Rigorous uncertainty quantification and design with uncertain material models

X. Sun, T. Kirchdoerfer, M. Ortiz

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We assess a method of quantification of margins and uncertainties (QMU) in applications where the main source of uncertainty is an imperfect knowledge or characterization of the material behavior. The aim of QMU is to determine adequate design margins given quantified uncertainties and a desired level of confidence in the design. We quantify uncertainties through rigorous probability bounds computed by exercising an existing deterministic code in order to sample the mean response and identify worst-case combinations of parameters. The resulting methodology is non-intrusive and can be wrapped around existing solvers. The use of rigorous probability bounds ensures that the resulting designs are conservative to within a desired level of confidence. We assess the QMU framework by means of an application concerned with sub-ballistic impact of AZ31B Mg alloy plates. We assume the design specification to be a maximum allowable backface deflection of the plate. As a simple scenario, we specifically assume that, under the conditions of interest, the plate is well-characterized by the Johnson-Cook model, but the parameters of the model are uncertain. In calculations, we use the commercial finite-element package LS-Dyna and DAKOTA Version 6.7. The assessment demonstrates the feasibility of the approach and how it results in high-confidence designs that are well-within the practical range of engineering application.

Original languageEnglish
Article number103418
JournalInternational Journal of Impact Engineering
Volume136
DOIs
StatePublished - Feb 2020

Bibliographical note

Funding Information:
We gratefully acknowledge the support of the U. S. Army Research Laboratory ( ARL ) through the Materials in Extreme Dynamic Environments (MEDE) Collaborative Research Alliance (CRA) under Award Number W911NF-11-R-0001 . We are grateful to Jaroslaw Knap, Richard Becker and Jeffrey Lloyd of the ARL at Aberdeen Proving Ground, MD, for useful input and illuminating discussions.

Funding Information:
We gratefully acknowledge the support of the U. S. Army Research Laboratory (ARL) through the Materials in Extreme Dynamic Environments (MEDE) Collaborative Research Alliance (CRA) under Award Number W911NF-11-R-0001. We are grateful to Jaroslaw Knap, Richard Becker and Jeffrey Lloyd of the ARL at Aberdeen Proving Ground, MD, for useful input and illuminating discussions.

Publisher Copyright:
© 2019 Elsevier Ltd

Keywords

  • AZ31B Mg alloy
  • Concentration of measure inequalities
  • Quantification of margins and uncertainities
  • Safe design
  • Sub-ballistic impact
  • Uncertainty quantification

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Automotive Engineering
  • Aerospace Engineering
  • Safety, Risk, Reliability and Quality
  • Ocean Engineering
  • Mechanics of Materials
  • Mechanical Engineering

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