# Averaging of elastic constants for polycrystals

## TL;DR

This paper reviews methods for calculating effective isotropic elastic constants of polycrystals from single crystal data, highlighting challenges especially in averaging third order elastic constants and discussing theoretical shortcomings.

## Contribution

It provides a critical review of existing averaging strategies for elastic constants, emphasizing the need to address theoretical limitations, particularly for third order constants.

## Key findings

- Averaging of second order elastic constants is well-established.
- Third order elastic constants are difficult to average accurately.
- Discrepancies may stem from both texturing and theoretical shortcomings.

## Abstract

Many materials of interest are polycrystals, i.e. aggregates of single crystals. Randomly distributed orientations of single crystals lead to macroscopically isotropic properties. Here, we briefly review strategies of calculating effective isotropic second and third order elastic constants from the single crystal ones. Our main emphasize is on single crystals of cubic symmetry. Especially the averaging of third order elastic constants has not been particularly successful in the past, and discrepancies have often been attributed to texturing of the polycrystal as well as to uncertainties in the measurement of elastic constants of both poly and single crystals. While this may well be true, we point out here also shortcomings in the theoretical averaging framework.