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Research Papers

Proper Orthogonal Decomposition–Radial Basis Function Surrogate Model-Based Inverse Analysis for Identifying Nonlinear Burgers Model Parameters From Nanoindentation Data

[+] Author and Article Information
Salah U. Hamim

Advanced Development Engineering,
Fiat Chrysler Automobiles,
Auburn Hills, MI 48326

Raman P. Singh

School of Mechanical and
Aerospace Engineering,
Oklahoma State University,
Stillwater, OK 74078
e-mail: raman.singh@okstate.edu

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received August 12, 2016; final manuscript received May 10, 2017; published online July 6, 2017. Assoc. Editor: Curt Bronkhorst.

J. Eng. Mater. Technol 139(4), 041010 (Jul 06, 2017) (8 pages) Paper No: MATS-16-1228; doi: 10.1115/1.4037022 History: Received August 12, 2016; Revised May 10, 2017

This study explores the application of a proper orthogonal decomposition (POD) and radial basis function (RBF)-based surrogate model to identify the parameters of a nonlinear viscoelastic material model using nanoindentation data. The inverse problem is solved by reducing the difference between finite element simulation-trained surrogate model approximation and experimental data through genetic algorithm (GA)-based optimization. The surrogate model, created using POD–RBF, is trained using finite element (FE) data obtained by varying model parameters within a parametric space. Sensitivity of the model parameters toward the load–displacement output is utilized to reduce the number of training points required for surrogate model training. The effect of friction on simulated load–displacement data is also analyzed. For the obtained model parameter set, the simulated output matches well with experimental data for various experimental conditions.

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Figures

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Fig. 1

abaqus finite element model

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Fig. 2

Nonlinear Burgers model

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Fig. 3

Effect of the friction coefficient f on nanoindentation data for different loading–unloading times and constant maximum loads (difference = depth for frictionless—depth for f = 0.125/0.25/0.5)

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Fig. 4

Effect of the friction coefficient f on nanoindentation data for different maximum loads and constant loading–unloading times (difference = depth for frictionless—depth for f = 0.125/0.25/0.5)

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Fig. 5

Output sensitivity toward different nonlinear Burgers model parameters

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Fig. 6

Experiment versus surrogate model for calibrated nonlinear Burgers model parameters: load time, t = 30 s (a), 45 s (b), 60 s (c), and 240 s (d)

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Fig. 7

Experiment versus finite element simulation for calibrated nonlinear Burgers model parameters: load time, t = 30 s (a), 45 s (b), 30 s (c), and 45 s (d)

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