Short cracks in knee meniscus tissue cause strain concentrations, but do not reduce ultimate stress, in single-cycle uniaxial tension

Tears are central to knee meniscus pathology and, from a mechanical perspective, are crack-like defects (cracks). In many materials, cracks create stress concentrations that cause progressive local rupture and reduce effective strength. It is currently unknown if cracks in meniscus have these consequences; if they do, this would have repercussions for management of meniscus pathology. The objective of this study was to determine if a short crack in meniscus tissue, which mimics a preclinical meniscus tear, (a) causes crack growth and reduces effective strength, (b) creates a near-tip strain concentration and (c) creates unloaded regions on either side of the crack. Specimens with and without cracks were tested in uniaxial tension and compared in terms of macroscopic stress–strain curves and digital image correlation strain fields. The strain fields were used as an indicator of stress concentrations and unloaded regions. Effective strength was found to be insensitive to the presence of a crack (potential effect < 0.86 s.d.; β = 0.2), but significant strain concentrations, which have the potential to lead to long-term accumulation of tissue or cell damage, were observed near the crack tip.


Introduction
Tears are the most common pathology to afflict the knee meniscus. Their direct symptoms include pain, mechanical deficiency and increased risk of osteoarthritis [1][2][3][4]. Meniscus tears can also cause serious secondary harm, as the most straightforward treatment for a tear-partial or total meniscectomy-further increases the risk of osteoarthritis [5][6][7][8][9]. Furthermore, repair of a torn meniscus, especially when the tear is in the inner avascular region, is not always feasible [1,10]. Some in vivo meniscus tears occur suddenly, suggestive of immediate rupture from a single overload event [11][12][13][14][15][16][17], whereas others grow over time [18,19]. Although short (less than 5-10 mm) tears often do not merit immediate clinical concern [15,[20][21][22], they have the potential to grow and become more serious with time. To aid efforts to prevent and to repair meniscus tears, it is important to understand the mechanics of how they form and grow.
A meniscus tear, viewed from an engineering perspective, is a macroscopic crack-like defect. In this work, 'meniscus tear' will be used to refer to the clinical pathology, and 'meniscus crack' will be used in the engineering sense to mean a macroscopic crack-like defect in the meniscus, regardless of whether it is a natural meniscus tear or an artificial crack-like defect such as a cut. A crack typically creates a stress concentration at its tip, which often, but not always, causes crack growth and reduces ultimate stress (maximum engineering stress prior to rupture) [23 -25]. Study of this type of failure comprises the field of fracture mechanics. The central question concerning meniscus cracks is: do cracks reduce the stress-bearing capacity of meniscus tissue, or is meniscus tissue insensitive to them?
The effect of a crack depends on the material's fracture toughness and the severity of the crack-induced stress concentration (figure 1) [23,24,26]. If the stress concentration is large relative to the material's fracture toughness, it causes local rupture at the crack tip, crack growth and a reduction in ultimate stress (fracture mechanics region, figure 1). In this case, a fracture mechanics approach should be used to quantify rupture. If the stress concentration is small relative to the material's fracture toughness, the crack has negligible effect, and the ultimate stress is equal to the ultimate tensile strength (limit stress analysis region, figure 1). In this case, limit stress analysis (comparison of applied stress to material properties, such as ultimate tensile strength) should be used to quantify rupture. Demonstration of limit stress analysisdominant rupture would not necessarily mean that defects such as microcracks are uninvolved in failure, but it would indicate that the primary impetus of rupture was not macroscale crack growth. To permit accurate failure analysis of meniscus bearing a short tear, it is crucial to determine if meniscus tissue containing a short crack ruptures by fracture mechanics-dominant processes or limit stress analysis-dominant processes.
The idea that the meniscus ruptures by fracture mechanics-dominant processes has some experimental support. Meniscus tears grow in vivo [18,19], suggesting that crack growth in the fracture mechanics sense may have a role. Superficial zone articular cartilage, which is similar to meniscus, has been observed to rupture by fracture mechanics-dominant processes [26,27]. However, cracks in tendon, which like meniscus contains highly aligned collagen fascicles, tend to become blunt instead of growing [28][29][30][31][32][33]. These findings suggest that limit stress analysis is more appropriate for cracked tendon, and by extension possibly also for meniscus. It remains uncertain which rupture process is relevant for meniscus, and mechanical tests are needed to resolve this uncertainty.
To determine if cracked meniscus fails by fracture mechanics-dominant processes, we chose to compare the ultimate stress of cracked meniscus specimens to identically tested intact control specimens. This test has low fracture toughness relative to stress concentration high fracture toughness relative to stress concentration ultimate stress (s u ) ultimate strength (s UTS ) fracture mechanics l i n e a r e l a s t i c f r a c t u r e ( e .g . s o d a l i m e g l a s s ) n o n li n e a r fr a c tu re (e .g . c ra c k e d lo w -s tr e n g th s te e l) limit stress analysis yield-dominant rupture (e.g. pristine low-strength steel) Figure 1. Schematic of ultimate stress variation with fracture toughness and stress concentration severity. Fracture mechanics governs failure when the material's fracture toughness is small relative to a local stress concentration. Limit stress analysis governs failure when the material is sufficiently tough to tolerate any stress concentrations that are present. In the fracture mechanics case, s u ,s UTS ; in the limit stress case, s u ¼ s UTS [23,24,26]. rsos.royalsocietypublishing.org R. Soc. open sci. 5: 181166 been specifically recommended for application to fibrous soft tissues for which the dominant failure process is not known [26]. Cracked specimens were prepared with crack length much longer than any pre-existing defects that may have been present. Because stress concentration severity increases with crack length, cracked specimens will lie to the left of the control specimens on figure 1. If the cracked specimens lie in the fracture mechanics region, they will have ultimate stress less than controls. If the cracked specimens instead lie in the limit stress analysis region, they will have ultimate stress equal to the controls. Observation of either outcome is valuable; either the results provide a necessary foundation to support subsequent fracture toughness measurements, or they rule out risk of crack-induced weakness for the tested crack geometry and loading conditions. Independent of which process governs rupture, the potential for cracks to alter stress and strain fields within the meniscus is also of interest-specifically, the potential for near-tip stress concentrations and unloaded regions on either side of the crack. A stress and strain concentration may cause stress to locally exceed the elastic limit and hence cause local tissue or cell damage. Conversely, unloaded regions may cause long-term cell-mediated degeneration by abolishing mechanical signals necessary for homeostasis. The idea that a near-tip stress concentration produces local damage is supported by the observation that tissue near the tip of a naturally occurring meniscus tear takes less energy to rupture than tissue in a crack-free contralateral control meniscus [21]. Concerning unloaded regions, a crack in a meniscus-mimicking synthetic scaffold has been observed to reduce strain in the regions that include material cut by the crack [34,35]. Quantification of any crack-induced stress -strain concentrations and unloaded regions is needed to determine if these mechanical phenomena may have a role in meniscus tear pathology.
The particular objectives of this study were, for meniscus tissue with a short crack: (a) to determine whether fracture mechanics or limit stress analysis is appropriate for failure analysis; (b) to quantify strain concentrations in the region near the crack tip and (c) to quantify the degree of unloading in the cut material to either side of a crack. Meniscus specimens with and without artificially introduced cracks were tested in both circumferential and radial uniaxial tension so as to examine both fibre and matrix rupture phenomena, and because tensile load support is a key aspect of meniscus function [36][37][38][39][40][41]. To test the hypothesis that meniscus cracks reduce ultimate stress and cause rupture by fracture mechanics-dominant processes (objective a), ultimate stress was compared between cracked and crack-free specimens as recommended by Taylor et al. [26]. To test the hypothesis that near-tip strain concentrations are present and to measure their magnitude (objective b), strain fields were measured using digital image correlation (DIC) and strain in cracked specimens was compared between their near-tip and away-from-tip regions. Similarly, to test the hypothesis that the regions to either side of a crack, which contain cut material, are unloaded (objective c), strain in cracked specimens was compared between their cut and intact regions. Results are discussed in terms of their significance with respect to whole-meniscus damage and failure.

Specimen preparation
Specimens were prepared for three test groups-circumferential tension with a 908 edge crack, circumferential tension with a 458 centre crack and radial tension with a 908 edge crack-with corresponding circumferential and radial tension crack-free control groups (figure 2). These test groups were chosen based on prior simulation results [42]. As established by prior work [43], circumferential specimens were made with expanded grip regions to facilitate fibre loading. Bovine menisci (age . 30 months and skeletally mature, mixed lateral and medial, mixed sex) were purchased fresh-frozen from Animal Technologies, Inc. (Tyler, TX) and stored sealed in plastic bags at 2208C in a non-defrosting freezer. Freezing is the preferred preservation method for mechanical tests of meniscus [44][45][46][47][48][49][50][51][52][53] and for meniscus allografts [54]. Medial and lateral menisci were pooled because previous work has found only slight or no differences in mechanical properties between medial and lateral menisci [52,53,55,56], so there was no reason to arbitrarily exclude either group.
One specimen per meniscus was prepared using a Leica SM2400 sledge microtome, with a freezing stage, to plane the meniscus to a target thickness of 1.0-1.5 mm, with the specimen plane normal to the proximal-distal axis [57]. Including the microtomy, each specimen underwent 3-4 freeze-thaw cycles. The specimen was then trimmed to its final in-plane dimensions, its cross-sectional area measured by scanning across its width with a laser displacement sensor [58,59], and its surface airbrushed with rsos.royalsocietypublishing.org R. Soc. open sci. 5: 181166 Verhoeff's stain to facilitate DIC from test video. Measured specimen dimensions are reported in table 1. Except when the specimens were being actively manipulated, they were kept covered under PBSdampened gauze to minimize dehydration.
Each edge crack was created by incision with a fresh #11 scalpel blade to a target length of 3 mm. Each centre crack was created by incision with a fresh razor blade broken to the target crack length of 3 mm. From a clinical perspective, the 3 mm crack length was chosen because it is representative of 'short' tears (less than 5-10 mm long) that have not yet grown to cause definite clinical concern. From an engineering perspective, the 3 mm length is a compromise-long cracks are useful in that they produce larger stress concentrations, but the crack must be short enough so that the crack tip-associated failure zone has sufficient space to develop fully and produce crack propagation in the fracture mechanics sense.

Tensile test protocol
Tensile testing was done following standard procedures [43,45,47,48,50,52,57,60]. The tensile test protocol consisted of (a) 20 kPa preload, which was used to establish the specimen's undeformed reference length, (b) 10 cycles of preconditioning to 4% grip-to-grip engineering strain and (c) stretch to failure. The displacement rate was 0.5 mm s 21 . Video of the test was recorded at 15 fps and 1392 Â 1000 px. The image scale was approximately 40 px mm 21 for circumferential specimens and approximately 60 px mm 21 for radial specimens.
Ruptures of tested specimens were classified according to published definitions [43]. Briefly, midsubstance rupture means the rupture zone touched neither grip line, mixed rupture means the  rupture zone was in the midsubstance but touched at least one grip line, and grip line rupture means the rupture was entirely within 1 mm of a grip line. Tests with rupture or slip inside the grips (longitudinal split, gripped region failure or no rupture) were excluded from analysis because mean stress in the failure region cannot be accurately calculated for these failure types. The counts of each type of rupture are presented in table 2. The counts of tests used for analysis are given by group in figure 2b. In prior work, grip line failures were often excluded from analysis as a precautionary measure [45,57,61,62], although quantitative comparison of at-grip and midsubstance failures in fibrous soft tissue has shown no difference [43,63,64]. In this study, midsubstance, mixed and grip line failures were all used for this analysis because, specifically under the present test protocol, they are known to not differ in their stressstrain responses [43].

Stress and strain data processing
The tensile tests' stress (s) -strain (1) curves were summarized using ultimate stress s u , strain at ultimate stress 1 u , tangent modulus (slope, measured at the yield point), yield stress and yield strain. (These points are visually marked in the results; figure 4.) Strain was calculated using the current grip-to-grip length l and the reference grip-to-grip length l 0 and reported as stretch ratio (l ¼ l/l 0 ) or Lagrange strain The yield point was identified as the inflection point in the stress -strain curve as done previously [43]. Note that for tissue tests the yield point is not customarily equated with the elastic limit, in part, because the role of plasticity with respect to tissue remains ambiguous [43,65 -71]. For cracked specimens, the uncut transverse cross-sectional area (thickness Â (total width 2 transverse axis component of crack length)) was used for stress calculations. Lagrange strain fields were computed across the specimen surface from the video recordings using two-dimensional DIC (Vic-2D 2009; Correlated Solutions, Columbia, SC) [31,43,72]. Three DIC strain components were analysed: longitudinal strain (grip-to-grip direction; E xx ), transverse strain (E yy ) and shear strain magnitude (jE xy j). The correlation window (subset size) was 0.7 Â 0.7 mm, and incremental correlation, exhaustive search and low-pass filtering were enabled. Strain accumulation error from incremental correlation was negligible; for this test, apparatus and the number of frames analysed, strain error for each pixel is less than or equal to 0.001. Post-processing used a 15 px exponential decay filter. Trial runs during study development showed that only the subset size setting had a strong influence on the calculated strain field. The choice of 0.7 Â 0.7 mm subset size was a compromise between the needs of (a) minimizing spurious correlations, which favours a large correlation window, and (b) retaining spatial resolution to identify strain concentrations and inter-fascicle sliding, which favours a small correlation window.
Quantitative analysis of strain fields was done by comparison of strain statistics between regions of interest (ROIs). To test for the existence of strain concentrations near the crack tip, the DIC strain field was partitioned into near-tip and away-from-tip ROIs (figure 5a). The ROI size was chosen to be of similar size to the strain concentrations visible in the strain field images. The near-tip ROIs for analysis of E xx extended, relative to the crack tip, þ0.7 mm in the crack pointing direction and +0.7 mm in the loading direction. The near-tip ROI size was set to approximately the subset window size because this is the smallest size that is reasonable for analysing spatial variation. The near-tip ROIs for analysis of E yy and E xy were similarly defined to extend þ0.7 mm in the crack pointing direction and, because features in the E yy and E xy strain fields were elongated in the loading direction, +1.05 mm in the loading direction.
To test for differences in strain between tissue cut and not cut by a crack, 'cut' and 'intact' ROIs were also defined (figure 7a). Comparisons of DIC strain statistics between paired (a) near-tip and away-from-tip and (b) cut and intact ROIs were made at stress levels from 0.25s u to 0.9s u for circumferential specimens and, due to loss of DIC tracking at high strain for several radial specimens, 0.25s u to 0.7s u for radial specimens. Measurement at relative stress levels ensures that each measurement reflects a similar phase of the stress-strain curve across all specimens.

Statistics and inference
The hypothesis that cracks reduce the ultimate stress of meniscus (related to objective a) was tested using unpaired Welch t-tests to compare ultimate stress between cracked and control specimens for each of the three test cases (circumferential tension 908 edge cracks, circumferential tension 458 centre cracks and radial tension 908 edge cracks). Since this hypothesis was specifically that cracked s u ,control s u , comparisons were made using a one-sided t-test to decrease the chance of type II error. The other stressstrain parameters did not have a specific hypothesized direction of change and so were compared between cracked and control specimens with two-sided t-tests. The type I error rate for all statistical tests was set to 0.05. The hypothesis that cracks generate strain concentrations near their tips was tested by comparing DIC strain (objective b) in the near-tip ROI to the away-from-tip ROI (figure 5a). Similarly, the hypothesis that cracks reduce strain in the region containing cut material (objective c) was tested by comparing DIC strain in the cut ROI to the intact ROI (figure 7a). The between-ROI differences in DIC strain had skewed and very heavy-tailed distributions, making t-tests unsuitable. Therefore, comparisons of DIC strain between ROIs within each specimen were done using the mean strain in each ROI by paired Wilcoxon tests.

Effect of cracks on stress -strain curve parameters
Whether fracture mechanics or limit stress analysis is appropriate for failure analysis of cracked meniscus tissue was determined by comparing ultimate stress (s u ) for each group of cracked specimens with its corresponding control group (figure 3; see figure 1 for rationale). None of the crack groups (circumferential 908 edge crack, circumferential 458 centre crack and radial 908 edge crack; figure 2) had ultimate stress significantly less than their corresponding controls ( p . 0.2 for all). The study had power ¼ 0.8 to detect a 0.86 s.d. decrease in circumferential ultimate stress and a 0.78 s.d. decrease in radial ultimate stress, so this negative result indicates that there was no meaningful difference. Therefore, the specimens failed by limit stress-dominant processes.
The other stress-strain curve parameters-strain at ultimate stress, tangent modulus, yield stress and yield strain-were also compared between the crack groups and their controls ( figure 3). The full table of stress-strain curve statistics is provided in electronic supplementary material, table S1 and the stressstrain curves are plotted in figure 4 for qualitative comparison. Owing to the large number of radial specimens, it was possible to (as a precaution) also do the radial analysis with only midsubstance failure tests (electronic supplementary material, table S2); this produced results equivalent to the full analysis (electronic supplementary material, table S1). Tangent modulus and yield stress were significantly greater in circumferential 908 edge crack specimens by 1.5-6.8 and 18-88 MPa, respectively (95% CIs). No other stress-strain parameter comparison showed a significant difference between the crack and control groups.

Effect of cracks on strain fields
The presence of crack-induced strain concentrations was tested by comparing, for each specimen, mean DIC strain near and away from the crack tip. Longitudinal strain (E xx ) was significantly greater near the rsos.royalsocietypublishing.org R. Soc. open sci. 5: 181166 crack tip for all groups at every stress level examined (figure 5). Transverse strain (E yy ) was not significantly different near the crack tip in circumferential tension specimens, but for s ! 0.5s u was significantly more compressive near the tip in radial edge crack specimens. Shear strain magnitude (jE xy j) was significantly greater near the crack tip in circumferential edge crack specimens for s ! 0.8s u and in circumferential centre crack and radial edge crack specimens for all stress levels examined. The complete table of strain field statistics is provided in electronic supplementary material, table S3. These results demonstrate that cracks in meniscus tissue create strain concentrations at their tips. The strain fields were qualitatively examined in terms of the near-tip strain concentrations' size and shape, as well as the strain fields' overall appearance. Strain fields for three representative cracked specimens are shown in figure 6. Strain fields for control specimens were similar to those reported previously [43]. The mottled appearance of each test's strain field, specifically the pattern of blobs of positive and negative strain, was established early in the test (approx. 0.01 strain) and retained the same pattern through failure.
Although the strain fields showed great variation between specimens, they had some consistent features. The near-tip E xx concentrations in circumferential and radial specimens tended to be small and subtle, extending approximately 0.5 mm from the crack. In radial specimens, the near-tip E xx concentrations sometimes (5/17 tests) grew to extend across the specimen as s approached s u and as rupture progressed from the crack tip. Near-tip E xy concentrations in both circumferential and radial specimens took the form of bands that extended longitudinally across 50-100% of the specimen. The crack-associated E xy bands switched sign between sides of the crack. For all strain components, strong strain concentrations tended to develop at multiple places within each specimen. E xx and E yy were on average greater near the crack tip because a strain concentration occurred there consistently across specimens, not because it was uniquely strong within each specimen. E xy concentrations, however, were more specific to the presence of a crack; in approximately one third of circumferential tests and approximately half of radial tests, the strongest and most extensive shear band was crack-associated.
To test if the cracks created unloaded regions in cracked specimens, mean strain in the cut ROI (on the crack flanks) was compared to the intact ROI (figure 7; also plotted as an attenuation ratio in electronic supplementary material, figure S1). Mean E xx in the cut ROI was significantly less than in the intact ROI for all crack groups at all stress levels. In edge crack specimens, both circumferential and radial, this effect almost completely abolished E xx in the cut ROI. Mean E yy in the cut ROI in circumferential specimens was not significantly different from the intact ROI, but in radial specimens it was significantly greater than in the intact ROI. Mean jE xy j in the cut ROI of circumferential edge and centre crack specimens was less than in the intact ROI, whereas in radial specimens it was greater. As E xx is the strain component most directly related to longitudinal stress, the large reductions in the cut ROIs' mean E xx values indicate that the crack unloaded the cut ROI.

Rupture morphology
Rupture morphology of cracked specimens, particularly whether rupture occurred by crack growth, was summarized to support interpretation regarding rupture mechanisms. Rupture in the circumferential edge crack specimens proceeded predominantly by inter-fascicle sliding, creating broad, irregular ruptures with extensive interdigitating fibre pull-out (as in figure 8a). In 13 out of 14 circumferential   edge crack tests, the region near the crack tip was the first to display visible rupture, but the crack blunted rapidly by inter-fascicle shear (figure 8b) and final rupture occurred simultaneously over a broad region. Crack blunting by inter-fascicle shear began very early in the test, between 0.2s u and 0.5s u . Rupture in circumferential centre crack specimens occurred similarly, except that the ruptures at the crack tip were smaller and developed in parallel with separate sites of rupture at the grip line (five tests) or specimen edge (nine tests). These separate sites of rupture typically joined the crack-associated rupture as they grew (10 tests; figure 8c). Inter-fascicle shear was ubiquitous in both edge and centre crack circumferential specimens, and often caused the rupture line to zigzag across the specimen between zones of interdigitating fibre pull-out; a striking example is shown in figure 8d.
Radial specimens, unlike circumferential specimens, sometimes displayed crack growth (incremental, local rupture growing from the crack tip) (figure 8e). In 9/17 radial tests, the crack tip-associated rupture grew incrementally such that total rupture occurred by crack growth. In five of these nine tests, a separate site of rupture developed away from the crack in parallel with the crack growth. Crack growth did not begin until strain approximately reached 1 u + 0.21 u . The 8/17 radial tests with no sign of crack growth ruptured such that the site of rupture touched the crack in three tests (figure 8f) and was away from the crack in five tests. Most (16/17) radial tests had some degree of local rupture at the crack tip even if this did not translate into crack growth. Regardless of the type of rupture, the rupture site was bridged by small fibres (figures 8e,f). Although in the circumferential specimens, the fascicle interfaces appeared to facilitate the formation of shear bands, in the radial specimens they appeared to facilitate incremental crack growth.
The effect of a crack on the type of rupture (midsubstance, mixed and grip line) was examined by comparing counts of rupture types between cracked specimen groups and their controls (table 2).      furthermore, to determine whether a crack alters the strain field by creating a near-tip strain concentration and an unloaded region in the cut material on either side of the crack. No reduction in ultimate stress in cracked specimens was detected relative to controls (figure 3), indicating that limit stress analysis is appropriate for failure analysis, and that fracture mechanics analysis is not required, in the tested conditions. Since the study was adequately powered to detect a meaningful (approx. 1 s.d.) decrease in ultimate stress, these results are robust evidence for preservation of ultimate stress in the presence of a short crack. Regarding strain concentrations, greater tissue strain was observed near the crack tip (figure 5), implying the existence of a corresponding near-tip stress concentration. Consistent with the presence of near-tip strain concentrations, the region containing material cut by the crack (the cut ROI) had reduced strain, implying that it was partially unloaded (figure 7). Although the alterations in the strain field did not measurably influence the meniscus' rupture in terms of the overall stress-strain curve, the near-tip stress concentration does pose a risk of sub-rupture local tissue damage.

Significance of preservation of ultimate stress
The preservation of ultimate stress in cracked specimens and the tendency for ruptures to occur simultaneously through the entire cross-section implies a high degree of resistance to crack growth (fracture toughness). Although half of radial specimens exhibited crack growth, this occurred at or past the ultimate stress point, by which time rupture was well underway by other mechanisms. There was no evidence of unstable crack growth. This crack growth may, therefore, be considered incidental, similar to the final fracture of a highly tough and ductile test piece [25]. High fracture toughness is desirable for meniscus because the maintenance of strength, despite the presence of a crack, lessens the risk of further failure and loss of function. Note that a crack will still reduce the cross-sectional area and, in proportion, the total force that the meniscus can support. However, the present study's circumferential circumferential circumferential circumferential radial radial results indicate that short (approx. 3 mm) tears in single-cycle loading are unlikely to accelerate failure by crack growth. Longer cracks, in principle, produce stronger stress concentrations. In vivo meniscus tears that are considered to definitely require clinical treatment are 5 to 25 mm long [15,[20][21][22]. These tears may exceed the critical crack length for fracture mechanics-dominant rupture (i.e. fracture) [73]. However, the apparently low risk associated with a short (natural) tear is still beneficial because it should delay the growth of the tear to a critical size. Attempts to replace meniscus tissue with engineered materials should consider replication of the meniscus' fracture toughness as a design requirement. This assessment of low risk for a short meniscus tear has caveats, as it is based on excised tissue tests with test conditions that were, by necessity, artificial. Specimen size and hence crack length was small, only edge and centre cracks were examined, specimens were cut only from the centre of the meniscus, specimens were loaded only in circumferential and radial uniaxial tension, cutting specimens may cause loss of fibre integrity, the loading rate was relatively slow (0.5 mm s 21 ), and unlike the natural enthesis tensile grips work by compression and friction rather than by individually anchoring each fibre. Use of dead and previously frozen tissue could also in principle have affected the results, although prior work indicates that freezing has a small (approx. 10%) or no effect on fibrous soft tissue properties, and it has not been shown to alter their fundamental mechanical behaviour [74][75][76][77][78][79][80][81][82][83]. In vivo, tears come in a wide variety of geometries and the meniscus is subjected to surface contact and multiaxial, heterogeneous stress [36,37,41,55,[84][85][86][87]. Considerable work remains to develop laboratory test methods that reproduce the wide variety of loading conditions under which the meniscus must function in vivo, and to quantify damage and failure in those conditions. Pending development of more advanced methods, however, the present results support a low risk of total rupture due to short tears.

Significance of crack tip strain concentrations
Although cracks did not decrease the meniscus specimens' ultimate stress, they did create regions of greater strain near their tips. These strain concentrations were substantial. Depending on the test scenario and stress level, mean longitudinal strain was increased by 20% to 50% and mean shear strain magnitude was increased by 20% to 80% (figure 5). Groups with more complete unloading of the cut ROI (circumferential and radial edge crack specimens) also had greater near-tip E xx concentrations, consistent with load redistribution around the crack being the cause of the strain concentrations. This near-tip overstrain has potential to cause local damage and failure under normal load levels. Damage is generally reported to begin at 0.05-0.08 strain in tendon and ligament [88 -91], with one study showing a damage threshold of approximately 0.02 strain [92], but thresholds for damage or permanent deformation are not known for meniscus. If the meniscus is similar to tendon and ligament, the stress threshold at which a crack makes meniscus tissue vulnerable to damage would be 25 -50% of its tensile strength; that is, 9-17 MPa. At these stress levels, crack blunting via inter-fascicle shear was prevalent in circumferential edge and centre crack specimens and rupture from the crack tip along fascicle boundaries was prevalent in circumferential edge crack specimens. These findings indicate that the near-tip shear concentrations facilitated sliding and rupture at the fascicle interfaces. Furthermore, the existence of zones of weakness near the tips of natural meniscus tears suggests that damage due to strain concentrations also occurs in vivo [21]. Local strain concentrations created by cracks in meniscus tissue, therefore, pose a high risk of causing local, subrupture damage.

Combined interpretation of preservation of ultimate stress and strain concentrations
The preservation of ultimate stress and general lack of crack growth in cracked meniscus tissue stands in contrast to the high risk of local damage due to strain concentrations near the crack tip. These risks may have an inherent trade-off. Fracture toughness represents the energy required for crack growth. Local energy dissipation around the crack tip (in the process region) increases fracture toughness [23,26]. The observed near-tip zone of local overstrain and probable damage may function as a dissipative zone, with the function of increasing toughness and limiting crack growth. Inter-fascicle shear, which was especially strong in circumferential specimens, may increase the meniscus' toughness by absorbing energy through fascicle sliding. Inter-fascicle sliding also deflects the path of rupture along fascicle boundaries (e.g. figure 8d ), which due to the circumferential specimens' geometry promotes rupture by processes other than mode I crack opening and crack growth. In radial specimens, the parallel alignment of the fascicles and the crack prevented fascicle sliding from acting as a crack rsos.royalsocietypublishing.org R. Soc. open sci. 5: 181166 deflection mechanism, which is probably why half of radial specimens exhibited crack growth, albeit still without measurable impact on ultimate stress. The roles of local damage, plasticity and crack deflection as toughening mechanisms in the meniscus warrant further investigation.
Strain concentrations near the tip of a meniscus tear, when subjected to long-term repeated loading, may cause incremental accumulation of damage and failure. In the circumferential tests, shear strain concentrations extended 5-10 mm from the crack tip along fascicle boundaries and were halted by the grip line. In vivo they would not be restricted in this manner and hence could provide a path for progressive growth of circumferential, bucket handle, vertical, or horizontal tears [55,85,93,94]. A strain concentration may also kill or damage cells even in a single loading cycle. In ligament, cell death has been shown to follow a linear no-threshold relationship with applied strain [88]. A meniscus tear is also likely to cause regional unloading as observed here for artificial cracks (figure 7), which may lead to pathology due to cells' dependence on load to maintain homeostasis [95 -97]. Altered cell loading and incremental accumulation of tissue and cell damage may mediate long-term development of in vivo meniscus pathology.

Increased tangent modulus and yield stress in edge crack circumferential tests
The observation of greater tangent modulus and yield stress in edge crack circumferential tests compared to controls (figure 3) was unexpected and its cause is indeterminate. One possibility is that it occurred by chance; i.e. that it is a type I statistical error. A second possibility is that the inner margin of a circumferential specimen has an effective stiffness less than the outer margin. If so, the edge crack, by eliminating the low-stiffness inner margin from the intact cross section, would cause the average modulus to increase. A lesser effective stiffness in the inner margin implies that the ultimate stress for circumferential edge crack specimens should have also increased; this is neither confirmed nor ruled out by the data ( p ¼ 0.07, post hoc two-tailed t-test). A lesser effective stiffness in the inner margin of circumferential specimens, if present, could have been caused by differences between the inner and outer margins in either (a) material properties or (b) fascicle loading.
The meniscus' material properties, specifically tissue composition and stiffness, have been observed to vary with radial position in the meniscus [55,93,98 -100]. However, these comparisons were of the outer, central and inner thirds, and the specimens in the present study were all cut from the central third. Electron microscopy and histology show homogeneous composition in the central third [101,102]. There is no prior evidence that the inner margin of specimens in the present study should have significantly different material properties from the rest of the specimen. The observation of greater tangent modulus and yield stress in edge crack circumferential specimens is therefore unlikely to have been caused by variation in material properties with radial position.
A reduction in fascicle loading within the inner margin of circumferential specimens could have been caused by the specimens' geometry. The meniscus' fascicles are aligned in arcs, but the specimens' edges were straight. A portion of the inner margin's fascicles were therefore discontinuous with the gripped region and were loaded indirectly by inter-fascicle shear. The fascicle interfaces are apparently compliant and shear readily (figures 6 and 8b), so load transfer to the discontinuous fascicles is likely to be slight. This effect has been quantified in annulus fibrosus and tendon [33,103]. The inner margin's fascicles may, therefore, be relatively unloaded, contributing little to the stiffness of the specimen. Unloading of inner margin fascicles would artificially decrease the average modulus in circumferential control and centre crack specimens, which have an intact inner edge, but not in edge crack specimens because the crack eliminates these inner margin fascicles from the load-bearing cross-sectional area.
The potential for fascicle unloading due to the mismatch between straight sides of conventional tensile test specimens and their arced fascicle geometry deserves further investigation. Interactions between specimen geometry and fibre continuity have been previously shown to alter the meniscus' apparent tensile properties [43], prompting the use of expanded grip regions. However, the present tangent modulus and yield stress results suggest that the meniscus' arced fascicle architecture remains a challenge. In vivo, the meniscus' entheses probably provide much more efficacious fibre loading than is currently possible in laboratory tests.

In vivo tear growth and future directions
The general lack of crack growth observed in this study, especially in the circumferential tension tests, leaves the mechanisms by which meniscus tears grow in vivo uncertain. In particular, it would be very useful to resolve uncertainty regarding the duration for which a short in vivo meniscus tear can rsos.royalsocietypublishing.org R. Soc. open sci. 5: 181166 be expected to remain short and hence low-risk. The observation of crack growth along fascicle boundaries in half of the radial specimens suggests that meniscus microstructure is important, although many in vivo tears do cross fascicles. Age and pre-existing degeneration may also contribute to tear formation and growth [104]. Age . 60 years is a moderate risk factor (OR ¼ 1.8 2 3.0) for meniscus tears, although they afflict patients of all ages [105][106][107][108]. High cycle loading, as has recently been undertaken for crack-free meniscus [44], is an especially promising approach. Loading rate is another potentially important factor. With greater strain rates, the meniscus is known to stiffen in compression [109,110] and possibly also in tension [111]. Meniscus tears often occur in the context of sports, implying involvement of high-rate loading [7,108], and ex vivo impact testing of rabbit knees has produced meniscus tears [112,113]. It is possible that a high-rate loading cycle (as would be expected from an impact) can produce a long (5-25 mm) tear of clinical concern immediately, without slow growth from a low-risk short tear. Although the focus of this study was on tensile loading, examining the behaviour of meniscus cracks under shear is also a promising direction for soft tissue [26,71,114]. The central task for future experiments is to produce physiologic growth of cracks under controlled laboratory conditions so that the mechanisms and time course of this pathology can be quantified.
Data accessibility. The underlying data for all results are available, hosted on the Open Science Framework, under a CC-BY license [115].