Transonic and Supershear Crack Propagation Driven by Geometric Nonlinearities.

Linear elastic fracture mechanics theory predicts that the speed of crack growth is limited by the Rayleigh wave speed. Although many experimental observations and numerical simulations have supported this prediction, some exceptions have raised questions about its validity. The underlying reasons for these discrepancies and the precise limiting speed of dynamic cracks remain unknown. Here, we demonstrate that tensile (mode I) cracks can exceed the Rayleigh wave speed and propagate at supershear speeds. We show that taking into account geometric nonlinearities, inherent in most materials, is sufficient to enable such propagation modes. These geometric nonlinearities modify the crack-tip singularity, resulting in different crack-tip opening displacements, cohesive zone behavior, and energy flows towards the crack tip.

Earthquake energy dissipation in a fracture mechanics framework.

Earthquakes are rupture-like processes that propagate along tectonic faults and cause seismic waves. The propagation speed and final area of the rupture, which determine an earthquake's potential impact, are directly related to the nature and quantity of the energy dissipation involved in the rupture process. Here, we present the challenges associated with defining and measuring the energy dissipation in laboratory and natural earthquakes across many scales. We discuss the importance and implications of distinguishing between energy dissipation that occurs close to and far behind the rupture tip, and we identify open scientific questions related to a consistent modeling framework for earthquake physics that extends beyond classical Linear Elastic Fracture Mechanics.

Collective relational inference for learning heterogeneous interactions.

Interacting systems are ubiquitous in nature and engineering, ranging from particle dynamics in physics to functionally connected brain regions. Revealing interaction laws is of fundamental importance but also particularly challenging due to underlying configurational complexities. These challenges become exacerbated for heterogeneous systems that are prevalent in reality, where multiple interaction types coexist simultaneously and relational inference is required. Here, we propose a probabilistic method for relational inference, which possesses two distinctive characteristics compared to existing methods. First, it infers the interaction types of different edges collectively by explicitly encoding the correlation among incoming interactions with a joint distribution, and second, it allows handling systems with variable topological structure over time. We evaluate the proposed methodology across several benchmark datasets and demonstrate that it outperforms existing methods in accurately inferring interaction types. The developed methodology constitutes a key element for understanding interacting systems and may find application in graph structure learning.

Mineral and cross-linking in collagen fibrils: The mechanical behavior of bone tissue at the nano-scale.

The mineralized collagen fibril is the main building block of hard tissues and it directly affects the macroscopic mechanics of biological tissues such as bone. The mechanical behavior of the fibril itself is determined by its structure: the content of collagen molecules, minerals, and cross-links, and the mechanical interactions and properties of these components. Advanced-Glycation-Endproducts (AGEs) cross-linking between tropocollagen molecules within the collagen fibril is one important factor that is believed to have a major influence on the tissue. For instance, it has been shown that brittleness in bone correlates with increased AGEs densities. However, the underlying nano-scale mechanisms within the mineralized collagen fibril remain unknown. Here, we study the effect of mineral and AGEs cross-linking on fibril deformation and fracture behavior by performing destructive tensile tests using coarse-grained molecular dynamics simulations. Our results demonstrate that after exceeding a critical content of mineral, it induces stiffening of the collagen fibril at high strain levels. We show that mineral morphology and location affect collagen fibril mechanics: The mineral content at which this stiffening occurs depends on the mineral's location and morphology. Further, both, increasing AGEs density and mineral content lead to stiffening and increased peak stresses. At low mineral contents, the mechanical response of the fibril is dominated by the AGEs, while at high mineral contents, the mineral itself determines fibril mechanics.

Advanced-Glycation Endproducts: How cross-linking properties affect the collagen fibril behavior.

Advanced-Glycation-Endproducts (AGEs) are known to be a major cause of impaired tissue material properties. In collagen fibrils, which constitute a major building component of human tissue, these AGEs appear as fibrillar cross-links. It has been shown that when AGEs accumulate in collagen fibrils, a process often caused by diabetes and aging, the mechanical properties of the collagen fibril are altered. However, current knowledge about the mechanical properties of different types of AGEs, and their quantity in collagen fibrils is limited owing to the scarcity of available experimental data. Consequently, the precise relationship between the nano-scale cross-link properties, which differ from type to type, their density in collagen fibrils, and the mechanical properties of the collagen fibrils at larger scales remains poorly understood. In our study, we use coarse-grained molecular dynamics simulations and perform destructive tensile tests on collagen fibrils to evaluate the effect of different cross-link densities and their mechanical properties on collagen fibril deformation and fracture behavior. We observe that the collagen fibril stiffens at high strain levels when either the AGEs density or the loading energy capacity of AGEs are increased. Based on our results, we demonstrate that this stiffening is caused by a mechanism that favors energy absorption via stretching rather than inter-molecular sliding. Hence, in these cross-linked collagen fibrils, the absorbed energy is stored rather than dissipated through friction, resulting in brittle fracture upon fibrillar failure. Further, by varying multiple AGEs nano-scale parameters, we show that the AGEs loading energy capacity is, aside from their density in the fibril, the unique factor determining the effect of different types of AGEs on the mechanical behavior of collagen fibrils. Our results show that knowing AGEs properties is crucial for a better understanding of the nano-scale origin of impaired tissue behavior. We further suggest that future experimental investigations should focus on the quantification of the loading energy capacity of AGEs as a key property for their influence on collagen fibrils.

Effect of non-enzymatic glycation on collagen nanoscale mechanisms in diabetic and age-related bone fragility.

Age and diabetes have long been known to induce an oxidative reaction between glucose and collagen, leading to the accumulation of advanced glycation end-products (AGEs) cross-links in collagenous tissues. More recently, AGEs content has been related to loss of bone quality, independent of bone mass, and increased fracture risk with aging and diabetes. Loss of bone quality is mostly attributed to changes in material properties, structural organization, or cellular remodeling. Though all these factors play a role in bone fragility disease, some common recurring patterns can be found between diabetic and age-related bone fragility. The main pattern we will discuss in this viewpoint is the increase of fibrillar collagen stiffness and loss of collagen-induced plasticity with AGE accumulation. This study focused on recent related experimental studies and discusses the correlation between fluorescent AGEs content at the molecular and fibrillar scales, collagen deformation mechanisms at the nanoscale, and resistance to bone fracture at the macroscale.

Advanced-Glycation Endproducts: How cross-linking properties affect the collagen fibril behavior.

Advanced-Glycation-Endproducts (AGEs) are known to be a major cause of impaired tissue material properties. In collagen fibrils, which constitute a major building component of human tissue, these AGEs appear as fibrillar cross-links. It has been shown that when AGEs accumulate in collagen fibrils, a process often caused by diabetes and aging, the mechanical properties of the collagen fibril are altered. However, current knowledge about the mechanical properties of different types of AGEs, and their quantity in collagen fibrils is limited owing to the scarcity of available experimental data. Consequently, the precise relationship between the nano-scale cross-link properties, which differ from type to type, their density in collagen fibrils, and the mechanical properties of the collagen fibrils at larger scales remains poorly understood. In our study, we use coarse-grained molecular dynamics simulations and perform destructive tensile tests on collagen fibrils to evaluate the effect of different cross-link densities and their mechanical properties on collagen fibril deformation and fracture behavior. We observe that the collagen fibril stiffens at high strain levels when either the AGEs density or the loading energy capacity of AGEs are increased. Based on our results, we demonstrate that this stiffening is caused by a mechanism that favors energy absorption via stretching rather than inter-molecular sliding. Hence, in these cross-linked collagen fibrils, the absorbed energy is stored rather than dissipated through friction, resulting in brittle fracture upon fibrillar failure. Further, by varying multiple AGEs nano-scale parameters, we show that the AGEs loading energy capacity is, aside from their density in the fibril, the unique factor determining the effect of different types of AGEs on the mechanical behavior of collagen fibrils. Our results show that knowing AGEs properties is crucial for a better understanding of the nano-scale origin of impaired tissue behavior. We further suggest that future experimental investigations should focus on the quantification of the loading energy capacity of AGEs as a key property for their influence on collagen fibrils.

The influence of AGEs and enzymatic cross-links on the mechanical properties of collagen fibrils.

Collagen, one of the main building blocks for various tissues, derives its mechanical properties directly from its structure of cross-linked tropocollagen molecules. The cross-links are considered to be a key component of collagen fibrils as they can change the fibrillar behavior in various ways. For instance, enzymatic cross-links (ECLs), one particular type of cross-links, are known for stabilizing the structure of the fibril and improving material properties, while cross-linking AGEs (Advanced-Glycation Endproducts) have been shown to accumulate and impair the mechanical properties of collageneous tissues. However, the reasons for whether and how a given type of cross-link improves or impairs the material properties remain unknown, and the exact relationship between the cross-link properties and density, and the fibrillar behavior is still not well understood. Here, we use coarse-grained steered molecular models to evaluate the effect of AGEs and ECLs cross-links content on the deformation and failure properties of collagen fibrils. Our simulations show that the collagen fibrils stiffen at high strain levels when the AGEs content exceeds a critical value. In addition, the strength of the fibril increases with AGEs accumulation. By analyzing the forces within the different types of cross-links (AGEs and ECLs) as well as their failure, we demonstrate that a change of deformation mechanism is at the origin of these observations. A high AGEs content reinforces force transfer through AGEs cross-links rather than through friction between sliding tropocollagen molecules, which leads to failure by breaking of bonds within the tropocollagen molecules. We show that this failure mechanism, which is associated with lower energy dissipation, results in more abrupt failure of the collagen fibril. Our results provide a direct and causal link between increased AGEs content, inhibited intra-fibrillar sliding, increased stiffness, and abrupt fibril fracture. Therefore, they explain the mechanical origin of bone brittleness as commonly observed in elderly and diabetic populations. Our findings contribute to a better understanding of the mechanisms underlying impaired tissue behavior due to elevated AGEs content and could enable targeted measures regarding the reduction of specific collagen cross-linking levels.

The influence of AGEs and enzymatic cross-links on the mechanical properties of collagen fibrils.

Cross-links are considered to be a key component of collagen fibrils as they can change the fibrillar behavior in various ways. Advanced-Glycation Endproducts (AGEs), one particular type of cross-links, have been shown to accumulate and impair the mechanical properties of collageneous tissues, whereas enzymatic cross-links (ECLs) are known for stabilizing the structure of the fibril. However, the reasons for whether a given type of cross-link improves or impairs the material properties remain unknown. Here, we use coarse-grained steered molecular models to evaluate the effect of AGEs and ECLs cross-links content on the deformation and failure properties of collagen fibrils. Our simulations show that the collagen fibrils stiffen at high strain levels when the AGEs content exceeds a critical value. In addition, the strength of the fibril increases with AGEs accumulation. By analyzing the forces within the different types of cross-links (AGEs and ECLs) as well as their failure, we demonstrate that a change of deformation mechanism is at the origin of these observations. A high AGEs content reinforces force transfer through AGEs cross-links rather than through friction between sliding tropocollagen molecules. We show that this failure mechanism, which is associated with lower energy dissipation, results in more abrupt failure of the collagen fibril. Our results provide a direct and causal link between increased AGEs content, inhibited intra-fibrillar sliding, increased stiffness, and abrupt fibril fracture. Therefore, they explain the mechanical origin of bone brittleness as commonly observed in elderly and diabetic populations. Our findings contribute to a better understanding of the mechanisms underlying impaired tissue behaviour due to elevated AGEs content and could enable targeted measures regarding the reduction of specific collagen cross-linking levels.

Creep fronts and complexity in laboratory earthquake sequences illuminate delayed earthquake triggering.

Earthquakes occur in clusters or sequences that arise from complex triggering mechanisms, but direct measurement of the slow subsurface slip responsible for delayed triggering is rarely possible. We investigate the origins of complexity and its relationship to heterogeneity using an experimental fault with two dominant seismic asperities. The fault is composed of quartz powder, a material common to natural faults, sandwiched between 760 mm long polymer blocks that deform the way 10 meters of rock would behave. We observe periodic repeating earthquakes that transition into aperiodic and complex sequences of fast and slow events. Neighboring earthquakes communicate via migrating slow slip, which resembles creep fronts observed in numerical simulations and on tectonic faults. Utilizing both local stress measurements and numerical simulations, we observe that the speed and strength of creep fronts are highly sensitive to fault stress levels left behind by previous earthquakes, and may serve as on-fault stress meters.

Earthquake breakdown energy scaling despite constant fracture energy.

In the quest to determine fault weakening processes that govern earthquake mechanics, it is common to infer the earthquake breakdown energy from seismological measurements. Breakdown energy is observed to scale with slip, which is often attributed to enhanced fault weakening with continued slip or at high slip rates, possibly caused by flash heating and thermal pressurization. However, seismologically inferred breakdown energy varies by more than six orders of magnitude and is frequently found to be negative-valued. This casts doubts about the common interpretation that breakdown energy is a proxy for the fracture energy, a material property which must be positive-valued and is generally observed to be relatively scale independent. Here, we present a dynamic model that demonstrates that breakdown energy scaling can occur despite constant fracture energy and does not require thermal pressurization or other enhanced weakening. Instead, earthquake breakdown energy scaling occurs simply due to scale-invariant stress drop overshoot, which may be affected more directly by the overall rupture mode - crack-like or pulse-like - rather than from a specific slip-weakening relationship.

Learning physics-consistent particle interactions.

Interacting particle systems play a key role in science and engineering. Access to the governing particle interaction law is fundamental for a complete understanding of such systems. However, the inherent system complexity keeps the particle interaction hidden in many cases. Machine learning methods have the potential to learn the behavior of interacting particle systems by combining experiments with data analysis methods. However, most existing algorithms focus on learning the kinetics at the particle level. Learning pairwise interaction, e.g., pairwise force or pairwise potential energy, remains an open challenge. Here, we propose an algorithm that adapts the Graph Networks framework, which contains an edge part to learn the pairwise interaction and a node part to model the dynamics at particle level. Different from existing approaches that use neural networks in both parts, we design a deterministic operator in the node part that allows to precisely infer the pairwise interactions that are consistent with underlying physical laws by only being trained to predict the particle acceleration. We test the proposed methodology on multiple datasets and demonstrate that it achieves superior performance in inferring correctly the pairwise interactions while also being consistent with the underlying physics on all the datasets. While the previously proposed approaches are able to be applied as simulators, they fail to infer physically consistent particle interactions that satisfy Newton's laws. Moreover, the proposed physics-induced graph network for particle interaction also outperforms the other baseline models in terms of generalization ability to larger systems and robustness to significant levels of noise. The developed methodology can support a better understanding and discovery of the underlying particle interaction laws, and hence, guide the design of materials with targeted properties.

Effective Toughness of Heterogeneous Materials with Rate-Dependent Fracture Energy.

We investigate the dynamic fracture of heterogeneous materials experimentally by measuring displacement fields as a rupture propagates through a periodic array of obstacles of controlled fracture energy. Our measurements demonstrate the applicability of the classical equation of motion of cracks at a discontinuity of fracture energy: the crack speed jumps at the entrance and exit of an obstacle, as predicted by the crack-tip energy balance within the brittle fracture framework. The speed jump amplitude is governed by the fracture energy contrast and by the combination of the rate dependency of the fracture energy and the inertia of the medium, which allows the crack to cross a fracture energy discontinuity at a constant energy release rate. This discontinuous dynamics and the rate dependence cause higher effective toughness, which governs the coarse-grained behavior of these cracks.

The onset of the frictional motion of dissimilar materials.

Frictional motion between contacting bodies is governed by propagating rupture fronts that are essentially earthquakes. These fronts break the contacts composing the interface separating the bodies to enable their relative motion. The most general type of frictional motion takes place when the two bodies are not identical. Within these so-called bimaterial interfaces, the onset of frictional motion is often mediated by highly localized rupture fronts, called slip pulses. Here, we show how this unique rupture mode develops, evolves, and changes the character of the interface's behavior. Bimaterial slip pulses initiate as "subshear" cracks (slower than shear waves) that transition to developed slip pulses where normal stresses almost vanish at their leading edge. The observed slip pulses propagate solely within a narrow range of "transonic" velocities, bounded between the shear wave velocity of the softer material and a limiting velocity. We derive analytic solutions for both subshear cracks and the leading edge of slip pulses. These solutions both provide an excellent description of our experimental measurements and quantitatively explain slip pulses' limiting velocities. We furthermore find that frictional coupling between local normal stress variations and frictional resistance actually promotes the interface separation that is critical for slip-pulse localization. These results provide a full picture of slip-pulse formation and structure that is important for our fundamental understanding of both earthquake motion and the most general types of frictional processes.

The equation of motion for supershear frictional rupture fronts.

The rupture fronts that mediate the onset of frictional sliding may propagate at speeds below the Rayleigh wave speed or may surpass the shear wave speed and approach the longitudinal wave speed. While the conditions for the transition from sub-Rayleigh to supershear propagation have been studied extensively, little is known about what dictates supershear rupture speeds and how the interplay between the stresses that drive propagation and interface properties that resist motion affects them. By combining laboratory experiments and numerical simulations that reflect natural earthquakes, we find that supershear rupture propagation speeds can be predicted and described by a fracture mechanics-based equation of motion. This equation of motion quantitatively predicts rupture speeds, with the velocity selection dictated by the interface properties and stress. Our results reveal a critical rupture length, analogous to Griffith's length for sub-Rayleigh cracks, below which supershear propagation is impossible. Above this critical length, supershear ruptures can exist, once excited, even for extremely low preexisting stress levels. These results significantly improve our fundamental understanding of what governs the speed of supershear earthquakes, with direct and important implications for interpreting their unique supershear seismic radiation patterns.

Impact of Patient Affect on Physician Estimate of Probability of Serious Illness and Test Ordering.

PURPOSE: The authors hypothesize patient facial affect may influence clinician pretest probability (PTP) estimate of cardiopulmonary emergency (CPE) and desire to order a computerized tomographic pulmonary angiogram (CTPA). METHOD: This prospective study was conducted at three Indiana University-affiliated hospitals in two parts: collecting videos of patients undergoing CTPA for suspected acute pulmonary embolism watching a humorous video (August 2014-April 2015) and presenting the medical histories and videos to clinicians to determine the impact of patient facial affect on physicians' PTP estimate of CPE and desire to order a CTPA (June-November 2015). Patient outcomes were adjudicated as CPE+ or CPE- by three independent reviewers. Physicians completed a standardized test of facial affect recognition, read standardized medical histories, then viewed videos of the patients' faces. Clinicians marked their PTP estimate of CPE and desire for a CTPA before and after seeing the video on a visual analog scale (VAS). RESULTS: Fifty physicians completed all 73 videos. Seeing the patient's face produced a > 10% absolute change in PTP estimate of CPE in 1,204/3,650 (33%) cases and desire for a CTPA in 1,095/3,650 (30%) cases. The mean area under the receiver operating characteristic curve for CPE estimate was 0.55 ± 0.15, and the change in CPE VAS was negatively correlated with physicians' standardized test scores (r = -0.23). CONCLUSIONS: Clinicians may use patients' faces to make clinically important inferences about presence of serious illness and need for diagnostic testing. However, these inferences may fail to align with actual patient outcomes.

Brittle Fracture Theory Predicts the Equation of Motion of Frictional Rupture Fronts.

We study rupture fronts propagating along the interface separating two bodies at the onset of frictional motion via high-temporal-resolution measurements of the real contact area and strain fields. The strain measurements provide the energy flux and dissipation at the rupture tips. We show that the classical equation of motion for brittle shear cracks, derived by balancing these quantities, well describes the velocity evolution of frictional ruptures. Our results demonstrate the extensive applicability of the dynamic brittle fracture theory to friction.

Properties of the shear stress peak radiated ahead of rapidly accelerating rupture fronts that mediate frictional slip.

We study rapidly accelerating rupture fronts at the onset of frictional motion by performing high-temporal-resolution measurements of both the real contact area and the strain fields surrounding the propagating rupture tip. We observe large-amplitude and localized shear stress peaks that precede rupture fronts and propagate at the shear-wave speed. These localized stress waves, which retain a well-defined form, are initiated during the rapid rupture acceleration phase. They transport considerable energy and are capable of nucleating a secondary supershear rupture. The amplitude of these localized waves roughly scales with the dynamic stress drop and does not decrease as long as the rupture front driving it continues to propagate. Only upon rupture arrest does decay initiate, although the stress wave both continues to propagate and retains its characteristic form. These experimental results are qualitatively described by a self-similar model: a simplified analytical solution of a suddenly expanding shear crack. Quantitative agreement with experiment is provided by realistic finite-element simulations that demonstrate that the radiated stress waves are strongly focused in the direction of the rupture front propagation and describe both their amplitude growth and spatial scaling. Our results demonstrate the extensive applicability of brittle fracture theory to fundamental understanding of friction. Implications for earthquake dynamics are discussed.

Decreased facial expression variability in patients with serious cardiopulmonary disease in the emergency care setting.

BACKGROUND AND OBJECTIVE: The hypothesis of the present work derives from clinical experience that suggests that patients who are more ill have less facial expression variability in response to emotional cues. METHODS: Prospective study of diagnostic accuracy from a convenience sample of adult patients with dyspnoea and chest pain in an emergency department. Patients viewed three stimulus slides on a laptop computer that were intended to evoke a change in facial affect. The computer simultaneously video recorded patients' facial expressions. Videos were examined by two independent blinded observers who analysed patients' facial expressions using the Facial Action Coding System (FACS). Patients were followed for predefined serious cardiopulmonary diagnosis (Disease+) within 14 days (acute coronary syndrome, pulmonary embolism, pneumonia, aortic or oesophageal disasters or new cancer). The main analysis compared total FACS scores, and action units of smile, surprise and frown between Disease+ and Disease-. RESULTS: Of 50 patients, 8 (16%) were Disease+. The two observers had 92% exact agreement on the FACS score from the first stimulus slide. During stimulus slide 1, the median of all FACS values from Disease+ patients was 3.4 (1st-3rd quartiles 1-6), significantly less than the median of 7 (3-14) from D-patients (p=0.019, Mann-Whitney U). Expression of surprise had the largest difference between Disease+ and Disease-(area under the receiver operating characteristic curve 0.75, 95% CI 0.52 to 0.87). CONCLUSIONS: With a single visual stimulus, patients with serious cardiopulmonary diseases lacked facial expression variability and surprise affect. Our preliminary findings suggest that stimulus-evoked facial expressions from emergency department patients with cardiopulmonary symptoms might be a useful component of gestalt pretest probability assessment.