On Anomalous Localized Resonance for the Elastostatic System

Abstract

We consider the anomalous localized resonance due to a plasmonic structure for the elastostatic system in $\mathbb{R}^2$. The plasmonic structure takes a general core-shell-matrix form with the metamaterial located in the shell. If there is no core, we show that resonance occurs for a very broad class of sources. If the core is nonempty and of an arbitrary shape, we show that there exists a critical radius such that resonance occurs for a certain class of sources lying within the critical radius, whereas resonance does not occur for a certain class of sources lying outside the critical radius. Our argument is based on a variational technique by making use of the primal and dual variational principles for the elastostatic system, along with the construction of suitable test functions.