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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., Journal of the Mechanical Behavior of Biomedical Materials, 143, ISSN:1751-6161, ISSN:1878-0180

Topological Interlocking Structures (TIS) have been increasingly studied in the past two decades. However, some fundamental questions concerning the effects of Young’s modulus and the friction coefficient on the structural mechanics of the most common type of TIS application – centrally loaded panels – are not yet clear. Here, we present a first-of-its-kind parametric study that aims to clarify how these two parameters affect multiple aspects of the behavior and failure of centrally-loaded TIS panels. This includes the evolution of the structural response up to and including failure, the foremost structural response parameters, and the residual carrying capacity. We find that the structural response parameters in TIS panels scale linearly with Young’s modulus, that they saturate with the friction coefficient, and that the saturated response provides an upper-bound on the capacity of centrally loaded TIS panels reported in the literature. This, together with additional findings, insights, and observations, comprise a novel contribution to our understanding of the interlocked structural form., International Journal of Solids and Structures, 269, ISSN:0020-7683, ISSN:1879-2146

The failure of heterogeneous materials with microstructures is a complex process of damage nucleation, growth and localisation. This process spans multiple length scales and is challenging to simulate numerically due to its high computational cost. One option is to use domain decomposed multi-scale methods with dynamical refinement. If needed, these methods refine coarse regions into a fine-scale representation to explicitly model the damage in the microstructure. However, damage evolution is commonly restricted to fine-scale regions only. Thus, they are unable to capture the full complexity and breath of the degradation process in the material. In this contribution, a generic procedure that allows to account for damage in all representations is proposed. The approach combines a specially designed orthotropic damage law, with a scheme to generate pre-damaged fine-scale microstructures. Results indicate that the damage approximation for the coarse representation works well. Furthermore, the generated fine-scale damage patterns are overall consistent with explicitly simulated damage patterns. Minor discrepancies occur in the generation but subsequently vanish when explicit damage evolution continuous; for instance under increased load. The presented approach provides a methodological basis for adaptive multi-scale simulation schemes with consistent damage evolution., European Journal of Mechanics. A, Solids, 100, ISSN:0997-7538, ISSN:1873-7285

SUMMARY Earthquake ruptures are generally considered to be cracks that propagate as fracture or frictional slip on pre-existing faults. Crack models have been used to describe the spatial distribution of fault offset and the associated static stress changes along a fault, and have implications for friction evolution and the underlying physics of rupture processes. However, field measurements that could help refine idealized crack models are rare. Here, we describe large-scale laboratory earthquake experiments, where all rupture processes were contained within a 3-m long saw-cut granite fault, and we propose an analytical crack model that fits our measurements. Similar to natural earthquakes, laboratory measurements show coseismic slip that gradually tapers near the rupture tips. Measured stress changes show roughly constant stress drop in the centre of the ruptured region, a maximum stress increase near the rupture tips and a smooth transition in between, in a region we describe as the earthquake arrest zone. The proposed model generalizes the widely used elliptical crack model by adding gradually tapered slip at the ends of the rupture. Different from the cohesive zone described by fracture mechanics, we propose that the transition in stress changes and the corresponding linear taper observed in the earthquake arrest zone are the result of rupture termination conditions primarily controlled by the initial stress distribution. It is the heterogeneous initial stress distribution that controls the arrest of laboratory earthquakes, and the features of static stress changes. We also performed dynamic rupture simulations that confirm how arrest conditions can affect slip taper and static stress changes. If applicable to larger natural earthquakes, this distinction between an earthquake arrest zone (that depends on stress conditions) and a cohesive zone (that depends primarily on strength evolution) has important implications for how seismic observations of earthquake fracture energy should be interpreted.

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 onset of frictional sliding between contacting bodies under shear load is nucleated by the quasi-static growth of localized slip patches. After reaching a certain critical size, known as the nucleation length, these patches become unstable and continue growing dynamically, eventually causing the sliding of the entire interface. Two different theories have been used to compute the nucleation length of such patches depending on the dominant process driving their growth. If it is only the yielding of contact asperities (large-scale yielding), a stress criterion is applied, based on linear stability analysis, whereas if fracture dominates (small-scale yielding), an energy criterion is applied (Griffith’s criterion), based on fracture mechanics and classical nucleation theory. Both approaches contain important underlying assumptions that are well-suited to describe either one situation or the other. However, what happens in-between is not captured by any of them. In this work, we use numerical simulations to study what is the dominant underlying process driving nucleation for different conditions of heterogeneity in the frictional strength of the interface and what are the implications for nucleation dynamics and the onset of frictional sliding. We show that large frictional heterogeneities enable a transition from a yielding-driven nucleation phase to a fracture-driven one. This transition occurs only above a certain level of heterogeneity and can either be quasi-static (stable) or dynamic (unstable), depending on the correlation length of frictional strength along the interface and the difference in strength between the strongest and the weakest point (the amplitude). Unstable transitions generate localized dynamic slip events, whose magnitude increases with higher correlation length and decreases with larger amplitude. Our work sheds new light on the role of heterogeneity and fracture in the nucleation of frictional slip, bridging the gap between the two main governing theories for nucleation., Journal of the Mechanics and Physics of Solids, 173, ISSN:0022-5096, ISSN:1873-4782

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., PNAS Nexus, 1 (5), ISSN:2752-6542

Topologically interlocked structures are architectured by fitting together blocks that are constrained geometrically through contact and friction by their neighboring blocks. As long as the frictional strength is nowhere exceeded, the blocks stick against each other, allowing for large rotations. Once the interfacial stresses exceed the frictional strength, relative sliding between the blocks alters the structure’s mechanical response. Improving the structural performance, precisely the strength and the toughness, has been one of the main focal points in the literature. However, many fundamental questions regarding the role and effect of the interface mechanisms (stick and slip) and rotation of the blocks have not been addressed yet. Here, we carry out a parametric analysis to understand the effect of Young’s modulus, friction coefficient, and geometry of the blocks on the dominance of the stick or slip-governed mechanism. We combine analytical and computational tools to analyze the failure mechanisms and the response capacities of beam-like topologically interlocked structures. This is achieved using the finite element method coupled with a penalty-based approach for enforcing contact constraints along interfaces. We show that the combination of the structure’s height and the friction coefficient controls whether the failure mechanism is slip-governed or stick-governed. Furthermore, we demonstrate that the sticking mechanism across all interfaces along with the rotation of the blocks dictates a saturation level to the mechanical performance of a given structure irrespective of geometric and material properties. This provides a theoretical upper bound for the structural response of topologically interlocked structures and establishes a theoretical benchmark of achievable performance., International Journal of Solids and Structures, 259, ISSN:0020-7683, ISSN:1879-2146

The dynamics of fault ruptures in natural and laboratory earthquakes is governed by a balance of released elastic energy and dissipated local fracture energy. The latter is the result of various friction weakening processes occurring at the fault and is thus often estimated indirectly and from small-scale friction experiments. We analyze high-frequency strain measurements from large-scale laboratory earthquakes with gages positioned slightly away from a granite fault. The strain measurements present rapid fluctuations during fault rupture propagation, as was also observed in other experiments. Characteristics of these strain fluctuations are compared with fracture mechanics theory to estimate local fault properties. We determine fracture energy for secondary rupture fronts, which appear behind the main front where local slip occurred already. Measured fracture energy is consistent with indirect estimates from rupture termination in independent experiments but is orders of magnitude lower than reported values from rotary shear friction experiments, which may be due to large differences in overall slip.

Physical Review Letters, 127 (3), ISSN:0031-9007, ISSN:1079-7114

The energy dissipated during the friction weakening process at the front of an earthquake rupture, which is known as the fracture energy, is a key earthquake property. It directly affects the nucleation, propagation and arrest of earthquake ruptures, and, is therefore related to important questions, including the maximum possible size of earthquakes at a given fault section. However, estimating the fracture energy in the field is a difficult task and current approaches remain limited. In this work, we present near-fault strain measurements of large-scale laboratory earthquakes on a granite fault. The strain measurements present high-frequency fluctuations while the fault is sliding. These strain fluctuations are indicative of rupture fronts that propagate across the entire fault and occasionally reflect at the boundaries. Here, we will characterize these strain fluctuations by applying fracture-mechanics theory. We will demonstrate that the shape and time scales of the strain fluctuations are well described by the proposed analytical solution. We will further show that by fitting the amplitude of the theory to the experimental measurement, we can estimate the local fracture energy. We apply this process to determine the fracture energy for secondary rupture fronts, which appear within the sliding rupture area. The results are consistent with fracture energy estimates from laboratory-earthquake arrest experiments, but are orders of magnitude lower than reported values from small-scale rotary shear friction experiments. We will discuss the implications and potential of these observations., EGUsphere

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.

A measurement of the double-polarization observable E for the reaction $$\gamma p\rightarrow \pi ^0 p$$ γ p → π 0 p is reported. The data were taken with the CBELSA/TAPS experiment at the ELSA facility in Bonn using the Bonn frozen-spin butanol (C$$_4$$ 4 H$$_9$$ 9 OH) target, which provided longitudinally-polarized protons. Circularly-polarized photons were produced via bremsstrahlung of longitudinally-polarized electrons. The data cover the photon energy range from $$E_\gamma =600$$ E γ = 600 to 2310 MeV and nearly the complete angular range. The results are compared to and have been included in recent partial wave analyses.

Earthquake ruptures arrest due to either encountering a barrier with high fracture energy or entering unfavorable stress conditions. Our large-scale laboratory earthquake experiments use heterogeneity in initial stress to confine the rupture within a 3-m long saw-cut granite fault. All earthquake processes, i.e., initiation, propagation, and arrest, were spontaneous and contained within the simulated fault. We proposed an analytical crack model to fit our experimental measurements and to better constrain the features in the spatial distribution of both slip and stress changes. Similar to natural earthquakes, laboratory measurements show coseismic slip that gradually tapers near the rupture tips. Measured stress changes show roughly constant stress drop in the center of the ruptured region, a maximum stress increase near the rupture tips, and a smooth transition in between, in a region we describe as the earthquake arrest zone. In our experiments, the earthquake arrest zone is more than one order of magnitude wider than the cohesive zone described by fracture mechanics. We propose that the transition in stress changes and the corresponding linear taper observed in the slip distribution are the result of rupture termination conditions primarily controlled by the initial stress distribution and are not related to the fault strength evolution. We also performed dynamic rupture simulations that confirm how arrest conditions can affect slip distribution and static stress changes, especially near the tip of an arrested rupture. If applicable to larger natural earthquakes, this distinction between the earthquake arrest zone resulted from heterogeneous initial stress and a cohesive zone that depends primarily on strength evolution has important implications for how seismic observations of earthquake fracture energy should be interpreted.

The onset of frictional motion is mediated by rupture-like slip fronts, which nucleate locally and propagate eventually along the entire interface causing global sliding. The static friction coefficient is a macroscopic measure of the applied force at this particular instant when the frictional interface loses stability. However, experimental studies are known to present important scatter in the measurement of static friction; the origin of which remains unexplained. Here, we study the nucleation of local slip at interfaces with slip-weakening friction of random strength and analyze the resulting variability in the measured global strength. Using numerical simulations that solve the elastodynamic equations, we observe that multiple slip patches nucleate simultaneously, many of which are stable and grow only slowly, but one reaches a critical length and starts propagating dynamically. We show that a theoretical criterion based on a static equilibrium solution predicts quantitatively well the onset of frictional sliding. We develop an efficient Monte-Carlo model by adapting the theoretical criterion and study the variability in global strength distribution caused by the stochastic properties of local frictional strength. The results demonstrate that an increasing spatial correlation length on the interface, representing geometric imperfections and roughness, causes lower global static friction. Conversely, smaller correlation length increases the macroscopic strength while its variability decreases. We further show that randomness in local friction properties is insufficient for the existence of systematic precursory slip events. Random or systematic non-uniformity in the driving force, such as potential energy or stress drop, is required for arrested slip fronts. Our model and observations provide a necessary framework for efficient stochastic analysis of macroscopic frictional strength and establish a fundamental basis for probabilistic design criteria for static friction., Journal of the Mechanics and Physics of Solids, 147, ISSN:0022-5096, ISSN:1873-4782

Natural faults experience a variety of frictional, rheological, and stress heterogeneities. To investigate the effects of these heterogeneities on seismic stability and the mode of fault slip behavior, laboratory experiments were conducted using a biaxial shearing apparatus with a 0.76 m by 0.076 m simulated fault where 2.5 to 5 mm thick gouge layers were sheared at applied normal stresses of 7 to 12 MPa for 25 mm of cumulative slip. Laboratory faults consisted of uniform layers of gouge, homogeneous mixtures, and/or heterogeneous patches of talc, quartz, and gypsum minerals. Experiments with a uniform layer of velocity weakening fault gouge revealed the development of two asperities at the highly stressed ends of the fault that could fail independently, and creep fronts that facilitated interaction between asperities. This behavior was also reproduced with simple numerical simulations that employ rate- and state-dependent friction. In other experiments, the fault consisted of patches of alternating velocity strengthening and velocity weakening fault gouges. Patch size and location were varied to understand how earthquake ruptures accelerate or decelerate in this heterogeneous environment. These experiments revealed that a velocity weakening fault patch was more likely to remain stable if located next to a velocity strengthening fault patch. However, stability was dependent on the patch sizes and location relative to where the load is applied. In certain cases, some sections of the fault slipped unstably while others slid stably. These experiments, and matching numerical models, highlight the complexity that can arise on natural faults due to frictional, rheological, and stress heterogeneities.

The delayed resonator concept uses time-delayed feedback control to convert an ordinary passive vibration absorber into an actively tuned resonator. Inspired by this idea, this study proposes to en...

The transition from sub-Rayleigh to supershear propagation of mode II cracks is a fundamental problem of fracture mechanics. It has extensively been studied in homogeneous uniform setups. When the applied shear load exceeds a critical value, transition occurs through the Burridge-Andrews mechanism at a well-defined crack length. However, velocity structures in geophysical conditions can be complex and affect the transition. Damage induced by previous earthquakes causes low-velocity zones surrounding mature faults and inclusions with contrasting material properties can be present at seismogenic depth. We relax the assumption of homogeneous media and investigate dynamic shear fracture in heterogeneous media using two-dimensional finite-element simulations and a linear slip-weakening law. We analyze the role of heterogeneities in the elastic media, while keeping the frictional interface properties uniform. We show that supershear transition is possible due to the sole presence of favorable off-fault heterogeneities. Sub-critical shear loads, for which propagation would remain permanently sub-Rayleigh in an equivalent homogeneous setup, will transition to supershear as a result of reflected waves. P-wave reflected as S-waves, followed by further reflections, affect the amplitude of the shear stress peak in front of the propagating crack, leading to supershear transition. A wave reflection model allows to uniquely describe the effect of off-fault inclusions on the shear stress peak. A competing mechanism of modified released potential energy affects transition and becomes predominant with decreasing distance between fault and inclusions. For inclusions at far distances, the wave reflection is the predominant mechanism.

Earthquakes are commonly modeled as shear cracks, where the slip profile of an earthquake rupture is the spatial distribution of relative displacement between fault surfaces. It is an accumulated r...

The onset of frictional motion is mediated by the dynamic propagation of a rupture front, analogous to a shear crack. The rupture front nucleates quasi-statically in a localized region of the frictional interface and slowly increases in size. When it reaches a critical nucleation length it becomes unstable, propagates dynamically and eventually breaks the entire interface, leading to macroscopic sliding. The nucleation process is particularly important because it determines the stress level at which the frictional interface fails, and therefore, the macroscopic friction strength. However, the mechanisms governing nucleation of frictional rupture fronts are still not well understood. Specifically, our knowledge of the nucleation process along a heterogeneous interface remains incomplete. Here, we study the nucleation of localized slip patches on linear slip-weakening interfaces with deterministic and stochastic heterogeneous friction properties. Using numerical simulations, we analyze the process leading to a slip patch of critical size for systems with varying correlation lengths of the local friction strength. Our deterministic interface model reveals that the growth of the critical nucleation patch at interfaces with small correlation lengths is non smooth due to the coalescence of neighboring slip patches. Existing analytical solutions do not account for this effect, which leads to an overestimation of global interface strength. Conversely, when the correlation length is large, the growth of the slip patch is continuous and our simulations match the analytical solution. Furthermore, nucleation by coalescence is also observed on stochastic interfaces with small correlation length. In this case, the applied load for a given slip patch size is a random variable. We show that its expectation follows a logistic function, which allows us to predict the strength of the interface well before failure occurs. Our model and observations provide new understanding of the nucleation process and its effect on the static frictional strength., International Journal of Solids and Structures, 225, ISSN:0020-7683, ISSN:1879-2146

The onset of frictional motion at the interface between two distinct bodies in contact is characterized by the propagation of dynamic rupture fronts. We combine friction experiments and numerical simulations to study the properties of these frictional rupture fronts. We extend previous analysis of slow and sub-Rayleigh rupture fronts and show that strain fields and the evolution of real contact area in the tip vicinity of supershear ruptures are well described by analytical fracture-mechanics solutions. Fracture-mechanics theory further allows us to determine long sought-after interface properties, such as local fracture energy and frictional peak strength. Both properties are observed to be roughly independent of rupture speed and mode of propagation. However, our study also reveals discrepancies between measurements and analytical solutions that appear as the rupture speed approaches the longitudinal wave speed. Further comparison with dynamic simulations illustrates that, in the supershear propagation regime, transient and geometrical (finite sample thickness) effects cause smaller near-tip strain amplitudes than expected from the fracture-mechanics theory. By showing good quantitative agreement between experiments, simulations and theory over the entire range of possible rupture speeds, we demonstrate that frictional rupture fronts are classic dynamic cracks despite residual friction., 20 pages including 11 figures

A measurement of the double-polarization observable E for the reaction \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma p\rightarrow \pi ^0 p$$\end{document}γp→π0p is reported. The data were taken with the CBELSA/TAPS experiment at the ELSA facility in Bonn using the Bonn frozen-spin butanol (C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_4$$\end{document}4H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_9$$\end{document}9OH) target, which provided longitudinally-polarized protons. Circularly-polarized photons were produced via bremsstrahlung of longitudinally-polarized electrons. The data cover the photon energy range from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_\gamma =600$$\end{document}Eγ=600 to 2310 MeV and nearly the complete angular range. The results are compared to and have been included in recent partial wave analyses.

The rupture of the interface joining two materials under frictional contact controls their macroscopic sliding. Interface rupture dynamics depend markedly on the mechanical properties of the bulk materials that bound the frictional interface. When the materials are similar, recent experimental and theoretical work has shown that shear cracks described by Linear Elastic Fracture Mechanics (LEFM) quantitatively describe the rupture of frictional interfaces. When the elastic properties of the two materials are dissimilar, many new effects take place that result from bimaterial coupling: the normal stress at the interface is elastodynamically coupled to local slip rates. At low rupture velocities, bimaterial coupling is not very significant and interface rupture is governed by `bimaterial cracks' that are described well by LEFM. As rupture velocities increase, we experimentally and theoretically show how bimaterial cracks become unstable at a subsonic critical rupture velocity, $c_T$. When the rupture direction opposes the direction of applied shear in the softer material, we show that $c_T$ is the subsonic limiting velocity. When ruptures propagate in the direction of applied shear in the softer material, we demonstrate that $c_T$ provides an explanation for how and when slip pulses (new rupture modes characterized by spatially localized slip) are generated. This work completes the fundamental physical description of how the frictional rupture of bimaterial interfaces takes place.

We approach the thermoacoustic instability problem in Rijke tubes from a mathematically novel perspective. In this benchmark experimental setting, the complex dynamic exchange between the unsteady heat release and the acoustic pressure variations creates the instability. When linearized, this behavior leads to a neutral class time-delayed dynamics with multiple independent delays, where our major contribution arrives. We aim to synthesize a series of stabilizing feedback control strategies for this dynamics. A recent mathematical paradigm, called the cluster treatment of characteristic roots (CTCR), is used to facilitate this objective. This paradigm, in essence, declares the necessary and sufficient stability conditions in the space of the system and controller parameters. The main contributions of this brief are in the first-time deployment of CTCR in the syntheses of various feedback control laws and validating experiments.

This paper studies the dynamics induced by interactions of rotating blades and the surrounding casing in turbomachinery such as aeroengines. Also known as “blade/casing rub dynamics,” this phenomenon results in vibrations that contribute to fatigue failure, especially in blades. Recently, it was proposed that the underlying dynamics of these interactions is analogous to internal milling operations. This introduces the concept of chatter and its intrinsic time-delay component in the dynamics, which is known to invite some nontrivial instability characteristics. The present paper investigates how the structural properties of the blade and casing components influence the stability of the combined interaction. The cluster treatment of characteristic roots paradigm is used for a delay-dependent stability analysis in the space of the operational parameters. An in-depth analysis reveals important aspects of the stability, which may provide valuable tools for designers. Analytical expressions are derived to calcu...

We present three-dimensional finite-element simulations showing the propagation of slip fronts at striped heterogeneous interfaces. The heterogeneous area consists of alternating stripes of weaker and stronger frictional properties, which is equivalent to a lower and higher fracture energy, respectively. By comparing the slip front propagation at interfaces that differ solely by the length scale of the heterogeneous pattern, we illustrate that two different propagation regimes exist. Interfaces with wide stripes present slip fronts with propagation speeds that transition from sub-Rayleigh to inter-sonic. Thinner stripes are, however, characterized by the propagation of sub-Rayleigh slip fronts, which are preceded by slip pulses of negligible slip in the weaker stripes. From a macroscopic point of view, an interface with a smaller heterogeneous pattern appears to be stronger than the equivalent coarser interface even though both have the same average properties. The numerical results as well as a theoretical approach based on fracture-mechanics considerations suggest that the origin of these two distinct propagation mechanisms lies in the interaction between the length scales of the cohesive zone and the heterogeneous configuration. We further show by estimating the relevant length scales that the occurring propagation mechanism is influenced by the friction weakening rate of the interface as well as the shear modulus of the bulk material. (C) 2015 Elsevier Ltd. All rights reserved.