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Register a new userDynamics of cracks in disordered materials
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Daniel Bonamy
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Predicting when rupture occurs or cracks progress is a major challenge in numerous elds of industrial, societal and geophysical importance. It remains largely unsolved: Stress enhancement at cracks and defects, indeed, makes the macroscale dynamics extremely sensitive to the microscale material disorder. This results in giant statistical uctuations and non-trivial behaviors upon upscaling dicult to assess via the continuum approaches of engineering. These issues are examined here. We will see: How linear elastic fracture mechanics sidetracks the diculty by reducing the problem to that of the propagation of a single crack in an eective material free of defects, How slow cracks sometimes display jerky dynamics, with sudden violent events incompatible with the previous approach, and how some paradigms of statistical physics can explain it, How abnormally fast cracks sometimes emerge due to the formation of microcracks at very small scales.
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Frictional interfaces are abundant in natural and engineering systems, and predicting their behavior still poses challenges of prime scientific and technological importance. At the heart of these challenges lies the inherent coupling between the interfacial constitutive relation -- the macroscopic friction law -- and the bulk elasticity of the bodies that form the frictional interface. In this feature paper, we discuss the generic properties of the macroscopic friction law and the many ways in which its coupling to bulk elasticity gives rise to rich spatiotemporal frictional dynamics. We first present the widely used rate-and-state friction constitutive framework, discuss its power and limitations, and propose extensions that are supported by experimental data. We then discuss how bulk elasticity couples different parts of the interface, and how the range and nature of this interaction are affected by the systems geometry. Finally, in light of the coupling between interfacial and bulk physics, we discuss basic phenomena in spatially-extended frictional systems, including the stability of homogeneous sliding, the onset of sliding motion and a wide variety of propagating frictional modes (e.g. rupture fronts, healing fronts and slip pulses). Overall, the results presented and discussed in this feature paper highlight the inseparable roles played by interfacial and bulk physics in spatially-extended frictional systems.
We employ numerical simulations to understand the evolution of elastic standing waves in disordered frictional disk systems, where the dispersion relations of rotational sound modes are analyzed in detail. As in the case of frictional particles on a lattice, the rotational modes exhibit an optical-like dispersion relation in the high frequency regime, representing a shoulder of the vibrational density of states and fast oscillations of the autocorrelations of rotational velocities. A lattice-based model describes the dispersion relations of the rotational modes for small wave numbers. The rotational modes are perfectly explained by the model if tangential elastic forces between the disks in contact are large enough. If the tangential forces are comparable with or smaller than normal forces, the model fails for short wave lengths. However, the dispersion relation of the rotational modes then follows the model prediction for transverse modes, implying that the fast oscillations of disks rotations switch to acoustic sound behavior. We evidence such a transition of the rotational modes by analyzing the eigen vectors of disordered frictional disks and identify upper and lower limits of the frequency-bands. We find that those are not reversed over the whole range of tangential stiffness as a remarkable difference from the rotational sound in frictional particles on a lattice.
Yielding transition in isotropic soft materials under superposition of orthogonal deformation fields is known to follow von Mises criterion. However, in anisotropic soft materials von Mises criterion fails owing to preferred directions associated with the system. In this work we study a model anisotropic yield stress system: electrorheological (ER) fluids that show structure formation in the direction of electric field. We subject the ER fluids to superposition of orthogonal stress fields that leads to different yield stress values. We obtain a yielding state diagram by plotting normalized rotational shear stress against normalized radial shear stress corresponding to yield point for a given electric field. Remarkably, the state diagram validates the Hill yielding criterion, which is a general yielding criterion for materials having anisotropy along three orthogonal directions, originally developed for metallic systems. Validation of Hill criterion suggests the universality of its application to anisotropic systems including conventional anisotropic soft materials having yield stress.
Entangled states are ubiquitous amongst fibrous materials, whether naturally occurring (keratin, collagen, DNA) or synthetic (nanotube assemblies, elastane). A key mechanical characteristic of these systems is their ability to reorganise in response to external stimuli, as implicated in e.g. hydration-induced swelling of keratin fibrils in human skin. During swelling, the curvature of individual fibres changes to give a cooperative and reversible structural reorganisation that opens up a pore network. The phenomenon is known to be highly dependent on topology, even if the nature of this dependence is not well understood: certain ordered entanglements (`weavings) can swell to many times their original volume while others are entirely incapable of swelling at all. Given this sensitivity to topology, it is puzzling how the disordered entanglements of many real materials manage to support cooperative dilation mechanisms. Here we use a combination of geometric and lattice-dynamical modelling to study the effect of disorder on swelling behaviour. The model system we devise spans a continuum of disordered topologies and is bounded by ordered states whose swelling behaviour is already known to be either vanishingly small or extreme. We find that while topological disorder often quenches swelling behaviour, certain disordered states possess a surprisingly large swelling capacity. Crucially, we show that the extreme swelling response previously observed only for certain specific weavings can be matched---and even superseded---by that of disordered entanglements. Our results establish a counterintuitive link between topological disorder and mechanical flexibility that has implications not only for polymer science but also for our broader understanding of collective phenomena in disordered systems.
Electronic instabilities in transition metal compounds often spontaneously form orbital molecules, which consist of orbital-coupled metal ions at low temperature. Recent local structural studies utilizing the pair distribution function revealed that preformed orbital molecules appear disordered even in the high-temperature paramagnetic phase. However, it is unclear whether preformed orbital molecules are dynamic or static. Here, we provide clear experimental evidence of the slow dynamics of disordered orbital molecules realized in the high-temperature paramagnetic phase of LiVS2, which exhibits vanadium trimerization upon cooling below 314 K. Unexpectedly, the preformed orbital molecules appear as a disordered zigzag chain that fluctuate in both time and space under electron irradiation. Our findings should advance studies on soft matter physics realized in an inorganic material due to disordered orbital molecules.
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