Papers in Physics, vol. 14, art. 140003 (2022) Received: 3 January 2022, Accepted: 2 February 2022 Edited by: K. Daniels, L. A. Pugnaloni, J. Zhao Licence: Creative Commons Attribution 4.0 DOI: https://doi.org/10.4279/PIP.140003 www.papersinphysics.org ISSN 1852-4249 Challenges and opportunities in measuring time-resolved force chain evolution in 3D granular materials Ryan C. Hurley1,2∗, Chongpu Zhai3† Granular materials are found throughout nature and industry: in landslides, avalanches, and river beds, and also in pharmaceutics, food, and mineral processing. Many behaviors of these materials, including the ways in which they pack, deform, flow, and transmit energy, can be fully understood only in the context of inter-particle forces. However, we lack techniques for measuring 3D inter-particle force evolution at subsecond timescales due to technological limitations. Measurements of 3D force chain evolution at subsecond timescales would help validate and extend theories and models that explicitly or implic- itly consider force chain dynamics in their predictions. Here, we discuss open challenges associated with force chain evolution on these timescales, challenges limiting such mea- surements, and possible routes for overcoming these challenges in the coming decade. I Introduction Granular materials play prominent roles in land- slides, avalanches, earthquakes, and river-bed mass transport, as well as in the pharmaceutical, food, and mineral processing industries [1–3]. The statis- tics, fluctuations, and organization of force chains – inter-particle forces with magnitudes greater than the average in a cohesion-less material – have been linked to: material stresses [4]; electrical and me- chanical energy transport [5–8]; mechanical failure via particle fracture and inter-particle slip [9, 10]; mechanical failure of confining vessels due to stress ∗rhurley6@jhu.edu †zhaichongpu@xjtu.edu.cn 1 Mechanical Engineering, Johns Hopkins University, Bal- timore, MD 21218, USA. 2 Hopkins Extreme Materials Institute, Johns Hopkins University, Baltimore, MD 21218, USA. 3 Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong Univer- sity, Xi’an, 710049 China. concentrations [11]; stick-slip on granular fault gouge [12]; hot spot formation during compaction of energetic powders [13]; the dynamics of intrud- ers penetrating granular beds [14]. However, mea- suring time-resolved 3D force chain evolution at timescales relevant to these and other applications remains a challenge due to technological limita- tions and the difficulty of such experiments. Here, we therefore summarize several open challenges re- lated to dynamic force chain evolution at subsecond timescales, describe the challenges associated with such measurements, and propose possible routes for overcoming these challenges in the coming decade. i A brief history of force measurements Researchers have pursued techniques to measure inter-particle forces in granular media since at least the 1970s [19]. Both 2D and 3D methods have been developed. 2D methods using photoelastic and rub- ber discs have been most commonly used [20, 21], as described in depth in several recent review arti- cles [22, 23]. Such methods must employ 2D grains that are more compliant and possess slower wave 140003-1 Papers in Physics, vol. 14, art. 140003 (2022) / R. C. Hurley et al. speeds than grains in many natural and industrial applications of granular materials. While the com- pliant nature of photoelastic grains may alter the interactions of grains relative to their natural coun- terparts, the slower wave speeds have a benefit: the ratio of compaction wave speed to loading veloc- ity in photoelastic granular matter may be similar to that in dynamically-loaded natural sands even when the loading velocity in the photoelastic case is significantly slower. This change in the timescales of information flow allows comparable dynamic pro- cesses, such as penetration, to be imaged at sig- nificantly reduced frame rates in 2D photoelastic granular matter as compared to 3D natural granu- lar matter [14]. Despite the differences in compliance, wave speeds, and dimensionality, 2D photoelasticity studies have revealed the role of force chain statis- tics and fluctuations on mechanical properties [20], stick-slip [24], dynamic penetration and com- paction [13, 14, 25], and electrical and mechani- cal wave transmission [6, 8]. A benefit of stud- ies employing 2D photoelastic and rubber discs is that measurements can be made over very short timescales using high-speed imaging. This has en- abled studies of force chain dynamics at subsec- ond (down to millisecond) timescales relevant to processes such as stick-slip, dynamic compaction, and wave transmission [7,18,24–26]. Unfortunately, many dynamic processes in granular materials oc- cur in 3D rather than 2D, motivating the need for quantifying dynamically-evolving forces in 3D. Advances in 3D full-field imaging, including in confocal microscopy, refractive index-matched scanning (RIMS), and X-ray computed tomogra- phy and diffraction, have enabled the first force measurements in 3D over the past two decades [27–30]. These advances have recently enabled re- lating force chain evolution to quasi-static gran- ular deformation, failure, and wave transmission [8, 9, 29]. A prevailing challenge impeding 3D mea- surements of dynamic force chain evolution is the limited timescales accessible by full-field imaging techniques. For example, in 2012, RIMS was possi- ble with 10 ms exposure time per image, enabling full-field imaging of a 3D granular medium in about one second [27]. However, data transfer rates and maximum write speeds of hard drives were the lim- iting factors hindering faster RIMS measurements. Even having overcome such technological limita- tions, it may be impossible to design a RIMS ex- periment to quantify subsecond force chain evolu- tion in many cases of interest due to the interaction of index-matched fluids with granular dynamics on such timescales. As another example, 3D X-ray to- mography measurements have been made in 20 sec- onds for glass beads and in less than one second for other materials such as batteries [31, 32]. Although tomographic imaging rates are expected to improve with new laboratory [33] and synchrotron [34] ca- pabilities, most tomographic imaging requires sam- ple rotation, which induces centrifugal forces. Such centrifugal forces are not present in many appli- cations of interest for 3D granular materials and therefore limit the extent to which 3D force chain dynamics can be meaningfully studied using X-ray tomography. These challenges associated with 3D measure- ment techniques have limited the experimental study of dynamic force chain evolution in a vari- ety of applications in which they are thought to be important. In the next section, we describe several such applications that would benefit from time- resolved force chain measurements in 3D. We then describe key developments that may provide oppor- tunities for overcoming the current timescale limi- tations of 3D inter-particle force measurements in the coming years. II Open challenges related to force chain evolution The following list summarizes open challenges re- lated to time-resolved 3D force chain evolution in granular materials, and how measurements of such evolution would benefit our understanding and pre- dictive capacity. Such measurements have not yet been made primarily because of the technological limitations and the difficulty of the associated ex- periments, as described in the prior section. Possi- ble routes to overcoming these limitations and dif- ficulties are described in Sec. III. The list of open challenges is partially summarized in Fig. 1. 1. Stick-slip and intermittent flow (Fig.1(a)) – Force chain buckling has been considered a possible mechanism of stick-slip and acoustic emissions in sheared granular fault gouge for decades [12, 35–38]. Stress-drop events asso- ciated with stick-slip and force chain buck- 140003-2 Papers in Physics, vol. 14, art. 140003 (2022) / R. C. Hurley et al. Fault gauge Granular flow Dynamic compaction Creep Shear thickening (a) (c) (d) (e) AAAB63icbVBNS8NAEJ3Ur1q/qh69LBbBU0mKqMeCF48V7Ae0oWy2m3bpbhJ2J0IJ/QtePCji1T/kzX/jps1BWx8MPN6bYWZekEhh0HW/ndLG5tb2Tnm3srd/cHhUPT7pmDjVjLdZLGPdC6jhUkS8jQIl7yWaUxVI3g2md7nffeLaiDh6xFnCfUXHkQgFo5hLA6TpsFpz6+4CZJ14BalBgdaw+jUYxSxVPEImqTF9z03Qz6hGwSSfVwap4QllUzrmfUsjqrjxs8Wtc3JhlREJY20rQrJQf09kVBkzU4HtVBQnZtXLxf+8forhrZ+JKEmRR2y5KEwlwZjkj5OR0JyhnFlCmRb2VsImVFOGNp6KDcFbfXmddBp177reeLiqNRtFHGU4g3O4BA9uoAn30II2MJjAM7zCm6OcF+fd+Vi2lpxi5hT+wPn8AR6njj8= ⌧ AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKewGiR4DXjxGMA9IljA7mU3GzGOZmRXCkn/w4kERr/6PN//GSbIHTSxoKKq66e6KEs6M9f1vr7CxubW9U9wt7e0fHB6Vj0/aRqWa0BZRXOluhA3lTNKWZZbTbqIpFhGnnWhyO/c7T1QbpuSDnSY0FHgkWcwItk5q9w0bCTwoV/yqvwBaJ0FOKpCjOSh/9YeKpIJKSzg2phf4iQ0zrC0jnM5K/dTQBJMJHtGeoxILasJsce0MXThliGKlXUmLFurviQwLY6Yicp0C27FZ9ebif14vtfFNmDGZpJZKslwUpxxZheavoyHTlFg+dQQTzdytiIyxxsS6gEouhGD15XXSrlWDerV2f1Vp1PI4inAG53AJAVxDA+6gCS0g8AjP8ApvnvJevHfvY9la8PKZU/gD7/MHmdmPGg== � (b) Force chains AAAB63icbVBNS8NAEJ3Ur1q/qh69LBbBU0mkqMeCF48V7Ae0oWy2m3bpbhJ2J0IJ/QtePCji1T/kzX/jps1BWx8MPN6bYWZekEhh0HW/ndLG5tb2Tnm3srd/cHhUPT7pmDjVjLdZLGPdC6jhUkS8jQIl7yWaUxVI3g2md7nffeLaiDh6xFnCfUXHkQgFo5hLA450WK25dXcBsk68gtSgQGtY/RqMYpYqHiGT1Ji+5yboZ1SjYJLPK4PU8ISyKR3zvqURVdz42eLWObmwyoiEsbYVIVmovycyqoyZqcB2KooTs+rl4n9eP8Xw1s9ElKTII7ZcFKaSYEzyx8lIaM5QziyhTAt7K2ETqilDG0/FhuCtvrxOOld177reeGjUmo0ijjKcwTlcggc30IR7aEEbGEzgGV7hzVHOi/PufCxbS04xcwp/4Hz+AAeajjM= ⌘ AAAB83icbVDLSsNAFL2pr1pfVZduBovgqiRS1GXBjcsK9gFNKJPppB06k4SZG6GE/oYbF4q49Wfc+TdO2yy09cDA4Zx7uHdOmEph0HW/ndLG5tb2Tnm3srd/cHhUPT7pmCTTjLdZIhPdC6nhUsS8jQIl76WaUxVK3g0nd3O/+8S1EUn8iNOUB4qOYhEJRtFKvj9MMPdHVCk6G1Rrbt1dgKwTryA1KNAaVL9snGWKx8gkNabvuSkGOdUomOSzip8ZnlI2oSPetzSmipsgX9w8IxdWGZIo0fbFSBbq70ROlTFTFdpJRXFsVr25+J/XzzC6DXIRpxnymC0XRZkkmJB5AWQoNGcop5ZQpoW9lbAx1ZShraliS/BWv7xOOld177reeGjUmo2ijjKcwTlcggc30IR7aEEbGKTwDK/w5mTOi/PufCxHS06ROYU/cD5/AGurkec= �̇ Force chains Force chains? Impacting intruder Force chains Figure 1: Open challenges in granular mechanics involving force chain dynamics include (a) chain buckling in fault gouge, (b) chain dynamics in granular flows, (c) stress concentrations during dynamic compaction, (d) force chain evolution during creep at the onset of catastrophic flow visualized through diffusing wave spectroscopy (DWS), and (e) force chain formation in discontinuous shear thickening. Images adapted from [15–17] (Open Access) and [18] with permission. ling likely occur over millisecond timescales [39]. Experimental measurements of force chain buckling in granular fault gouge have been made only in model 2D photoelastic sys- tems [24] and only with coarser time resolu- tion (order of seconds) before and after stress drop events. Experiments employing 3D force chain measurements at short timescales, ide- ally with subsecond and approaching millisec- ond resolution, would support the notion that force chain buckling is responsible for stress drops and acoustic emissions in granular fault gouge. These measurements could be used to validate and extend models of fault gouge me- chanics relevant to short timescales. 2. Hypotheses underlying models of granular flow (Fig.1(b)) – Mathematical models of granu- lar flow, such as non-local fluidity and shear transformation zone theories, feature non-local Laplacian terms and other quantities that cap- ture the role of force fluctuations around the core of a rearrangement event [40–42]. Such force fluctuations likely occur over the millisec- ond timescales associated with stress drops [43]. Although the kinematics associated with such fluctuations have been made over longer timescales in 2D [44], they have not been made in 3D. Experiments quantifying 3D force fluc- tuations around rearrangement events at mil- lisecond to second timescales would provide some of the first in-situ data with which to calibrate, validate, and extend models that ex- plicitly or implicitly incorporate such fluctua- tions (e.g., [45, 46]). 3. Stress concentrations and hot spots during dy- namic compaction (Fig.1(c)) – Rapid com- paction of granular media plays an important role in manufacturing, defense, planetary sci- ence, and manufacturing processes [47]. In energetic materials, force chains that develop during rapid compaction are also thought to nucleate hot-spots that eventually lead to ma- terial ignition [48]. Many compaction and ig- nition events of scientific and technological im- portance take place over millisecond or shorter timescales. Prior rapid-compaction and im- pact studies investigating force chains have primarily employed 2D photoelastic and poly- mer discs [13, 25, 49], or numerical simulations. Experiments quantifying force chain evolution during 3D granular compaction events would provide new insight into the joint evolution of porosity, stresses, and forces experienced by these materials, quantities currently available only through numerical modeling despite their critical importance for predicting the outcome 140003-3 Papers in Physics, vol. 14, art. 140003 (2022) / R. C. Hurley et al. of impact and material processing events. 4. Creep and the onset of catastrophic flow (Fig.1(d)) – Creep leading to catastrophic flow occurs in nature in a variety of gran- ular media, including ice and snow prior to avalanches, soils prior to landslides, and river beds prior to submarine landslides [50]. Glassy dynamics and force chain fluctuations have been implicated in the progression of creep leading to the onset of flow [50, 51]; however, direct measurement of force chain evolution throughout the creep process has not been made in 3D. Two-dimensional measurements of creep have been made across a broad range of timescales and length scales using diffus- ing wave spectroscopy (DWS) (pioneered for granular matter by Crassous and colleagues [44, 52, 53]), but force measurements during the creep process have been made neither in 2D nor 3D. Depending on the the geometry and stresses imposed on a granular material, creep may occur over a range of timescales, from hours to seconds. Experimental measure- ments of 3D force chain evolution across this range of timescales would validate conceptual models of creep and provide valuable data sup- porting mechanistic model development. 5. Force chain formation in discontinuous shear thickening (Fig.1(e)) – Discontinuous shear thickening (DST), the ubiquitous increase in viscosity with shear of flowing dense suspen- sions, is thought to be related to force chain development on millisecond timescales [54, 55]. Discontinuous shear thickening has been stud- ied both experimentally and computationally, but no in-situ measurements of force chain de- velopment have been made in either 2D or 3D in such studies. Such direct measurements would provide vital information needed to cal- ibrate and validate models of DST and related jamming phenomena in suspensions. III Future opportunities for time- resolved force chain measure- ment The following list summarizes key advances that may enable measuring time-resolved force chain evolution in 3D. It is not meant to be exhaustive but rather to reflect the current perspective of the authors. The list primarily contains technological developments that may enable full-field measure- ments on millisecond to second timescales. This list is also summarized in Fig. 2. 1. High-speed RIMS with image-based force infer- ence (Fig.2(a) and (d)) – RIMS allows full- field imaging of granular materials submerged in index-matched fluids and, as described in Sec. I, permits imaging rates around 1 Hz [27]. By combining RIMS with quantitative analysis of particle deformation (e.g., in hy- drogels [56]), inter-particle forces can be in- ferred in 3D. Further advances in camera hard- ware and data storage capabilities may enable subsecond full-field imaging with RIMS. Imag- ing rates currently accessible by RIMS make it amenable to studies of stick-slip, non-local constitutive laws used to predict slow granular flows, and creep. Future subsecond imaging rates will improve resolution of individual force chain buckling events during such phenomena. Reducing full-field RIMS imaging rates far be- low subsecond resolution is unrealistic due to the interaction of the index-matched fluid dy- namics with the “true” dynamics of a granular material. Nevertheless, we envision that care- fully designed experiments employing RIMS may provide new and important insight into force chain fluctuations on second timescales in compliant materials like hydrogels. 2. Time-resolved 3D X-ray imaging for compliant materials (Fig.2(b) and (d)) – Advances in micro-focus computed tomography hardware and software in the past decade provide a route to infer contact forces between compli- ant grains (e.g., [57]) at synchrotron [58] or laboratory settings [33] by using quantitative analysis of particle deformation (e.g., in rub- ber [57]). Imaging rates can approach 1 Hz but, as described in Sec. I, are now limited by maximum rotation rates at which centrifugal forces become significant. A gantry-based X- ray device eliminates the need for sample rota- tion and therefore eliminates centrifugal forces [33]; however, such a device will also have X- ray flux limitations that practically limit full- field imaging to about 1 Hz. Imaging rates of 140003-4 Papers in Physics, vol. 14, art. 140003 (2022) / R. C. Hurley et al. Contact deformation, ! UndeformedDeformed Grain A Grain B Camera La se r Stage Granular packing Scan volume Forces Granular packing (a) (b) (c) (e) (c) RIMS 2D images 3D reconstruction Force inference Tomography Compliant materials Stiff materials Short time scales Detector Diffracted x-rays Detector for tomography X-ray beam Granular material Load frame Rotation Figure 2: Possible approaches to dynamic force inference. (a) RIMS. (b) XRCT. (c) X-ray tomography and diffraction (d) Time-resolved 2D X-ray imaging with 3D reconstruction. (e) 2D imaging with 3D microstructure. (d) An illustration of how forces are inferred using RIMS and XRCT data for compliant particles. (e) adapted from [30] with permission. about 1 Hz make X-ray tomography amenable to studies of stick-slip, non-local constitutive laws used to predict slow granular flows, and creep. As is the case for RIMS, X-ray to- mography alone only allows inter-particle force measurements for compliant materials, and the timescale capabilities again limit access to the dynamics of force chain buckling events. Nev- ertheless, we envision that carefully designed experiments employing X-ray tomography – ei- ther rotation-based or gantry-based – may pro- vide new and important insight into stick-slip, non-local constitutive laws, and creep in com- pliant materials. 3. Time-resolved 3D X-ray imaging and diffrac- tion for stiff materials (Fig.2(c)) – Rapid ad- vances in 3D X-ray diffraction have, in the past five years, provided a means to study forces in stiff sand-like materials [29], shedding light on the role of forces in material failure, ultrasound transmission, and rearrangements [8, 9]. The technical approach to studying forces with X-ray imaging and diffraction in- volves using tomography for quantifying pack- ing structure (particle shapes, sizes, and con- tacts) and diffraction for quantifying particle stress tensors. Measurements have historically been made in as little as about 10 minutes. Upgrades in X-ray flux and hardware at syn- chrotron facilities are likely to bring rates to as low as 1 Hz in the coming decades. Achiev- ing rates below 1 Hz is impractical due to the need for sample rotation which will induce cen- trifugal forces to samples. Combined imaging and diffraction therefore will allow studies of stick-slip, non-local constitutive laws used to predict slow granular flows, and creep in stiff materials, but will not provide access to the subsecond dynamics of force chain buckling. 4. Time-resolved 2D imaging with 3D reconstruc- tion (Fig.2(e)) – Time-resolved 2D imag- ing, using laboratory-based X-ray systems or synchrotron-based X-ray phase contrast imag- ing, has emerged as a powerful tool for study- ing dynamic compaction and flow of gran- ular materials [30, 59–61]. These imaging techniques provide only 2D images, but al- low temporal image spacing as low as 153 ns at synchrotron facilities and 30 Hz in labo- ratory settings [30, 62]. While such imaging 140003-5 Papers in Physics, vol. 14, art. 140003 (2022) / R. C. Hurley et al. is not 3D, novel algorithms have emerged in the last decade that enable reconstruction of 3D microstructures from 2D images, includ- ing flash X-ray tomography, projection-based digital volume correlation, and Fourier-space reconstruction methods [30, 61, 63–65]. We en- vision that these techniques, coupled with ap- propriate deformation-based force inference al- gorithms, can be used to study force chain dy- namics at time scales relevant to all of the open challenges described in Sec. II. The challenge of using this approach for studying force chain dynamics is to develop robust algorithms for 3D microstructure reconstruction and force in- ference from 2D time-resolved images. IV Discussion and conclusion Time-resolved 3D force chain measurements at mil- lisecond to second timescales have been challeng- ing due to hardware and technical limitations. In this paper, we articulated five topics in which dy- namic force chain evolution plays an important role across these timescales: stick-slip and intermittent flow; hypotheses underlying granular flow models; stress concentrations and hot spots during dynamic compaction; creep prior to catastrophic flow; force chain formation in discontinuous shear thickening. 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