Self-consistent homogenization approach for polycrystals within second gradient elasticity

TL;DR

This paper introduces a generalized self-consistent homogenization method for polycrystals within second-gradient elasticity, accounting for grain shape and orientation to predict effective elastic moduli.

Contribution

It extends Kröner's scheme using Eshelby's inclusion method to evaluate both standard and gradient elastic properties considering grain shape and orientation.

Findings

Predicts absence of strong gradient effects for spherical grains.

Derives nonlinear relations for effective moduli with non-spherical grains.

Provides a framework for more accurate modeling of polycrystalline materials.

Abstract

In this paper, we propose a generalized variant of Kr\"oner's self-consistent scheme for evaluation of the effective standard and gradient elastic moduli of polycrystalline materials within Mindlin-Toupin second-gradient elasticity theory. Assuming random orientation of crystallites (grains) we use an extended Eshelby's equivalent inclusion method and mapping conditions between the prescribed linear distribution of macro-strain and corresponding micro-scale field variables averaged over the volume and all possible orientations of single grain. It is found that developed self-consistent scheme predicts the absence of strong gradient effects at the macro-scale level for the model of spherical grains. However, for the more general shape of the grains, considered approach allows to obtain a set of non-linear relations for determination of all effective standard and gradient elastic moduli of polycrystals.