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Solutions of the elastic fields in a half-plane region containing multiple inhomogeneities with the equivalent inclusion method and the applications to properties of composites

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Abstract

This paper presents a solution of the elastic fields of a half-plane composite structure containing distributed multiple circular inhomogeneities under boundary loading. The solution is obtained with a semi-analytical approach by combining the Green’s function and the equivalent inclusion method. This approach can achieve high accuracy and can be easily implemented with less computational effort compared with other numerical methods. Then, this solution is further used to explore the boundary effects on the elastic fields and effective elastic properties of the half-plane composite structure containing square periodically distributed circular inhomogeneities. Influences of the boundary and the inhomogeneity volume fraction on the elastic fields are examined in detail. Local effective elastic constants of the composite structure are predicted using the unit cells. The results show that the boundary has a significant effect on the elastic fields and elastic properties of the half-plane composite structure. The average displacement predicted with the conventional effective elastic constants of unit cells may deviate from the real value. Thus, we propose a design of a composite structure with a uniform elastic constant and develop an analytical model to calculate the average displacement.

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Acknowledgements

X. Dang, L. J. Wang and J. Wang thank the support of the National Natural Science Foundation of China under Grant Nos. 11872075 and 11521202.

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Authors and Affiliations

  1. State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing, 100871, China

    Xiangxin Dang, Linjuan Wang & Jianxiang Wang

  2. Department of Civil and Environmental Engineering, Duke University, Durham, NC, 27708, USA

    Yingjie Liu

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  1. Xiangxin Dang
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Dang, X., Liu, Y., Wang, L. et al. Solutions of the elastic fields in a half-plane region containing multiple inhomogeneities with the equivalent inclusion method and the applications to properties of composites. Acta Mech 230, 1529–1547 (2019). https://doi.org/10.1007/s00707-018-2340-y

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