Anisotropic and dispersive wave propagation within strain-gradient framework

TL;DR

This paper investigates anisotropic and dispersive wave propagation in strain-gradient elasticity, revealing frequency-dependent anisotropy and the importance of distinguishing group and energy velocities in microstructured materials.

Contribution

It introduces a theoretical and numerical analysis of wave behavior in strain-gradient elasticity, highlighting anisotropy and dispersion effects in hexagonal lattices at high frequencies.

Findings

Wave propagation becomes anisotropic at higher frequencies.

Strain-gradient elasticity exhibits dispersive wave behavior.

Group and energy velocities differ in the studied materials.

Abstract

In this paper anisotropic and dispersive wave propagation within linear strain-gradient elasticity is investigated. This analysis reveals significant features of this extended theory of continuum elasticity. First, and contrarily to classical elasticity, wave propagation in hexagonal (chiral or achiral) lattices becomes anisotropic as the frequency increases. Second, since strain-gradient elasticity is dispersive, group and energy velocities have to be treated as different quantities. These points are first theoretically derived, and then numerically experienced on hexagonal chiral and achiral lattices. The use of a continuum model for the description of the high frequency behavior of these microstructured materials can be of great interest in engineering applications, allowing problems with complex geometries to be more easily treated.