Elastic properties of solid material with various arrangements of spherical voids

TL;DR

This study uses finite element simulations to analyze how different arrangements and fractions of spherical voids affect the elastic properties of solid materials, providing detailed quantitative comparisons and insights into anisotropic behaviors.

Contribution

It offers a comprehensive finite element analysis of elastic properties across various void arrangements and fractions, including connected voids and anisotropic effects, with detailed data for future research.

Findings

Young's modulus varies significantly with void arrangement and orientation.

FCC and HCP structures show notable differences in elastic response.

Poisson ratios can exceed isotropic bounds depending on void structure.

Abstract

In this work the linear elastic properties of materials containing spherical voids are calculated and compared using finite element simulations. The focus is on homogeneous solid materials with spherical, empty voids of equal size. The voids are arranged on crystalline lattices (SC, BCC, FCC and HCP structure) or randomly, and may overlap in order to produce connected voids. In that way, the entire range of void fraction between 0.00 and 0.95 is covered, including closed-cell and open-cell structures. For each arrangement of voids and for different void fractions the full stiffness tensor is computed. From this, the Young's modulus and Poisson ratios are derived for different orientations. Special care is taken of assessing and reducing the numerical uncertainty of the method. In that way, a reliable quantitative comparison of different void structures is carried out. Among other things, this work shows that the Young's modulus of FCC in the (1 1 1) plane differs from HCP in the (0 0 0 1) plane, even though these structures are very similar. For a given void fraction SC offers the highest and the lowest Young's modulus depending on the direction. For BCC at a critical void fraction a switch of the elastic behaviour is found, as regards the direction in which the Young's modulus is maximised. For certain crystalline void arrangements and certain directions Poisson ratios between 0 and 1 were found, including values that exceed the bounds for isotropic materials. For subsequent investigations the full stiffness tensor for a range of void arrangements and void fractions are provided in the supplemental material.