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Hierarchical multiscale quantification of material uncertainty

Liu, Burigede and Sun, Xingsheng and Bhattacharya, Kaushik and Ortiz, Michael (2021) Hierarchical multiscale quantification of material uncertainty. Journal of the Mechanics and Physics of Solids, 153 . Art. No. 104492. ISSN 0022-5096. doi:10.1016/j.jmps.2021.104492.

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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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Liu, Burigede0000-0002-6518-3368
Bhattacharya, Kaushik0000-0003-2908-5469
Ortiz, Michael0000-0001-5877-4824
Additional Information:© 2021 Elsevier Ltd. Received 4 February 2021, Revised 26 April 2021, Accepted 8 May 2021, Available online 21 May 2021. We are grateful to Dennis Kochmann for making available to us the single-crystal and Taylor averaging codes used in this work to generate data. This research was sponsored by the Army Research Laboratory and was accomplished, United States under Cooperative Agreement Number W911NF-12-2-0022. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Funding AgencyGrant Number
Army Research LaboratoryW911NF-12-2-0022
Subject Keywords:Material uncertainty; Multiscale modeling; Rigorous uncertainty quantification; Materials-by-design
Record Number:CaltechAUTHORS:20210225-132735184
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Official Citation:Burigede Liu, Xingsheng Sun, Kaushik Bhattacharya, Michael Ortiz, Hierarchical multiscale quantification of material uncertainty, Journal of the Mechanics and Physics of Solids, Volume 153, 2021, 104492, ISSN 0022-5096, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108209
Deposited By: George Porter
Deposited On:26 Feb 2021 15:06
Last Modified:26 May 2021 16:58

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