arXiv subjects
Publications and source records attributed to Stefano Zapperi.
The physics of sliding friction is gaining impulse from nanoscale and mesoscale experiments, simulations, and theoretical modeling. This Colloquium reviews some recent developments in modeling and in atomistic simulation of friction, covering open-ended directions, unconventional nanofrictional systems, and unsolved problems.
Typically, the plastic yield stress of a sample is determined from a stress-strain curve by defining a yield strain and reading off the stress required to attain it. However, it is not a priori clear that yield strengths of microscale samples measured this way should display the correct finite size scaling. Here we study plastic yield as a depinning transition of a 1+1 dimensional interface, and consider how finite size effects depend on the choice of yield strain, as well as the presence of hardening and the strength of elastic coupling. Our results indicate that in sufficiently large systems, the choice of yield strain is unimportant, but in smaller systems one must take care to avoid spurious effects.
We present a unified theory of fracture in disordered brittle media that reconciles apparently conflicting results reported in the literature. Our renormalization group based approach yields a phase diagram in which the percolation fixed point, expected for infinite disorder, is unstable for finite disorder and flows to a zero-disorder nucleation-type fixed point, thus showing that fracture has mixed first order and continuous character. In a region of intermediate disorder and finite system sizes, we predict a crossover with mean-field avalanche scaling. We discuss intriguing connections to other phenomena where critical scaling is only observed in finite size systems and disappears in the thermodynamic limit.
Microcrystals deform very differently from their macroscopic counterparts, displaying a size-dependent yield stress and intermittent plastic strain bursts. Here we demonstrate that size effects and strain bursts may be just two different signatures of fundamental collective phenomena that govern the dynamics of dislocation systems on all scales. We confirm this conjecture by demonstrating agreement between the results of 2D and 3D dislocation dynamics simulations and experimental results on compressed micropillars. Our results indicate that many peculiarities of small-sample plasticity may arise from the finite-size scaling properties of collective dislocation dynamics, rather than from changes in the physical mechanisms governing dislocation motion.
We introduce a systematic method for extracting multivariable universal scaling functions and critical exponents from data. We exemplify our insights by analyzing simulations of avalanches in an interface using simulations from a driven quenched Kardar-Parisi-Zhang (qKPZ) equation. We fully characterize the spatial structure of these avalanches- we report universal scaling functions for size, height and width distributions, and also local front heights. Furthermore, we resolve a problem that arises in many imaging experiments of crackling noise and avalanche dynamics, where the observed distributions are strongly distorted by a limited field of view. Through artificially windowed data, we show these distributions and their multivariable scaling functions may be written in terms of two control parameters, the window size and the characteristic length scale of the dynamics. For the entire system and the windowed distributions we develop accurate parameterizations for the universal scaling functions, including corrections to scaling and systematic error bars, facilitated by a novel software environment SloppyScaling.
We study the asymptotic properties of fracture strength distributions of disordered elastic media by a combination of renormalization group, extreme value theory, and numerical simulation. We investigate the validity of the `weakest-link hypothesis' in the presence of realistic long-ranged interactions in the random fuse model. Numerical simulations indicate that the fracture strength is well described by the Duxbury-Leath-Beale (DLB) distribution which is shown to flow asymptotically to the Gumbel distribution. We explore the relation between the extreme value distributions and the DLB type asymptotic distributions, and show that the universal extreme value forms may not be appropriate to describe the non-universal low-strength tail.
Motivated by recent experiments on the finite temperature Mott transition in VO2 films, we propose a classical coarse-grained dielectric breakdown model where each degree of freedom represents a nanograin which transitions from insulator to metal with increasing temperature and voltage at random thresholds due to quenched disorder. We describe the properties of the resulting non-equilibrium metal-insulator transition and explain the universal characteristics of the resistance jump distribution. We predict that by tuning voltage, another critical point is approached, which separates a phase of "bolt"-like avalanches from percolation-like ones.
The intermittent transition between slow growth and rapid shrinkage in polymeric assemblies is termed dynamic instability, a feature observed in a variety of biochemically distinct assemblies including microtubules, actin and their bacterial analogs. The existence of this labile phase of a polymer has many functional consequences in cytoskeletal dynamics, and its repeated appearance suggests that it is relatively easy to evolve. Here, we consider the minimal ingredients for the existence of dynamic instability by considering a single polymorphic filament that grows by binding to a substrate, undergoes a conformation change, and may unbind as a consequence of the residual strains induced by this change. We identify two parameters that control the phase space of possibilities for the filament: a structural mechanical parameter that characterizes the ratio of the bond strengths along the filament to those with the substrate (or equivalently the ratio of longitudinal to lateral interactions in an assembly), and a kinetic parameter that characterizes the ratio of time scales for growth and conformation change. In the deterministic limit, these parameters serve to demarcate a region of uninterrupted growth from that of collapse. However, in the presence of disorder in either the structural or the kinetic parameter the growth and collapse phases can coexist where the filament can grow slowly, shrink rapidly, and transition between these phases, thus exhibiting dynamic instability. We exhibit the window for the existence of dynamic instability in a phase diagram that allows us to quantify the evolvability of this labile phase.
We introduce a lattice model able to describe damage and yielding in heterogeneous materials ranging from brittle to ductile ones. Ductile fracture surfaces, obtained when the system breaks once the strain is completely localized, are shown to correspond to minimum energy surfaces. The similarity of the resulting fracture paths to the limits of brittle fracture or minimum energy surfaces is quantified. The model exhibits a smooth transition from brittleness to ductility. The dynamics of yielding exhibits avalanches with a power-law distribution.
We consider numerically the roughness of a planar crack front within the long-range elastic string model, with a tunable disorder correlation length $ξ$. The problem is shown to have two important length scales, $ξ$ and the Larkin length $L_c$. Multiscaling of the crack front is observed for scales below $ξ$, provided that the disorder is strong enough. The asymptotic scaling with a roughness exponent $ζ\approx 0.39$ is recovered for scales larger than both $ξ$ and $L_c$. If $L_c > ξ$, these regimes are separated by a third regime characterized by the Larkin exponent $ζ_L \approx 0.5$. We discuss the experimental implications of our results.
We report the measurement of multivariable scaling functions for the temporal average shape of Barkhausen noise avalanches, and show that they are consistent with the predictions of simple mean-field theories. We bypass the confounding factors of time-retarded interactions (eddy currents) by measuring thin permal- loy films, and bypass thresholding effects and amplifier distortions by applying Wiener deconvolution. We find experimental shapes that are approximately symmetric, and track the evolution of the scaling function. We solve a mean- field theory for the magnetization dynamics and calculate the form of the scaling function in the presence of a demagnetizing field and a finite field ramp-rate, yielding quantitative agreement with the experiment.
We study avalanches in a model for a planar crack propagating in a disordered medium. Due to long-range interactions, avalanches are formed by a set of spatially disconnected local clusters, the sizes of which are distributed according to a power law with an exponent $τ_{a}=1.5$. We derive a scaling relation $τ_a=2τ-1$ between the local cluster exponent $τ_a$ and the global avalanche exponent $τ$. For length scales longer than a cross-over length proportional to the Larkin length, the aspect ratio of the local clusters scales with the roughness exponent of the line model. Our analysis provides an explanation for experimental results on planar crack avalanches in Plexiglas plates, but the results are applicable also to other systems with long-range interactions.
We study the plastic yielding of disordered media using the perfectly plastic random fuse model. The yield surfaces are shown to be different from those obtained minimizing the sum of the local yield thresholds, i.e. the so-called minimum 'energy' surfaces. As a result, the global yield stress is lower than expected from naive optimization and the difference persists as the sample size increases. At variance with minimum energy surfaces, height-height fluctuations of yield surfaces exhibit multiscaling. We provide a theoretical argument that explains how this behavior arises from the very different nature of the optimization problem in both cases.
We study the effect of long range dipolar forces on the dynamics and morphology of domain walls in magnetic thin films by numerical simulations of the spin-1 random field Ising model. By studying the size distribution of avalanches of domain wall motion arising as a response to quasistatic external driving, we observe a cross-over from the case dominated by short range interactions to another universality class where the long range dipolar forces become important. This crossover is accompanied with a change of the domain wall morphology from a rough wall to walls with zigzag structure.
We present a line-based model of transverse domain walls in thin magnetic strips, to study the effect of bulk disorder on the domain wall dynamics within the thermally activated creep regime. The creep velocity is found to exhibit a non-linear dependence on both applied magnetic fields and electric currents, characterized by similar creep exponents for both forms of the external drive. We discuss briefly the significance of the inherently stochastic thermally activated domain wall motion from the point of view of spintronics applications, where it generally is essential to be able to control the domain wall displacement in a deterministic manner.
Mechanical vibrations are known to affect frictional sliding and the associated stick-slip patterns causing sometimes a drastic reduction of the friction force. This issue is relevant for applications in nanotribology and to understand earthquake triggering by small dynamic perturbations . We study the dynamics of repulsive particles confined between a horizontally driven top plate and a vertically oscillating bottom plate. Our numerical results show a suppression of the high dissipative stick-slip regime in a well defined range of frequencies that depends on the vibrating amplitude, the normal applied load, the system inertia and the damping constant. We propose a theoretical explanation of the numerical results and derive a phase diagram indicating the region of parameter space where friction is suppressed. Our results allow to define better strategies for the mechanical control of friction.
We review statistical theories and numerical methods employed to consider the sample size dependence of the failure strength distribution of disordered materials. We first overview the analytical predictions of extreme value statistics and fiber bundle models and discuss their limitations. Next, we review energetic and geometric approaches to fracture size effects for specimens with a flaw. Finally, we overview the numerical simulations of lattice models and compare with theoretical models.
We study the growth of slip line in a plastically deforming crystal by numerical simulation of a double-ended pile-up model with a dislocation source at one end, and an absorbing wall at the other end. In presence of defects, the pile-up undergoes a second order non-equilibrium phase transition as a function of stress, which can be characterized by finite size scaling. We obtain a complete set of critical exponents and scaling functions that describe the spatiotemporal dynamics of the slip line. Our findings allow to reinterpret earlier experiments on slip line kinematography as evidence of a dynamic critical phenomenon.