Scattering, Trapping and Cloaking-Type Effects of Plane Waves by Point Scatterers in Strain Gradient Elasticity

Wave scattering by localized constraints in microstructured solids is strongly influenced by the interplay of material length scales, dispersion and geometry.

This work investigates plane-strain scattering of time-harmonic P and SV waves by clusters of rigid point constraints embedded in an infinite strain gradient elastic medium.

A closed-form dynamic Green's tensor is derived for the plane-strain problem.

Unlike the classical elastodynamic Green's tensor, the strain gradient Green's tensor remains bounded at the source, enabling point constraints to be introduced directly through superposition of fundamental solutions.

The multiple-scattering problem is reduced to a finite-dimensional algebraic system for the pin reaction amplitudes.

A frequency-domain procedure is developed to identify resonance-like amplification and trapping.

Candidate resonant frequencies are associated with local minima of the Green matrix determinant, while higher-order curvature criteria distinguish trapping-dominated resonances from non-localized scattering responses.

The results show that the response is governed primarily by the ratio of the microinertial and energetic strain gradient lengths.

In the anomalous dispersion regime, sharp resonances produce strong displacement localization, including perimeter-localized trapping modes in dense circular arrays.

In the normal dispersion regime, these resonances are strongly attenuated and the pins behave as weak scatterers, producing a cloaking-type response in which the incident field is only weakly perturbed.

The influence of Poisson's ratio, incidence angle and compound pin configurations is also examined, demonstrating how intrinsic material lengths and geometric arrangement can be used to tune scattering, trapping and wave-screening mechanisms in microstructured elastic media.