The symmetry and loading-independency of multiple inclusions enclosing uniform stresses in an infinite elastic plane
- PDF / 91,565 Bytes
- 4 Pages / 612 x 792 pts (letter) Page_size
- 69 Downloads / 201 Views
APPLIED MATHEMATICS AND MECHANICS (ENGLISH EDITION) https://doi.org/10.1007/s10483-020-2667-7
The symmetry and loading-independency of multiple inclusions enclosing uniform stresses in an infinite elastic plane∗ Ming DAI1 , P. SCHIAVONE2,† 1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China; 2. Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta T6G 1H9, Canada (Received Jun. 5, 2020 / Revised Jul. 22, 2020) 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. Key words
uniform stress, Eshelby’s conjecture, multiple inclusion
Chinese Library Classification O343 2010 Mathematics Subject Classification
1
74B05, 74G45
Introduction
Significant efforts[1–5] have been devoted to the design of multiple (interacting) inclusions, each of which achieves a uniform stress field in the presence of certain uniform remote loadings imposed on the surrounding elastic matrix (or equivalently uniform eigenstrains imposed on the inclusions themselves). Among these inclusions, those with geometric symmetry ( for example, see Figs. 1–3 in Ref. [1], Fig. 2 in Ref. [2], Figs. 2, 3, and 7 in Ref. [3], Figs. 5–8 in Ref. [4], and Figs. 8–13 in Ref. [5]) and those whose shapes can be designed independently of any specific (uniform) external loadings (for example, see Figs. 2–4 in Ref. [3], Figs. 2(a), 2(c), 4(a), 7, and 8 ∗ 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 † Corresponding author, E-mail: [email protected] 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) c The Author(s) 2020
1494
Ming DAI and P. SCHIAVONE
in Ref. [4], and Figs. 3, 6, 9, and 12 in Ref. [5]) are particularly attracti
Data Loading...
