Hierarchical multiscale quantification of material uncertainty

TL;DR

This paper introduces a hierarchical multiscale approach to quantify material uncertainty efficiently by bounding uncertainties at each scale and combining them, avoiding costly integral calculations, demonstrated on magnesium ballistic impact.

Contribution

The paper presents a novel hierarchical method to bound overall material uncertainty across scales without expensive integral computations.

Findings

Bounded uncertainty at each scale improves understanding of material behavior.

The approach provides conservative estimates of overall uncertainty.

Demonstrated on magnesium impact, relevant for lightweight materials.

Abstract

The macroscopic behavior of many materials is complex and the end result of mechanisms that operate across a broad range of disparate scales. An imperfect knowledge of material behavior across scales is a source of epistemic uncertainty of the overall material behavior. However, assessing this uncertainty is difficult due to the complex nature of material response and the prohibitive computational cost of integral calculations. In this paper, we exploit the multiscale and hierarchical nature of material response to develop an approach to quantify the overall uncertainty of material response without the need for integral calculations. Specifically, we bound the uncertainty at each scale and then combine the partial uncertainties in a way that provides a bound on the overall or integral uncertainty. The bound provides a conservative estimate on the uncertainty. Importantly, this approach does not require integral calculations that are prohibitively expensive. We demonstrate the framework on the problem of ballistic impact of a polycrystalline magnesium plate. Magnesium and its alloys are of current interest as promising light-weight structural and protective materials. Finally, we remark that the approach can also be used to study the sensitivity of the overall response to particular mechanisms at lower scales in a materials-by-design approach.