Identification of higher-order continua equivalent to a Cauchy elastic composite

TL;DR

This paper introduces a new method to identify higher-order elastic continua equivalent to heterogeneous Cauchy materials, combining the accuracy of asymptotic homogenization with the simplicity of identification techniques.

Contribution

A novel identification strategy for second-gradient Mindlin solids that balances asymptotic accuracy with practical simplicity.

Findings

The proposed method yields reasonably accurate results.

Perturbation functions are evaluated on finite, periodically repeated domains.

The approach effectively approximates the behavior of complex heterogeneous materials.

Abstract

A heterogeneous Cauchy elastic material may display micromechanical effects that can be modeled in a homogeneous equivalent material through the introduction of higher-order elastic continua. Asymptotic homogenization techniques provide an elegant and rigorous route to the evaluation of equivalent higher-order materials, but are often of difficult and awkward practical implementation. On the other hand, identification techniques, though relying on simplifying assumptions, are of straightforward use. A novel strategy for the identification of equivalent second-gradient Mindlin solids is proposed in an attempt to combine the accuracy of asymptotic techniques with the simplicity of identification approaches. Following the asymptotic homogenization scheme, the overall behaviour is defined via perturbation functions, which (differently from the asymptotic scheme) are evaluated on a finite domain obtained as the periodic repetition of cells and subject to quadratic displacement boundary conditions. As a consequence, the periodicity of the perturbation function is satisfied only in an approximate sense, nevertheless results from the proposed identification algorithm are shown to be reasonably accurate.