On the validity range of strain-gradient elasticity: a mixed static-dynamic identification procedure

TL;DR

This paper demonstrates that strain-gradient elasticity effectively models wave dispersion in microstructured materials, with a broad validity range that surpasses classical homogenization, validated through static-dynamic identification and finite element comparisons.

Contribution

It introduces a mixed static-dynamic identification procedure to determine strain-gradient parameters, extending the model's validity for wave propagation in microstructured solids.

Findings

Strain-gradient elasticity accurately describes wave behavior over a wider frequency range.

The model outperforms classical homogenization in capturing dispersion effects.

Validation against finite element simulations confirms the model's practical applicability.

Abstract

Wave propagation in architectured materials, or materials with microstructure, is known to be dependent on the ratio between the wavelength and a characteristic size of the microstructure. Indeed, when this ratio decreases (i.e. when the wavelength approaches this characteristic size) important quantities, such as phase and group velocity, deviate considerably from their low frequency/long wavelength values. This well-known phenomenon is called dispersion of waves. Objective of this work is to show that strain-gradient elasticity can be used to quantitatively describe the behaviour of a microstructured solid, and that the validity domain (in terms of frequency and wavelength) of this model is sufficiently large to be useful in practical applications. To this end, the parameters of the overall continuum are identified for a periodic architectured material, and the results of a transient problem are compared to those obtained from a finite element full field computation on the real geometry. The quality of the overall description using a strain-gradient elastic continuum is compared to the classical homogenization procedure that uses Cauchy continuum. The extended model of elasticity is shown to provide a good approximation of the real solution over a wider frequency range.