Tear resistance of soft collagenous tissues

Abstract

Fracture toughness characterizes the ability of a material to maintain a certain level of strength despite the presence of a macroscopic crack. Understanding this tolerance for defects in soft collagenous tissues (SCT) has high relevance for assessing the risks of fracture after cutting, perforation or suturing. Here we investigate the peculiar toughening mechanisms of SCT through dedicated experiments and multi-scale simulations, showing that classical concepts of fracture mechanics are inadequate to quantify and explain the high defect tolerance of these materials. Our results demonstrate that SCT strength is only modestly reduced by defects as large as several millimeters. This defect tolerance is achieved despite a very narrow process zone at the crack tip and even for a network of brittle fibrils. The fracture mechanics concept of tearing energy fails in predicting failure at such defects, and its magnitude is shown to depend on the chemical potential of the liquid environment.

Fig. 1

Near field analysis of notch-like defects. a Mode I fracture test configuration: a wide and short (initial length L₀) testpiece with a preexisting notch is elongated up to failure. Soft collagenous tissue (SCT) simulations are performed with a hybrid approach, combining a continuum model (CM) in the far field of the defect and a discrete network model (DNM) in the near field. The fiber force law in the DNM is shown, with a small strain stiffness k₀ and large strain stiffness k₁ for ε > ε_s, slackness strain, and limited by a critical fiber strain of ε_c. b The global failure stretch λ_F depends on L₀ as indicated by the fiber failure behavior. c Reversibility of fiber network deformation mechanisms: nearfield morphology in the reference state, (subcritical) loading and unloading for simulations and corresponding experiments in the multiphoton microscope (MPM, scale bar: 50 μm), for which the second harmonic generation signal (SHG) is shown. d 3D reconstruction of the defect with stained cell nuclei from MPM stacks in loaded condition (scale bar: 50 μm). e Degree of fiber alignment in MPM images at the notch along the direction of loading (y) and perpendicular to it (x), reported for reference, loaded and unloaded states. f Corresponding SHG signal intensity decay in the x-direction, normalized with respect to the intensity of the far field. g Fiber strain distribution from simulations in the nearfield along x and y-direction. h Fiber alignment is determined for three superimposed images of simulations, similar as in e. Results in (e, f) are shown as mean ± standard deviation

Fig. 2

Apparent tearing energy depends on sample dimensions. a Images from mode I fracture experiments on Glisson’s capsule (GC) in reference and loaded state. b A representative force vs. relative displacement curve is shown for experiments on GC, indicating the reference state (filled circle), crack propagation (dot), catastrophic failure (cross) and the work until crack propagation U, which can be used to calculate the (apparent) tearing energy. c, d In-silico study (n = 3, in green, represented in mean and standard deviation) on the dependence of the apparent tearing energy Γ_a and the critical global elongation λ_F on the initial sample length L₀. In d, the fracture mechanics prediction of λ_F based on Γ (dashed) and the critical elongation of intact samples (n = 3, dotted) are indicated. e–h Experiments on GC (n = 6, 9, and 5 for L₀ = 2 mm, 15 mm and 30 mm, resp.) and CCC (n = 4, 4, 6, and 3 for L₀ = 1 mm, 2 mm, 15 mm and 30 mm, resp.) in which Γ_a (e, f) and λ_F (g, h) are determined for different L₀, reported as boxplots. Similarly as in d, fracture mechanics-based prediction of λ_F (based on mean Γ, dashed) and mean λ_F of intact samples (dotted) are shown in (g, h). In e–h, boxes represent upper and lower quartiles and lines inside the boxes define the median, while dots represent outliers, and whiskers 10–90 percentiles. Significant differences (p < 0.05) are indicated by * (Kruskal–Wallis)

Fig. 3

Defect tolerance of SCT and elastomers. a Biaxial tests of SCT containing a small defect: the simulated load case is illustrated, with the discrete fiber network model in the near field of the defect. b Results of the corresponding in-silico study for GC (n = 3), represented as mean and standard deviation. The computed global failure stretch λ_F is shown for different defect sizes. c The reduction of λ_F as a consequence of defects in an elastomer (Sy184) from fracture mechanics-based simulations using Γ = 80 J m⁻² . d Sy184 (in red) and GC (in green) simulations are compared using the normalized λ_F with respect to the critical elongation of intact samples. e Experimental setup of the inflation experiments, where λ_F for defects of 0.2 mm, 1 mm and 5 mm (n = 10 for each defect size) is determined. Leakage is prevented by a layer of soft elastomer material. Representative top and side images for GC are shown and a 5 mm crack is indicated (scale bar: 10 mm). Black ink markers are visible on the tissue surface which were applied to facilitate measurement of deformations (see Methods). A MPM image documents the shape of a small defect with nominal length of 0.2 mm (defect in yellow, scale bar: 100 μm). f Experimental results for GC (in blue) and Sy184 (in red) for λ_F normalized with respect to the critical elongation in uniaxial tension (n = 5 each) experiments. The trendline from simulation (dotted red and blue) is indicated and experimental data are reported in boxplots, where boxes represent upper and lower quartiles and lines inside the boxes define the median, while dots represent outliers, and whiskers 10–90 percentiles. g Experimental results for the material tearing energy $\overline{\Gamma }$ (Sy184 from ref. ) and the work to rupture W^* in uniaxial tensile (n = 5 each) experiments, represented with mean and standard deviation

Fig. 4

Analysis of suture retention strength. a Suture retention strength (SRS) test, illustrated based on the corresponding model for hybrid simulation, based on ref. . The defect is shown in yellow and the suture in black. b MPM image of a SRS experiment on GC, with SHG visualization of collagen fibers alignment. The shape of the defect is visible (in yellow, scale bar: 100 μm). c Images of suture retention strength experiments immediately before failure initiation for testpieces made of electrospun networks (polyurethane, PU), Glisson’s capsule (GC) and Sylgard184 (Sy184). Defects are highlighted in yellow, scale bar: 5 mm. d Pulling force on suture at failure initiation (BSS) as measured in SRS tests on GC (in blue, n = 5) and Sy184 (in red, n = 5). The experimental data are compared with model predictions based on fracture mechanics using Γ. The prediction based on the hybrid model approach is also reported. The dashed line corresponds to perfect agreement between experiments and computations. e BSS is normalized with respect to the critical force (F_R) measured in uniaxial tensile tests. n = 5 SRS tests and n = 5 uniaxial tests were performed for each material. Results in (d, e) are presented as mean and standard deviation. f The shape of notches in mode I fracture experiments on PU, GC, and Sy184 are shown for a state close to crack propagation (scale bar: 5 mm)

Fig. 5

Osmolarity of the liquid environment influences the toughness of SCT. a Illustration of the 3D discrete fiber network model with volumetric chemoelastic contributions used to analyze the network deformation in the nearfield of the notch. Reference and elongated states are shown, together with the volume change J vs. λ curves. b The influence of bath osmolarity on the network kinematics at the notch tip is quantified in terms of the relative fraction of fibers with a strain larger than their slackness (5%). c Schematic illustration of the experimental procedure used for the investigation of the sample specific effect of bath osmolarity on fracture behavior of SCT. GC testpieces were immersed in physiological saline solution (PS) and in distilled water (DW), were elongated up to the point of crack propagation, then unloaded, after which the bath was either changed or not, before reloading to crack propagation. d Sample-specific difference in critical stretch Δλ_F between subsequent loadings with (PS-DW, n = 5, and DW-PS, n = 5) or without (PS-PS, n = 6, and DW-DW, n = 7) bath change. e Experimentally determined tearing energy of GC in PS (n = 9) and DW (n = 5). f Suture retention strength tests on GC leading to smaller BSS in DW (n = 7) than in PS (n = 7). Results in (d–f) are presented as boxplots, where boxes represent upper and lower quartiles and lines inside the boxes define the median, while dots represent outliers, and whiskers 10–90 percentiles. Significant differences are indicated for p < 0.05 by * (Student t-test)