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  4. Estimation of the Deformation Gradient Tensor by Particle Tracking Near a Free Boundary with Quantified Error
 
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research article

Estimation of the Deformation Gradient Tensor by Particle Tracking Near a Free Boundary with Quantified Error

Benkley, T.
•
Li, C.  
•
Kolinski, J.
August 11, 2023
Experimental Mechanics

BackgroundObtaining accurate displacement measurements for large material deformation and/or rotation presents a distinct challenge to digital image correlation (DIC) due to cumulative and decorrelation errors, particularly near material boundaries.ObjectiveWe aim to accurately measure the deformation gradient tensor near boundary discontinuities in situations of large deformation and large deformation gradients.MethodsTo achieve this goal, the locations of randomly distributed particles are tracked using an open-source particle-tracking software, Trackpy. A least-squares estimate of the deformation gradient tensor field uses nearest-neighbor material vectors and a first-order Finite Difference (FD) approximation, circumventing common errors in other methods. The error caused by FD approximation and that incurred by measurement are derived and tested with exhaustive numerical simulations. Furthermore, a uniaxial tensile test and mode-I fracture experiment are conducted with particle-embedded hydrogels to validate the method.ResultsNumerical results corroborate a theoretical expression of measurement error. They show that the FD error increases while the measurement error decreases for a growing estimating radius. Moreover, measurement error is linearly correlated to displacement noise. A benchmark uniaxial tensile test validates the accuracy of the proposed estimator, and the near-crack-tip measurements in a tensile fracture experiment demonstrate the estimator's capabilities near a free surface, when a material undergoes large deformation and rotation. The results of the displacement and strain data are benchmarked against kinematic data obtained using an open-source DIC software, Ncorr. Computation time for both methods is compared.ConclusionsA deformation gradient tensor estimator is developed based on a particle tracking technique and a least squares routine. Theoretical error bounds on the estimator are verified by numerical simulations, and the method's capability is confirmed by physical experiments in evaluating large deformation and rotation near a free boundary. The proposed estimator is expected to open a door towards future material tests and experimental mechanics studies, especially in large deformation and large rotation scenarios.

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Type
research article
DOI
10.1007/s11340-023-00981-8
Web of Science ID

WOS:001046553400002

Author(s)
Benkley, T.
•
Li, C.  
•
Kolinski, J.
Date Issued

2023-08-11

Publisher

SPRINGER

Published in
Experimental Mechanics
Subjects

Materials Science, Multidisciplinary

•

Mechanics

•

Materials Science, Characterization & Testing

•

Materials Science

•

deformation gradient tensor

•

particle tracking

•

error quantification

•

fracture mechanics

•

digital image correlation

•

velocimetry

•

displacement

•

interferometry

•

fields

Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
LMR  
Available on Infoscience
August 28, 2023
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/200102
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