The Convexity of Inclusions and Gradient’s Concentration for Lamé Systems with Partially Infinite Coefficients
Year: 2024
Author: Yuanyuan Hou, Haigang Li
Analysis in Theory and Applications, Vol. 40 (2024), Iss. 3 : pp. 240–310
Abstract
It is interesting to study the stress concentration between two adjacent stiff inclusions in composite materials, which can be modeled by the Lamé system with partially infinite coefficients. To overcome the difficulty from the lack of maximum principle for elliptic systems, we use the energy method and an iteration technique to study the gradient estimates of the solution. We first find a novel phenomenon that the gradient will not blow up any more once these two adjacent inclusions fail to be locally relatively strictly convex, namely, the top and bottom boundaries of the narrow region are partially “flat”. In order to further explore the blow-up mechanism of the gradient, we next investigate two adjacent inclusions with relative convexity of order m and finally reveal an underlying relationship between the blow-up rate of the stress and the order of the relative convexity of the subdomains in all dimensions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-2023-0019
Analysis in Theory and Applications, Vol. 40 (2024), Iss. 3 : pp. 240–310
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 71
Keywords: Gradient estimates convex inclusions blowup analysis linear elasticity composite materials.
Author Details
Yuanyuan Hou Email
Haigang Li Email