Estimating mechanical properties from spherical indentation using Bayesian approaches

Patxi Fernandez-Zelaia, V. Roshan Joseph, Surya R. Kalidindi, Shreyes N. Melkote

Research output: Contribution to journalArticlepeer-review

68 Scopus citations

Abstract

Instrumented indentation enables rapid characterization of mechanical behavior in small material volumes. The heterogeneous deformation fields beneath the indenter however make it difficult to infer the intrinsic constitutive properties (e.g., Young's modulus, yield strength). This inverse problem is addressed in the literature using optimization techniques that are generally unable to yield robust values for the properties of interest and cannot quantify property uncertainty. Furthermore, current approaches tend to exhibit very high sensitivity to the error definitions and the optimization techniques employed. In order to overcome these difficulties, we propose an alternate approach that involves two main steps: (i) Development of a Gaussian Process (or kriging) surrogate model using finite element models of spherical indentation, and (ii) inverse solution using a Bayesian framework and Markov Chain Monte Carlo sampling. These approaches are demonstrated using selected case studies.

Original languageEnglish
Pages (from-to)92-105
Number of pages14
JournalMaterials and Design
Volume147
DOIs
StatePublished - Jun 5 2018
Externally publishedYes

Funding

The authors would like to thank Georgia Tech's Partnership for an Advanced Computing Environment (PACE) for providing the resources and support to run the FEA models. Financial support of the work by the Morris M. Bryan, Jr. Professorship of the fourth author is also acknowledged. The third author wishes to acknowledge support from NSF award 1435237. The authors would like to thank Georgia Tech's Partnership for an Advanced Computing Environment (PACE) for providing the resources and support to run the FEA models. Financial support of the work by the Morris M. Bryan, Jr. Professorship of the fourth author is also acknowledged. The third author wishes to acknowledge support from NSF award 1435237 .

Keywords

  • Constitutive properties
  • Finite element surrogate modeling
  • Gaussian process modeling
  • Instrumented indentation
  • Kriging

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