Anisotropic effective higher-order response of heterogeneous Cauchy elastic materials

TL;DR

This paper extends homogenization results for heterogeneous Cauchy-elastic materials to include non-isotropic inertia tensors, revealing how local isotropy can coexist with nonlocal orthotropy and how aligned elliptical holes induce orthotropic nonlocal effects.

Contribution

It introduces a generalized homogenization framework accounting for non-isotropic inertia tensors, highlighting the impact on effective higher-order elastic responses.

Findings

Composite can be locally isotropic but nonlocally orthotropic.

Aligned elliptical holes induce orthotropic nonlocal effects.

Nonlocal effects depend on inertia and elastic tensor differences.

Abstract

The homogenization results obtained by Bacca et al. (Homogenization of heterogeneous Cauchy-elastic materials leads to Mindlin second-gradient elasticity. Part I: Closed form expression for the effective higher-order constitutive tensor. arXiv:1305.2365 Submitted, 2013), to define effective second-gradient elastic materials from heterogeneous Cauchy elastic solids, are extended here to the case of phases having non-isotropic tensors of inertia. It is shown that the nonlocal constitutive tensor for the homogenized material depends on both the inertia properties of the RVE and the difference between the effective and the matrix local elastic tensors. Results show that: (i.) a composite material can be designed to result locally isotropic but nonlocally orthotropic; (ii.) orthotropic nonlocal effects are introduced when a dilute distribution of aligned elliptical holes and, in the limit case, of cracks is homogenized.