of the geometric shape of the rectangular crack and the distance between two rectangular cracks on the stress intensity factors (SIFs) in an orthotropic elastic media are concluded.

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Section: Introductionmentioning

confidence: 83%

Basic solution of two 3D rectangular cracks in an orthotropic elastic media

Liu

Zhou

2014

Z Angew Math Mech

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“…The governing equations (5) need to be simplified by introducing displacement potential functions as discussed in reference [13] . Let …”

Section: Solution Proceduresmentioning

confidence: 99%

Analytical Solution for Dynamic Fracture of Two Coplanar Limited-Permeable Cracks in Magneto-Electro-Elastic Material

Zhang¹

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. Two coplanar limited-permeable rectangular cracks in magneto-electro-elastic material are modeled and solved using generalized Almansi's theorem. The mixed boundary value problem is formulated into three pairs of dual integral equations with the help of Fourier transform, in which the unknown functions are the jumps of displacements across the crack-surface. By directly expanding the unknown functions into infinite series form of Jacobi polynomials, the dual integral equations are solved, and the analytical expressions of generalized intensity factors are derived strictly. Based on the generalized intensity factors, the dynamic behaviors of two cracks are estimated under P-wave loads. To show the trends of effects of loading frequency and geometry of cracks on the generalized intensity factors, top finite terms of infinite series are numerically calculated based on the Schmidt method. Numerical results are then drawn graphically. It reveals that the trend of two cracks forming a larger crack by propagating depends strongly on crack geometry and load frequency. This work illuminate the condition inducing different crack propagation patterns, which will benifit the forecast of damage forms of transversely isotropic magneto-electro-elastic material.

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“…Although it sounds theoretically more reasonable, experiment based verification is still desired. It is mentioned here that mono-harmonic potential functions can be found in Chen et al (2004), but some simpler results, obtained by the author of this paper, are presented for the reader's convenience.…”

Section: Introductionmentioning

confidence: 99%

Green’s function for a multifield material with a heat source

Rogowski¹

2016

jtam

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Green's functions for a multifield material subjected to a point heat source are presented in an explicit analytical form. The study concerns the steady-state thermal loading infinite region, half-space region and two-constituent magneto-electro-thermo-elastic material region. The new mono-harmonic potential functions, obtained by the author, are used in the analysis. The elastic displacement, electric potential, magnetic potential and induced by those coupled multifield physical quantities, caused by internal or external heat sources, are limited and presented in a very useful form, exactly and explicitly.

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General solution for transversely isotropic magneto-electro-thermo-elasticity and the potential theory method

Cited by 168 publications

References 38 publications

Basic solution of two 3D rectangular cracks in an orthotropic elastic media

Basic solution of two 3D rectangular cracks in an orthotropic elastic media

Analytical Solution for Dynamic Fracture of Two Coplanar Limited-Permeable Cracks in Magneto-Electro-Elastic Material

Green’s function for a multifield material with a heat source

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