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Micromechanical investigation of thermal stresses of a finite plane containing multiple elliptical inclusions based on the equivalent inclusion method and distributed dislocation method

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Abstract

This paper presents a micromechanical method to analyze the thermal stresses in a finite plane containing multiple elliptical inclusions. Firstly, the Eshelby’s equivalent inclusion method is employed to solve the elastic fields of a two-dimensional infinite plane containing multiple elliptical inclusions under a uniform temperature change. Both the interior Eshelby’s tensor and the exterior Eshelby’s tensor are employed. Then the boundary of the plane is modeled by continuous distributions of dislocation densities. By combining the two steps, a system of singular integral equations is formulated based on the traction-free boundary condition. Then the thermal stresses of the plane can be obtained by the superposition of the stresses obtained by the Eshelby’s equivalent inclusion method and distributed dislocation method. Additionally, some examples are given to show the effects of the presented method. The effects of the material constants, geometric parameters and fiber packing arrangement on the thermal stresses are also studied.

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Abbreviations

N inc :

Number of inclusions

α :

Thermal expansion

μ :

Shear moduli

ν :

Poisson’s ratio

κ :

Kolosov’s constant

ϕ :

Orientation angle of the inclusion

a,c :

Two semi-axes of the inclusion

N b :

Number of the boundary crack segments

σ ΔT :

Stresses induced by the temperature change

σ Dislocation :

Stresses induced by the dislocations

σ p kl :

Strain induced by the temperature change

σ * kl :

Eigenstrain strain

S ijkl :

Interior Eshelby’s tensor

G ijkl :

Exterior Eshelby’s tensor

C ijkl :

Elastic modules of the matrix

C ijkl′:

Elastic modules of the inclusion

G ijkl :

Stress influence function

b x, b y :

Burgers vector

B x, B y :

Density functions for the dislocations

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Acknowledgments

This work was financially supported by National Natural Science Foundation of China (No. 51802229 and No. 41702323) and Natural Science Foundation of Guangdong Province (No. 2018A030313430 and No. 2018A030313561) and Innovation and Strong School Engineering Foundation of Guangdong Province (No. 2017KQNCX201, No. 2017KQNCX186, No. 2016 KQNCX169 and No. 2018KZDXM072).

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Authors and Affiliations

  1. School of Civil Engineering and Architecture, Wuyi University, 22 Dongcheng Village, Jiangmen, 529020, China

    Jiong Zhang, Yunhai Huang, Liankun Wang & Chao Yang

  2. College of Energy and Electrical Engineering, Hohai University, No. 8 Fochengxi Road, Nanjing, 211100, China

    Weidong Liu

  3. Department of Sports, Wuyi University, 22 Dongcheng Village, Jiangmen, 529020, China

    Lin Zuo

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  1. Jiong Zhang
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  2. Yunhai Huang
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  4. Liankun Wang
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  5. Chao Yang
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  6. Lin Zuo
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Corresponding author

Correspondence to Lin Zuo.

Additional information

Lin Zuo is a Professor of Department of Sports at Wuyi University. His research interests include movement mechanics, solid mechanics and finite element analysis.

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Zhang, J., Huang, Y., Liu, W. et al. Micromechanical investigation of thermal stresses of a finite plane containing multiple elliptical inclusions based on the equivalent inclusion method and distributed dislocation method. J Mech Sci Technol 35, 247–256 (2021). https://doi.org/10.1007/s12206-020-1224-y

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