TY - JOUR
T1 - On Field Concentration Between Nearly-Touching Multiscale Inclusions in the Quasi-Static Regime
AU - Deng , Youjun
AU - Kong , Lingzheng
AU - Liu , Hongyu
AU - Zhu , Liyan
JO - Advances in Applied Mathematics and Mechanics
VL - 5
SP - 1252
EP - 1276
PY - 2024
DA - 2024/07
SN - 16
DO - http://doi.org/10.4208/aamm.OA-2023-0104
UR - https://global-sci.org/intro/article_detail/aamm/23293.html
KW - Field concentration, gradient estimates, Helmholtz system, high-contrast inclusions, blow up, quasi-static, multi-scale, curvature.
AB - <p style="text-align: justify;">Strong field concentration may occur between two nearly-touching high-contrast material inclusions due to an incident field. The degree of concentration is
characterised by the blowup rate of the underlying gradient field. This phenomenon
has received considerable attention in the literature due to its practical implications
in the theory of composite materials. However, most of the existing studies are concerned with the static cases. In this paper, we present a comprehensive numerical
investigation of this intriguing phenomenon associated to the Helmholtz system in
the quasi-static frequency regime. On the one hand, we present extensive numerical
results to corroborate the theoretical findings in [16], and on the other hand, we derive new findings that cannot be handled by the theoretical analysis yet. Our focus is
on the static effect, frequency effect, the geometric (curvature) effect to the gradient
estimates.</p>