Abstract
We have developed and employed a 3D particle stress tensor and contact force inference technique that employs synchrotron X-ray tomography and diffraction with an optimization algorithm. We have used this technique to study stress and force heterogeneity, particle fracture mechanics, contact-level energy dissipation, and the origin of wave phenomena in 3D granular media for the past five years. Here, we review the technique, describe experimental and numerical sources of uncertainty, and use experimental data and discrete element method simulations to study the method’s accuracy. We find that inferred forces in the strong force network of a 3D granular material are accurately determined even in the presence of noisy stress measurements.
Highlights
We have employed 3D X-ray di↵raction (3DXRD) measurements at various syn-Determining inter-particle forces in 3D, opaque granular materials has been a major pursuit in soft matter physics for decades
Techniques for determining interparticle forces include those leveraging photoelastic discs [1], compliant grains imaged with X-ray tomography [2], intra-particle speckle patterns combined with digital image correlation [3], and sand grains analyzed with X-ray computed tomography (XRCT) and 3D X-ray di↵raction (3DXRD) [4]
We discuss stress and inferred force uncertainties in 3D granular materials studied with XRCT and 3DXRD
Summary
Determining inter-particle forces in 3D, opaque granular materials has been a major pursuit in soft matter physics for decades. The second type of uncertainty arises from algorithms employed in image processing, such as particle segmentation, and data processing These uncertainties bias inter-particle contact point locations and orientations and may lead to the presence of false contacts or absence of true contacts in the force inference procedure. Uncertainties in particle strain tensors arise from the finite resolution of Bragg peaks on X-ray area detectors and the propagation of peak position and magnitude uncertainties through data processing algorithms (ImageD11, heXRD, MIDAS). These stresses are again similar to what would be obtained from directly multiplying nominal sti↵ness tensor components with standard deviations of strain tensor components We note that these uncertainties are very close to quoted uncertainties from the developers of 3DXRD software [14, 15]
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