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

Area of Science:

• Experimental Mechanics
• Material Science
• Image Analysis

Background:

• Digital image correlation (DIC) faces challenges in measuring large material deformation and rotation due to errors, especially near boundaries.
• Accurate displacement measurements are crucial for understanding material behavior under extreme conditions.

Purpose of the Study:

• To develop a method for accurately measuring the deformation gradient tensor near boundary discontinuities during large deformations.
• To address limitations of existing techniques in capturing complex material responses.

Main Methods:

• Utilized open-source particle tracking software (Trackpy) to monitor particle movement.
• Employed a least-squares estimation with nearest-neighbor vectors and Finite Difference (FD) approximation for the deformation gradient tensor.
• Validated the approach through numerical simulations and physical experiments, including tensile and fracture tests on hydrogels.

Main Results:

• Numerical simulations confirmed theoretical error bounds and demonstrated the trade-off between FD and measurement errors with increasing estimation radius.
• Experimental validation showed accurate measurements of large deformation and rotation near free surfaces, outperforming traditional DIC in specific scenarios.
• The proposed method showed comparable accuracy to Ncorr for displacement and strain data, with variations in computation time.

Conclusions:

• A novel deformation gradient tensor estimator based on particle tracking and least squares was successfully developed and validated.
• The method accurately quantifies large deformations and rotations near boundaries, offering an advancement for experimental mechanics.
• This technique is poised to benefit future material testing and experimental studies involving significant deformation and rotation.