Volume 49, Issue 19 e2022GL099971
Research Letter
Open Access

Evolution of Pulverized Fault Zone Rocks by Dynamic Tensile Loading During Successive Earthquakes

Zachary D. Smith

Corresponding Author

Zachary D. Smith

Department of Earth and Planetary Science, University of California, Berkeley, Berkeley, CA, USA

School of Earth Sciences, The Ohio State University, Columbus, OH, USA

Correspondence to:

Z. D. Smith and W. A. Griffith,

[email protected];

[email protected]

Contribution: Conceptualization, Methodology, Formal analysis, ​Investigation, Writing - original draft

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W. Ashley Griffith

Corresponding Author

W. Ashley Griffith

School of Earth Sciences, The Ohio State University, Columbus, OH, USA

Correspondence to:

Z. D. Smith and W. A. Griffith,

[email protected];

[email protected]

Contribution: Conceptualization, Methodology, Formal analysis, ​Investigation, Resources, Writing - original draft, Writing - review & editing, Funding acquisition

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First published: 22 September 2022
Citations: 3


Large strike-slip faults experience numerous earthquakes during which transient tensile and compressive mean normal stress perturbations travel along opposing sides of the fault. Research exploring dynamic rock fracture through multiple earthquake cycles has focused predominantly on transient compressive loading, but little is known about off-fault damage development due to successive tensile loading. We investigate damage accumulation by transient tensile loading over multiple earthquake cycles using a modified sample configuration for uniaxial compressive loading apparatuses consisting of a Westerly granite rock disk bonded to two lead disks. We show that fracture density increases during each successive loading cycle, and pulverized rock can be produced under tension at strain rates as low as 10−3 s−1. Therefore, pulverized rock can form at low strain rates, and its texture and extent may be controlled by the size of the coseismic tensile stress perturbation and the number of slip events on the fault.

Key Points

  • Fracture density increases and fragment size decreases during each successive tensile loading event

  • Tensile pulverization of crystalline rock does not require high strain rates and can be produced tens of meters from large faults

  • Finely pulverized rock may represent the accumulation of damage by successive earthquakes over thousands to millions of years

Plain Language Summary

Earthquakes produce transient compressive and tensile stresses on either side of the rupture. Fault damage accumulates during multiple earthquake cycles associated with these events. Damage accumulation due to successive compressive loading has been explored through rock mechanics experiments, but similar experiments under tension have been challenging to produce. We use a new experimental technique for subjecting a rock sample to repeated tensile loading cycles to explore how damage accumulates due to successive loading through multiple earthquakes. Our experiments show that fracture density in rock increases during each successive tensile loading event, and this is an effective mechanism for the formation of pulverized fault zone rocks.

1 Introduction

Fault damage zones in the upper crust are commonly composed of complex fracture networks that decrease in density with distance from the fault (e.g., Chester & Logan, 1986; Faulkner et al., 2011; J. E. Wilson et al., 2003; Mitchell & Faulkner, 2009; Rempe et al., 2013; Savage & Brodsky., 2011). Fault damage zones may form by interaction and coalescence of microcracks, interaction of multiple fault tips, fracturing in fault tip process zones, slip on wavy fault surfaces, and impulsive stresses associated with earthquake rupture tips (e.g., Mitchell & Faulkner, 2009). The latter mechanism has been specifically associated with the occurrence of pulverized fault zone rocks (PFZRs), characterized by substantial grain size reduction by brittle fracturing, negligible shear strain, isotropic crack orientation, and preservation of the original rock fabric (B. Wilson et al., 2005; Dor, Ben-Zion, et al., 2006; Doan & Gary, 2009; Dor, Rockwell, et al., 2006, Dor et al., 20082009; Fondriest et al., 2015; Mitchell et al., 2011; Ostermeijer et al., 2022; Rempe et al., 2013; Rockwell et al., 2009; Sullivan & Peterman, 2017; Wechsler et al., 2011). Here, we evaluate the roles of transient tensile stress perturbations during dynamic shear ruptures in the fragmentation of damage zone rocks and sustained rupture directivity during successive earthquakes as a mechanism for PFZR formation.

PFZR have been the focus of many studies because of their potential for preserving a record of near-field earthquake deformation (e.g., Dor, Ben-Zion, et al., 2006; Doan & Gary, 2009; Griffith et al., 2018; Rowe & Griffith, 2015). Most studies investigating PFZR have used high strain rate compressive loading techniques to simulate their formation in the lab (Aben et al., 20162017; Barber & Griffith, 2017; Braunagel & Griffith, 2019; Doan & Gary, 2009; Yao et al., 2020; Yuan et al., 2011). Rock pulverization by uniaxial compression requires strain rates urn:x-wiley:00948276:media:grl64894:grl64894-math-0001102 s−1, far exceeding peak coseismic strain rates for subshear ruptures at distances greater than a few centimeters from the principal slip zone (Figure 1). Two possible mechanisms for lowering the strain rate threshold for pulverization include progressive damage formation by compressive loading during successive ruptures (Aben et al., 2016; Doan & d’Hour, 2012) and compressive cyclic loading during a single earthquake (Braunagel & Griffith, 2019). Aben et al. (2016) demonstrated that the strain rate threshold for compressive pulverization of quartz monzonite is reduced from 180 s−1 to 90 s−1 after successive compressive loadings. This threshold is still several orders of magnitude higher than expected strain rates tens of meters from the fault for subshear ruptures (Figure 1a). An alternative mechanism for producing asymmetrically distributed PFZR about faults is sub-Rayleigh rupture in a preferred direction along a bimaterial fault interface, during which transient isotropic tensile stresses on one side of the fault can produce inelastic deformation at large distances from the fault (Ben-Zion & Shi, 2005; Griffith et al., 2018; Xu & Ben-Zion, 2017). Modeling suggests that these isotropic tensile stresses are maintained at distances of 100–200 m from the main fault under strain rates on the order of 10−3–100 s−1 (Xu & Ben-Zion, 2017).

Details are in the caption following the image

Volumetric strain rate (a) and stress decay (b) magnitude with distance from the fault for a subshear mode-II rupture through homogeneous material based on 2D plane strain analytical Linear Elastic Fracture Mechanics solution (Freund, 1998). See Text S6 in Supporting Information S1 for description model parameters. Examples of experimental pulverization strain rate thresholds for single and successive compressive loading (1—Aben et al., 2016; 2—Barber & Griffith, 2017), and the range of strain rates for which pulverized rock have been produced in the laboratory under tensile loading (3—Griffith et al., 2018) are given. Stress and strain rate ranges associated with each study indicate the range where pulverization was achieved. Red and blue lines with arrows indicate the range of conditions where pulverization is expected to be possible during a subshear rupture. urn:x-wiley:00948276:media:grl64894:grl64894-math-0002 and urn:x-wiley:00948276:media:grl64894:grl64894-math-0003 are uniaxial compressive strength and tensile strength, respectively.

Griffith et al. (2018) developed an experimental technique designed to simulate transversely isotropic tensile fragmentation during subshear rupture on a bimaterial interface (e.g., Xu & Ben-Zion, 2017). They argued that rock fragmentation under isotropic tension should not require fast strain rates, providing a potential solution for why PFZR can be found 100–200 m from faults (Figure 1). The experimental results suggest that the spatial limitation on pulverization under tension is controlled by the magnitude and extent of the stress field, not strain rate (Griffith et al., 2018). Although initial results suggest there is not a strain rate threshold for pulverization under tension (Figure 1; Griffith et al., 2018), the relatively coarser fragment size and lower fracture density produced during these experiments are less consistent with natural pulverized fault rocks than those of pulverized rocks formed during compressive loading experiments (Barber & Griffith, 2017; Yao et al., 2020).

In this study, we investigate whether volumetric strain during successive tensile loading events will be accommodated by reactivating preexisting fractures or if new fractures form to decrease fragment size. Experiments were performed on Westerly granite so that the results can be compared to other experimental studies on rock pulverization that used similar rock types (e.g., Aben et al., 2016; Braunagel & Griffith, 2019; Griffith et al., 2018). If successive loading events cause further grain size reduction, this could provide a viable mechanism for the formation of PFZR tens to hundreds of meters from the fault core. Furthermore, if average fragment size is a strong function of the number of loading events, this would imply that natural PFZR may provide textural clues about the minimum number of earthquake events leading to their formation.

2 Material and Methods

2.1 Tensile Loading Experiments

The Split Hopkinson Pressure Bar (SHPB) is a standard tool for dynamic uniaxial compression tests (e.g., Kolsky, 1949; Xia & Yao, 2015). The SHPB is composed of a striker bar, incident bar, and transmission bar (Figure S1a in Supporting Information S1). Collision between the striker and incident bars produces a compressive wave that travels down the incident bar and loads a sample mounted between the incident and transmission bars (see Text S1 in Supporting Information S1 for further information on the SHPB). We use a modified SHPB configuration to induce a transversely isotropic stress state (axial compression and radial and circumferential tension) in a rock disk bonded between two lead disks (Figure 2, Figures S1a and S1b in Supporting Information S1). Axial shortening of the sample results in lateral expansion and plastic flow in the compliant outer lead disks, inducing radial and circumferential tension in the rock disk (Figure 2 and Figure S1 in Supporting Information S1; Griffith et al., 2018). See Text S5 in Supporting Information S1 and Griffith et al. (2018) for further information on experimental limitations and comparison of layered tension experiments to natural fault damage zones.

Details are in the caption following the image

Records of surface fracture initiation with successive tensile loading as visualized from high-speed images and circumferential strain fields derived from digital image correlation compared to thin section images (right) of the rock disks.

Nine Westerly granite samples were used for successive loading experiments (Table S2 in Supporting Information S1). The nine samples were divided into three sets, each consisting of three samples that were loaded one, two, or three times resulting in a total of 18 experiments (Table S1 in Supporting Information S1). Strain rates for each successive loading trial were varied by changing the dimensions of copper pulse shapers and the striker bar velocity (11.56–13.05 m/s) (Table S1 in Supporting Information S1). A strain gauge was attached circumferentially to the rock sample and a new gauge was applied for each experiment (Figure S1a in Supporting Information S1).

A high-speed camera (Shimadzu HPV-2) was used to determine the time of macroscopic failure to infer the tensile strength (Smith & Griffith, 2022). During each experiment, the sample strain gauge was placed on the side of the sample opposite the side viewed by the camera. Digital image correlation (DIC) was performed for each experiment using the open-source MATLAB software Ncorr (Blaber et al., 2015). DIC uses image registration algorithms to determine the displacement of points between a reference image and a deformed image, providing a way to document continuous velocity fields during an experiment (Blaber et al., 2015). We use both strain gauge and DIC data to aid in the calculation of tensile strength (Figure S3 in Supporting Information S1; Smith & Griffith, 2022). Tensile strength is defined following Griffith et al. (2018) and Smith and Griffith (2022) as the circumferential normal stress corresponding to a sharp change in slope in circumferential stress, strain, and strain rate time series collected during each SHPB test, and this interpretation can be further confirmed by the first appearance of microcracks in high-speed photographs (Figure S3 in Supporting Information S1).

To investigate the fragmentation process in distal portions of the damage zone where strain rates are expected to be <<100 s−1, we conducted simple quasi-static tensile fragmentation experiments using a manually operated uniaxial hydraulic press. These allow us to compare fragment sizes produced under the same sample configuration but at slow strain rates. Two cameras were used to simultaneously record (a) the axial stress gauge and (b) the layered tension sample to match the analog axial stress measurements with DIC strain and strain rate measurements in the layered tension sample. See Text S3 in Supporting Information S1 and Smith and Griffith (2022) for more information on DIC and quasi-static loading experiments.

2.2 Damage Characterization

We performed manual and automated image analysis techniques on thin sections to measure fracture density, fragment size, and porosity in thin sections cut perpendicular to the sample axis. Fracture networks were digitized from photomicrographs in ArcGIS Pro using methods described in Smith and Maxwell (2021). Porosity changes were measured by running a supervised image classification in ArcGIS Pro using the support vector machine algorithm. Fragments were constructed using the digitized fracture lines as boundaries. During successive loading tests the fracture aperture increases significantly. To remove pore space from fragment size measurements, void space was masked using the porosity data sets produced from image classification (see Text S4 in Supporting Information S1 for additional information on fracture density and fragment size measurements).

3 Results

Consecutive experiments using our modified sample configuration result in increased fragmentation and fracture density with each successive load cycle. Figure 2 shows circumferential strain fields, derived from DIC, associated with growth of new fractures during successive loading events. Surface fracture initiation (FI in Figure 2) can be seen by localized, nearly instantaneous strain increases along thin horizontal lines cutting across the specimen in the DIC records. These fractures in the DIC records can be correlated with fractures identified during petrographic analysis, documenting nucleation and growth of new fractures during successive loading events.

All dynamic and quasi-static experiments resulted in highly fractured and fragmented samples (Figure 2). Fracture density increases and mean fragment size (measured as an equivalent diameter urn:x-wiley:00948276:media:grl64894:grl64894-math-0004, where urn:x-wiley:00948276:media:grl64894:grl64894-math-0005 is mean fragment area) decreases with increasing number of loading events (Table S2 in Supporting Information S1). The evolution of fracture density (urn:x-wiley:00948276:media:grl64894:grl64894-math-0006) and mean fragment size (urn:x-wiley:00948276:media:grl64894:grl64894-math-0007) with the number of loading events can be described by power law functions of the form
where urn:x-wiley:00948276:media:grl64894:grl64894-math-0010 is the number of loading events, urn:x-wiley:00948276:media:grl64894:grl64894-math-0011 and urn:x-wiley:00948276:media:grl64894:grl64894-math-0012 are the fracture density and average fragment size produced by a single loading event respectively, m is an exponent describing the increase in fracture density, and urn:x-wiley:00948276:media:grl64894:grl64894-math-0013 describes the decay in fragment size. Power law fits for dynamic successive tensile loading experiments have exponents of m = 0.74 and l = 0.58 indicating an increase in fracture density and decrease in fragment size with each new loading event. For example, fragment size varies between 1.66 and 3.08 mm for the first loading event, but then reduces to 1.34–1.58 and 1.02–1.43 mm for the second and third loadings respectively (Table S2 in Supporting Information S1). Extrapolating to 100 loading events, the mean fragment size would be 150 microns.

Strain rate measurements at failure show that fragmentation can occur at strain rates as low as 10−3 s−1. Quasi-static tensile strength ranged between 12 and 15 MPa, consistent with values of 10–25 MPa reported in the literature (e.g., Chau & Wong, 1996; Yong & Wang, 1980). Smith and Griffith (2022) compared tensile strength measurements for granite, diabase, welded tuff, and sandstone from layered tension experiments with both direct and indirect tension experiments from multiple studies and found excellent agreement, providing validation for this method. In all experiments, the axial compressive stress never exceeds 1/3 of the uniaxial compressive strength of the rocks being tested (Smith & Griffith, 2022).

4 Discussion

Whereas the strain rate threshold for inducing pulverization under successive compressive loading is ∼−90 s−1 (Figure 3; Aben et al., 2016), our experiments show that coarse pulverization can occur even at low strain rates (∼10−3 s−1) under transversely isotropic tensile loading assuming the stress magnitude exceeds the rock strength. A comparison of our experimental data with dynamic and quasi-static compressive and tensile loading experiments on Westerly granite, and similar rock types (e.g., Aben et al., 2016), shows that strength generally follows a sigmoidal trend (Figure 3), capped at high positive (extensional: Cohn & Ahrens, 1981) and negative (contractional: Barber & Griffith, 2017; Ghaffari et al., 2019) strain rates. In this study, strain rate at FI is defined as the strain rate when fractures are observed in high-speed photography. For isotropic tensile fragmentation, only the extent and magnitude of the stress perturbation produced by the passing rupture tip is important in pulverization and the strain rate is inconsequential in the formation of PFZR.

Details are in the caption following the image

Strain rate at fracture initiation (FI) versus peak strength for successive tensile loading experiments from this study in comparison to single and successive loading tension and compression experiments on Westerly granite and quartz monzonite. (a) Peak stress as a function of strain rate at FI for studies on both compressive and tensile pulverization, and (b) peak stress as a function of strain rate for tensile loading.

The results of successive layered tension experiments show that fracture density increases by a factor of two between each successive event. New fractures form in three distinct ways in our experiments: (a) linkage of micro-scale flaws/fractures enlarged during previous loading events, (b) completion of partially formed macroscopic fractures, and (c) distributed fracturing surrounding primary fractures (Figure S10 in Supporting Information S1). We set a limit of three loading cycles for this sample configuration because with more loadings the fracture aperture increases to the point where significant amounts of fragments may be lost, which would inhibit post-mortem analysis and skew results. After the initial loading event, approximately 99% or more of the rock mass consists of large (>1 mm) fragments while the remaining material consists of fine fragments within the primary fractures. However, as larger fractures form throughout the rock during subsequent loading events, the fine fraction increases relative to the large fragments.

Griffith et al. (2018) showed that tensile fragmentation under a range of strain rates (100–102 s−1) resulted in similar fragment sizes for single loading events. Their results are consistent with the energy-based fragmentation model proposed by Glenn and Chudnovsky (1986). This model considers the energy balance of the system during fragmentation to be ΔT = ΔP + ΔΓ, where ΔT, ΔP, and ΔΓ are the changes in kinetic, strain, and surface energy respectively, and the energy balance can be rewritten in terms of fragment radius to derive a model for fragment radius (urn:x-wiley:00948276:media:grl64894:grl64894-math-0014) as a function of strain rate (urn:x-wiley:00948276:media:grl64894:grl64894-math-0015):
The terms urn:x-wiley:00948276:media:grl64894:grl64894-math-0017, urn:x-wiley:00948276:media:grl64894:grl64894-math-0018, and urn:x-wiley:00948276:media:grl64894:grl64894-math-0019 are:
where urn:x-wiley:00948276:media:grl64894:grl64894-math-0021 and urn:x-wiley:00948276:media:grl64894:grl64894-math-0022 are initial radius, mass density, and p-wave velocity. The model assumes that fragmentation does not occur until a critical stress (urn:x-wiley:00948276:media:grl64894:grl64894-math-0023), corresponding to the rock tensile strength. For fractures to propagate unstably toward rock failure, the stress intensity factor urn:x-wiley:00948276:media:grl64894:grl64894-math-0024 must exceed the fracture toughness (urn:x-wiley:00948276:media:grl64894:grl64894-math-0025), a material property that quantifies resistance to crack growth. This model predicts that below a rock specific strain rate threshold, fragment size remains constant under tensile loading because strain energy dominates the fragmentation process at low strain rates (<103 s−1 for Westerly granite; Griffith et al. (2018)). Above this threshold kinetic energy dominates the fragmentation process and fragment size becomes strain rate-dependent. Failure in tension occurs at lower absolute stress magnitudes in granitic rocks (∼5 to 50 MPa) compared to compressive failure (∼100 to 450 MPa). Therefore, most tensile fragmentation associated with a passing earthquake rupture tip at distances greater than a few meters from the fault occur below the strain rate threshold for rate-dependent fragmentation (Glenn & Chudnovsky, 1986), and all of the layered tension experiments fall within the strain energy dominant regime (Figure 4c). The three experiments performed at quasi-static strain rates (10−2–10−3 s−1) produced similar fragment sizes as those at strain rates of 101–102 s−1 (Figure 4c, Figures S7–S9 and S11 in Supporting Information S1). Our results are consistent with Griffith et al. (2018) and Smith and Griffith (2021) for single loading experiments, but our successive loading experiments show a clear reduction in fragment size with increasing number of loading events.
Details are in the caption following the image

Evolution of damage with successive loading events. (a) Fracture density and (b) fragment diameter with successive loadings for dynamic loading experiments. (c) Fragment diameter as a function of strain rate with experimental results from layered tension tests compared to an energy-based fragmentation model (Glenn & Chudnovsky, 1986). (d) Fragment diameter power law fit for experimentally pulverized rocks compared to the range of fragment sizes of pulverized fault zone rock (Rockwell et al., 2009; Wechsler et al., 2011).

In Equation 1, three terms play a dominant role in controlling grain size reduction: fracture toughness (urn:x-wiley:00948276:media:grl64894:grl64894-math-0026), tensile strength (urn:x-wiley:00948276:media:grl64894:grl64894-math-0027), and the initial radius (urn:x-wiley:00948276:media:grl64894:grl64894-math-0028). If the reduction in urn:x-wiley:00948276:media:grl64894:grl64894-math-0029 outpaces the reduction in tensile strength, fragment size will decrease (Equation 3). Decreasing the size of the initial radius of the rock mass being subjected to tensile loading also reduces the final fragment size. Nasseri et al. (2007) conducted heat treatments on Westerly granite to induce distributed microcracks and study the relationship between crack density and urn:x-wiley:00948276:media:grl64894:grl64894-math-0030. They found that with increasing crack density, urn:x-wiley:00948276:media:grl64894:grl64894-math-0031 decreases. Feng et al. (2019) conducted similar experiments to study the relationship between urn:x-wiley:00948276:media:grl64894:grl64894-math-0032 and tensile strength with different rock types. Analysis of their data for granitic rocks shows that the reduction in urn:x-wiley:00948276:media:grl64894:grl64894-math-0033 outpaces the reduction in tensile strength with increasing heat treatments (increasing crack density). This implies that reduction in urn:x-wiley:00948276:media:grl64894:grl64894-math-0034 in correlation with reduction in initial radius will drive further fragmentation during successive tensile loading (Figure 4).

Dynamic tensile fragmentation during earthquake rupture presents a viable solution to the problem of pulverized zone width. Furthermore, our quasi-static experiments confirm the predictions of energy-based fragmentation models (Glenn & Chudnovsky, 1986) that below strain rates of 103 s−1 fragment size will be uniform under tensile loading. Therefore, we argue it is possible to pulverize rocks at distances up to 200 m from a fault where plane strain Linear Elastic Fracture Mechanics solutions for subshear mode-II rupture predict strain rates of 10−3 s−1 (Figures 1 and 4).

An extrapolation of our power law fit for fragment diameter as a function of the number of loading events shows the potential number of earthquakes required to produce finely pulverized rock if tensile loading is only considered (Figure 4d). We show a gradient in the size of natural pulverized rocks because there are measurement limitations in constraining the minimum grain size (Figure 4d). Note that some differences exist in the fragment size measurements for single loading events between studies (Figure 4c) due to different methods used for mapping fractures and fragments (Text S4 in Supporting Information S1).

Our results suggest that finely pulverized rocks, like those observed along the San Andreas or San Jacinto faults may be the result of at least 10–15 earthquakes. It may have required as many as one thousand earthquakes to produce the most finely PFZR if tensile pulverization is the sole mechanism (Figure 4). This is consistent with earthquake activity over thousands to millions of years and is realistic for large strike-slip faults such as the seismogenic portions of the San Andreas or San Jacinto faults (Onderdonk et al., 2018). This presumes that scaling our experimental results to natural settings is straightforward. In our experiments, the loading geometry remains static throughout each successive experiment. In reality, fragmented damage zone rocks are expected to be subjected to constantly evolving stress states throughout hundreds to thousands of successive earthquake cycles. We discuss these and related scaling limitations further in Text S5 in Supporting Information S1.

Finally, we applied three different testing regimes for each set of experiments (Table S2 in Supporting Information S1), and yet the fracture density increases and fragment size decreases uniformly after several loading events (Figures 4a and 4b). This convergence on a uniform increase in fracture density and decrease in fragment size with repeated loading cycles presents the potential to match fracture density to earthquake recurrence interval if PFZR is indeed formed coseismically during subshear rupture. For faults with strongly preferred earthquake rupture directivity over time, our results suggest that it may be possible to relate the fracture density or fragment size to the number of slip events on a fault.

5 Conclusion

This study demonstrates that (a) dynamic tensile loading during earthquake rupture is a viable mechanism for producing pulverized rock 100–200 m from a fault and (b) successive tensile loading can decrease fragment size toward finely pulverized rock as observed in nature. Successive layered tension experiments show that fracture density increases through successive dynamic tensile loading events despite the existence of preexisting fractures. During a single loading event, Westerly granite can reach coarse pulverization at strain rates as low as 10−3 s−1. Energy-based fragmentation models suggest that a reduction in the fracture toughness and fragment size that outpace the reduction in the tensile strength may allow fragmentation under tensile loading to progress after initial fragmentation. Our results show that finely pulverized rock observed in asymmetric fault damage zones may be the product of tens to thousands of successive earthquakes.


This study was funded by the American Chemical Society Petroleum Research Fund Grant No. PRF#58951-ND8, the National Science Foundation under award EAR 1351931, and the Army Research Laboratory under Grant No. W911NF-14-1-0876, all awarded to W. Ashley Griffith. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for government purposes notwithstanding any copyright notation herein. Zachary Smith was supported by The Ohio State University Susan L. Huntington Dean's Distinguished University Fellowship. Finally, the authors thank Alexis Ault and an anonymous reviewer of this paper for their feedback.

    Data Availability Statement

    All data from dynamic and quasi-static loading experiments are available on Mendeley (https://data.mendeley.com/datasets/4wgxsd2r4r/1) or in Supporting Information S1.