Topological Defect Formation in Slow Three-Dimensional Fracture.

Cracks develop various surface patterns as they propagate in three-dimensional (3D) materials. Symmetry-breaking topological defects in nominally tensile (mode-I) fracture emerge in the slow (noninertial) regime, taking the form of surface steps. We show that the same phase-field framework that recently shed basic light on dynamic (inertial) tensile fracture in three dimensions, also gives rise to crack surface steps.

Size Selection of Crack Front Defects: Multiple Fracture-Plane Interactions and Intrinsic Length Scales.

Material failure is mediated by the propagation of cracks which, in realistic 3D materials, typically involves multiple coexisting fracture planes. Multiple fracture-plane interactions create poorly understood out-of-plane crack structures, such as step defects on tensile fracture surfaces. Steps form once a slowly moving, distorted crack front segments into disconnected overlapping fracture planes separated by a stabilizing distance h_{max}.

Quenched disorder and instability control dynamic fracture in three dimensions.

Materials failure in 3D still poses basic challenges. We study 3D brittle crack dynamics using a phase-field approach, where Gaussian quenched disorder in the fracture energy is incorporated. Disorder is characterized by a correlation length R and strength σ.

Enumerating low-frequency nonphononic vibrations in computer glasses.

In addition to Goldstone phonons that generically emerge in the low-frequency vibrational spectrum of any solid, crystalline or glassy, structural glasses also feature other low-frequency vibrational modes. The nature and statistical properties of these modes-often termed "excess modes"-have been the subject of decades-long investigation. Studying them, even using well-controlled computer glasses, has proven challenging due to strong spatial hybridization effects between phononic and nonphononic excitations, which hinder quantitative analyses of the nonphononic contribution DG(ω) to the total spectrum D(ω), per frequency ω.

Dynamics of crack front waves in three-dimensional material failure.

Crack front waves (FWs) are dynamic objects that propagate along moving crack fronts in three-dimensional (3D) materials. We study FW dynamics in the framework of a 3D phase-field platform that features a rate-dependent fracture energy Γ(v) (v is the crack propagation velocity) and intrinsic length scales, and quantitatively reproduces the high-speed oscillatory instability in the quasi-2D limit. We show that in-plane FWs feature a rather weak time dependence, with decay rate that increases with dΓ(v)/dv>0, and largely retain their properties upon FW-FW interactions, similarly to a related experimentally observed solitonic behavior.

The dynamics of unsteady frictional slip pulses.

Self-healing slip pulses are major spatiotemporal failure modes of frictional systems, featuring a characteristic size [Formula: see text] and a propagation velocity [Formula: see text] ([Formula: see text] is time). Here, we develop a theory of slip pulses in realistic rate- and state-dependent frictional systems. We show that slip pulses are intrinsically unsteady objects-in agreement with previous findings-yet their dynamical evolution is closely related to their unstable steady-state counterparts.

Boson-peak vibrational modes in glasses feature hybridized phononic and quasilocalized excitations.

A hallmark of structural glasses and other disordered solids is the emergence of excess low-frequency vibrations on top of the Debye spectrum DDebye(ω) of phonons (ω denotes the vibrational frequency), which exist in any solid whose Hamiltonian is translationally invariant. These excess vibrations-a signature of which is a THz peak in the reduced density of states D(ω)/DDebye(ω), known as the boson peak-have resisted a complete theoretical understanding for decades. Here, we provide direct numerical evidence that vibrations near the boson peak consist of hybridizations of phonons with many quasilocalized excitations; the latter have recently been shown to generically populate the low-frequency tail of the vibrational spectra of structural glasses quenched from a melt and of disordered crystals.

Self-healing solitonic slip pulses in frictional systems.

A prominent spatiotemporal failure mode of frictional systems is self-healing slip pulses, which are propagating solitonic structures that feature a characteristic length. Here, we numerically derive a family of steady state slip pulse solutions along generic and realistic rate-and-state dependent frictional interfaces, separating large deformable bodies in contact. Such nonlinear interfaces feature a nonmonotonic frictional strength as a function of the slip velocity, with a local minimum.

Characteristic energy scales of active fluctuations in adherent cells.

Cell-matrix and cell-cell adhesion play important roles in a wide variety of physiological processes, from the single-cell level to the large scale, multicellular organization of tissues. Cells actively apply forces to their environment, either extracellular matrix or neighboring cells, as well as sense its biophysical properties. The fluctuations associated with these active processes occur on an energy scale much larger than that of ordinary thermal equilibrium fluctuations, yet their statistical properties and characteristic scales are not fully understood.

Cellular orientational fluctuations, rotational diffusion and nematic order under periodic driving.

The ability of living cells to sense the physical properties of their microenvironment and to respond to dynamic forces acting on them plays a central role in regulating their structure, function and fate. Of particular importance is the cellular sensitivity and response to periodic driving forces in noisy environments, encountered in vital physiological conditions such as heart beating, blood vessel pulsation and breathing. Here, we first test and validate two predictions of a mean-field theory of cellular reorientation under periodic driving, which combines the minimization of cellular anisotropic elastic energy with active remodeling forces.

Advancing the Mechanical Performance of Glasses: Perspectives and Challenges.

Glasses are materials that lack a crystalline microstructure and long-range atomic order. Instead, they feature heterogeneity and disorder on superstructural scales, which have profound consequences for their elastic response, material strength, fracture toughness, and the characteristics of dynamic fracture. These structure-property relations present a rich field of study in fundamental glass physics and are also becoming increasingly important in the design of modern materials with improved mechanical performance.

Low-energy quasilocalized excitations in structural glasses.

Glassy solids exhibit a wide variety of generic thermomechanical properties, ranging from universal anomalous specific heat at cryogenic temperatures to nonlinear plastic yielding and failure under external driving forces, which qualitatively differ from their crystalline counterparts. For a long time, it has been believed that many of these properties are intimately related to nonphononic, low-energy quasilocalized excitations (QLEs) in glasses. Indeed, recent computer simulations have conclusively revealed that the self-organization of glasses during vitrification upon cooling from a melt leads to the emergence of such QLEs.

Unified quantifier of mechanical disorder in solids.

Mechanical disorder in solids, which is generated by a broad range of physical processes and controls various material properties, appears in a wide variety of forms. Defining unified and measurable dimensionless quantifiers, allowing quantitative comparison of mechanical disorder across widely different physical systems, is therefore an important goal. Two such coarse-grained dimensionless quantifiers (among others) appear in the literature: one is related to the spectral broadening of discrete phononic bands in finite-size systems (accessible through computer simulations) and the other is related to the spatial fluctuations of the shear modulus in macroscopically large systems.

Does mesoscopic elasticity control viscous slowing down in glassforming liquids?

The dramatic slowing down of relaxation dynamics of liquids approaching the glass transition remains a highly debated problem, where the crux of the puzzle resides in the elusive increase in the activation barrier ΔE(T) with decreasing temperature T. A class of theoretical frameworks-known as elastic models-attribute this temperature dependence to the variations of the liquid's macroscopic elasticity, quantified by the high-frequency shear modulus G(T). While elastic models find some support in a number of experimental studies, these models do not take into account the spatial structures, length scales, and heterogeneity associated with structural relaxation in supercooled liquids.

Unconventional singularities and energy balance in frictional rupture.

A widespread framework for understanding frictional rupture, such as earthquakes along geological faults, invokes an analogy to ordinary cracks. A distinct feature of ordinary cracks is that their near edge fields are characterized by a square root singularity, which is intimately related to the existence of strict dissipation-related lengthscale separation and edge-localized energy balance. Yet, the interrelations between the singularity order, lengthscale separation and edge-localized energy balance in frictional rupture are not fully understood, even in physical situations in which the conventional square root singularity remains approximately valid.

Statistical mechanics of local force dipole responses in computer glasses.

Soft quasilocalized modes (QLMs) are universally featured by structural glasses quenched from a melt, and are involved in several glassy anomalies such as the low-temperature scaling of their thermal conductivity and specific heat, and sound attenuation at intermediate frequencies. In computer glasses, QLMs may assume the form of harmonic vibrational modes under a narrow set of circumstances; however, direct access to their full distribution over frequency is hindered by hybridizations of QLMs with other low-frequency modes (e.g.

Elastic moduli fluctuations predict wave attenuation rates in glasses.

The disorder-induced attenuation of elastic waves is central to the universal low-temperature properties of glasses. Recent literature offers conflicting views on both the scaling of the wave attenuation rate Γ(ω) in the low-frequency limit (ω → 0) and its dependence on glass history and properties. A theoretical framework-termed Fluctuating Elasticity Theory (FET)-predicts low-frequency Rayleigh scattering scaling in -d spatial dimensions, Γ(ω) ∼ γ ω, where γ = γ(V) quantifies the coarse-grained spatial fluctuations of elastic moduli, involving a correlation volume V that remains debated.

Extracting the properties of quasilocalized modes in computer glasses: Long-range continuum fields, contour integrals, and boundary effects.

Low-frequency nonphononic modes and plastic rearrangements in glasses are spatially quasilocalized, i.e., they feature a disorder-induced short-range core and known long-range decaying elastic fields.

Universality of the Nonphononic Vibrational Spectrum across Different Classes of Computer Glasses.

It has been recently established that the low-frequency spectrum of simple computer glass models is populated by soft, quasilocalized nonphononic vibrational modes whose frequencies ω follow a gapless, universal distribution D(ω)∼ω^{4}. While this universal nonphononic spectrum has been shown to be robust to varying the glass history and spatial dimension, it has so far only been observed in simple computer glasses featuring radially symmetric, pairwise interaction potentials. Consequently, the relevance of the universality of nonphononic spectra seen in simple computer glasses to realistic laboratory glasses remains unclear.

Cellular contractile forces are nonmechanosensitive.

Cells' ability to apply contractile forces to their environment and to sense its mechanical properties (e.g., rigidity) are among their most fundamental features.

Pinching a glass reveals key properties of its soft spots.

It is now well established that glasses feature quasilocalized nonphononic excitations-coined "soft spots"-, which follow a universal [Formula: see text] density of states in the limit of low frequencies ω. All glass-specific properties, such as the dependence on the preparation protocol or composition, are encapsulated in the nonuniversal prefactor of the universal [Formula: see text] law. The prefactor, however, is a composite quantity that incorporates information both about the number of quasilocalized nonphononic excitations and their characteristic stiffness, in an apparently inseparable manner.

Wave attenuation in glasses: Rayleigh and generalized-Rayleigh scattering scaling.

The attenuation of long-wavelength phonons (waves) by glassy disorder plays a central role in various glass anomalies, yet it is neither fully characterized nor fully understood. Of particular importance is the scaling of the attenuation rate Γ(k) with small wavenumbers k → 0 in the thermodynamic limit of macroscopic glasses. Here, we use a combination of theory and extensive computer simulations to show that the macroscopic low-frequency behavior emerges at intermediate frequencies in finite-size glasses, above a recently identified crossover wavenumber k, where phonons are no longer quantized into bands.

Anisotropic structural predictor in glassy materials.

There is growing evidence that relaxation in glassy materials, both spontaneous and externally driven, is mediated by localized soft spots. Recent progress made it possible to identify the soft spots inside glassy structures and to quantify their degree of softness. These softness measures, however, are typically scalars, not taking into account the tensorial, anisotropic nature of soft spots, which implies orientation-dependent coupling to external deformation.