# Stochastic mechanical modeling of metallic foams to determine onset of mesoscale behavior

## TL;DR

This paper develops a stochastic modeling approach to identify the transition from feature-scale to mesoscale behavior in metallic foams, enabling better prediction of their mechanical properties and response to hypervelocity impacts.

## Contribution

It introduces the Kentucky Random Structure Toolkit (KRaSTk) to determine the feature-to-mesoscale transition in metallic foams, validated against experimental data.

## Key findings

- Transition occurs when sample size is ~10x characteristic length.
- KRaSTk predictions match experimental stiffness distributions.
- Impact features are ~30x smaller than the feature-to-mesoscale transition.

## Abstract

Metallic foams are crucial to many emerging applications, among them shielding against hypervelocity impacts caused by micrometeoroids and orbital debris. The variability of properties at feature-scale and mesoscale lengths originating from the foam's inherently random microstructure makes predictive models of their properties challenging. It also hinders the optimization of components fabricated with such foams, an especially serious problem for spacecraft design where the balance between cost and mass must also be balanced against the catastrophic results of component failure. To address this problem, we compute the critical transition length between the feature-scale, where mechanical properties are determined by individual features, and the mesoscale, where behavior is determined by ensembles of features. At the mesoscale, distributions of properties -- with respect to both expectation value and standard variability -- are consistent and predictable. The Kentucky Random Structure Toolkit (KRaSTk) is applied to determine the transition from feature-scale to mesoscale for computational volumes representing metallic foams at a range of reduced densities. The transition is found to occur when the side length of a cubic sample volume is ~10x greater than the characteristic length. Comparing KRaSTk-computed converged stiffness distributions with experimental measurements of a commercial metallic foam found excellent agreement for both expectation value and standard variability at all reduced densities. Lastly, we observe that the diameter of a representative MMOD strike is ~30x shorter than the feature-scale to mesoscale transition for the foam at any reduced density. Therefore, features will determine response to hypervelocity impacts, rather than bulk (or even mesoscale) structure.