Abstract
The identification of multiple interacting inclusions with uniform internal stresses in an infinite elastic matrix subjected to a uniform remote loading is of fundamental importance in the mechanics and design of particulate composite materials. In anti-plane shear and plane deformations, certain sufficient conditions have been established in the literature which guarantee uniform internal stresses inside multiple interacting inclusions displaying various symmetries when the matrix is subjected to specific uniform remote loading. Correspondingly, sufficient conditions which allow for the design of multiple interacting inclusions independent of any specific form of (uniform) remote loading have also been established. In this paper, we demonstrate rigorously that, in all cases, these sufficient conditions are also necessary conditions and indeed allow for the identification of all possible collections of such inclusions.
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Citation: DAI, M. and SCHIAVONE, P. The symmetry and loading-independency of multiple inclusions enclosing uniform stresses in an infinite elastic plane. Applied Mathematics and Mechanics (English Edition) 41(10), 1493–1496 (2020) https://doi.org/10.1007/s10483-020-2667-7
Project supported by the National Natural Science Foundation of China (Nos. 11902147, 11872203, and 51921003), the Natural Science Foundation of Jiangsu Province of China (No. BK20190393), and the Natural Sciences and Engineering Research Council of Canada (No.RGPIN–2017-03716115112)
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Dai, M., Schiavone, P. The symmetry and loading-independency of multiple inclusions enclosing uniform stresses in an infinite elastic plane. Appl. Math. Mech.-Engl. Ed. 41, 1493–1496 (2020). https://doi.org/10.1007/s10483-020-2667-7
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DOI: https://doi.org/10.1007/s10483-020-2667-7