arXiv subjects

Tom W. J. de Geus

Publications and source records attributed to Tom W. J. de Geus.

15 recordsLinked to original sources

arXiv2025

Short-range depinning in the presence of velocity-weakening

Phenomena including friction and earthquakes are complicated by the joint presence of disorder and non-linear instabilites, such as those triggered by the presence of velocity weakening. In [de Geus and Wyart, Phys. Rev. E 106, 065001 (2022)], we provided a theory for the nucleation of flow and the magnitude of hysteresis, building on recent results on disorder-free systems described by so called rate-and-state descriptions of the frictional interface, and treating disorder perturbatively. This theory was tested for models of frictional interfaces, where long range elastic interactions are present. Here we test it for short-range depinning, and confirm that (i) nucleation is triggered by avalanches, governed by a critical point at some threshold force $f_c$ close to the minimum of the flow curve and that (ii) due to an armouring mechanism by which the elastic manifold displays very little plasticity after a big slip event, very slowly decaying finite size effects dominate the hysteresis magnitude, with an exponent we can relate to other observables.

cond-mat.dis-nn↗

arXiv2024

Armouring of a frictional interface by mechanical noise

A dry frictional interface loaded in shear often displays stick-slip. The amplitude of this cycle depends on the probability that a microscopic event nucleates a rupture and on the rate at which microscopic events are triggered. The latter is determined by the distribution of soft spots, $P(x)$, which is the density of microscopic regions that yield if the shear load is increased by some amount $x$. In minimal models of a frictional interface - that include disorder, inertia and long-range elasticity - we discovered an 'armouring' mechanism by which the interface is greatly stabilised after a large slip event: $P(x)$ then vanishes at small argument as $P(x)\sim x^θ$ [1]. The exponent $θ$ is non-zero only in the presence of inertia (otherwise $θ=0$). It was found to depend on the statistics of the disorder in the model, a phenomenon that was not explained. Here, we show that a single-particle toy model with inertia and disorder captures the existence of a non-trivial exponent $θ>0$, which we can analytically relate to the statistics of the disorder.

cond-mat.soft↗

arXiv2024

Stick-slip in a stack: how slip dissonance reveals aging

We perform physical and numerical experiments to study the stick-slip response of a stack of slabs in contact through dry frictional interfaces driven in quasistatic shear. The ratio between the drive's stiffness and the slab's shear stiffness controls the presence or absence of slip synchronization. A sufficiently high stiffness ratio leads to synchronization, comprising periodic slip events in which all interfaces slip simultaneously. A lower stiffness ratio leads to asynchronous slips and, experimentally, to the stick-slip amplitude becoming broadly distributed as the number of layers in the stack increases. We interpret this broadening in light of the combined effect of complex loading paths due to the asynchronous slips and creep. Consequently, the aging rate of the interfaces can be readily extracted from the stick-slip cycles, and it is found to be of the same order of magnitude as existing experimental results on a similar material. Finally, we discuss the emergence of slow slips and an increase in aging-rate variations when more slabs are added to the stack.

cond-mat.soft↗

arXiv2024

Dynamical heterogeneities of thermal creep in pinned interfaces

Disordered systems under applied loading display slow creep flows at finite temperature, which can lead to the material rupture. Renormalization group arguments predicted that creep proceeds via thermal avalanches of activated events. Recently, thermal avalanches were argued to control the dynamics of liquids near their glass transition. Both theoretical approaches are markedly different. Here we provide a scaling description that seeks to unify dynamical heterogeneities in both phenomena, confirm it in simple models of pinned elastic interfaces, and discuss its experimental implications.

cond-mat.dis-nn↗

arXiv2022

Scaling theory for the statistics of slip at frictional interfaces

Slip at a frictional interface occurs via intermittent events. Understanding how these events are nucleated, can propagate, or stop spontaneously remains a challenge, central to earthquake science and tribology. In the absence of disorder, rate-and-state approaches predict a diverging nucleation length at some stress $σ^*$, beyond which cracks can propagate. Here we argue for a flat interface that disorder is a relevant perturbation to this description. We justify why the distribution of slip contains two parts: a powerlaw corresponding to `avalanches', and a `narrow' distribution of system-spanning `fracture' events. We derive novel scaling relations for avalanches, including a relation between the stress drop and the spatial extension of a slip event. We compute the cut-off length beyond which avalanches cannot be stopped by disorder, leading to a system-spanning fracture, and successfully test these predictions in a minimal model of frictional interfaces.

cond-mat.dis-nn↗

arXiv2022

Scaling description of creep flow in amorphous solids

Amorphous solids such as coffee foam, toothpaste or mayonnaise display a transient creep flow when a stress $Σ$ is suddenly imposed. The associated strain rate is commonly found to decay in time as $\dotγ \sim t^{-ν}$, followed either by arrest or by a sudden fluidisation. Various empirical laws have been suggested for the creep exponent $ν$ and fluidisation time $τ_f$ in experimental and numerical studies. Here, we postulate that plastic flow is governed by the difference between $Σ$ and the transient yield stress $Σ_t(γ)$ that characterises the stability of configurations visited by the system at strain $γ$. Assuming the analyticity of $Σ_t(γ)$ allows us to predict $ν$ and asymptotic behaviours of $τ_f$ in terms of properties of stationary flows. We test successfully our predictions using elastoplastic models and published experimental results.

cond-mat.soft↗

arXiv2022

Mean-field description for the architecture of low-energy excitations in glasses

In amorphous materials, groups of particles can rearrange locally into a new stable configuration. Such elementary excitations are key as they determine the response to external stresses, as well as to thermal and quantum fluctuations. Yet, understanding what controls their geometry remains a challenge. Here we build a scaling description of the geometry and energy of low-energy excitations in terms of the distance to an instability, as predicted for instance at the dynamical transition in mean field approaches of supercooled liquids. We successfully test our predictions in ultrastable computer glasses, with a gapped and ungapped (regular) spectrum. Overall, our approach explains why excitations become less extended, with a higher energy and displacement scale upon cooling.

cond-mat.soft↗

arXiv2020

Thermal origin of quasi-localised excitations in glasses

Key aspects of glasses are controlled by the presence of excitations in which a group of particles can rearrange. Surprisingly, recent observations indicate that their density is dramatically reduced and their size decreases as the temperature of the supercooled liquid is lowered. Some theories predict these excitations to cause a gap in the spectrum of quasi-localised modes of the Hessian that grows upon cooling, while others predict a pseudo-gap ${D_L(ω)} \sim ω^α$. To unify these views and observations, we generate glassy configurations of controlled gap magnitude $ω_c$ at temperature ${T=0}$, using so-called `breathing' particles, and study how such gapped states respond to thermal fluctuations. We find that \textit{(i)}~the gap always fills up at finite $T$ with ${D_L(ω) \approx A_4(T) \, ω^4}$ and ${A_4 \sim \exp(-E_a / T)}$ at low $T$, \textit{(ii)}~$E_a$ rapidly grows with $ω_c$, in reasonable agreement with a simple scaling prediction ${E_a\sim ω_c^4}$ and \textit{(iii)}~at larger $ω_c$ excitations involve fewer particles, as we rationalise, and eventually become string-like. We propose an interpretation of mean-field theories of the glass transition, in which the modes beyond the gap act as an excitation reservoir, from which a pseudo-gap distribution is populated with its magnitude rapidly decreasing at lower $T$. We discuss how this picture unifies the rarefaction as well as the decreasing size of excitations upon cooling, together with a string-like relaxation occurring near the glass transition.

cond-mat.soft↗

arXiv2020

Thermally activated flow in models of amorphous solids

Amorphous solids yield at a critical value $Σ_c$ of the imposed stress $Σ$ through a dynamical phase transition. While sharp in athermal systems, the presence of thermal fluctuations leads to the rounding of the transition and thermally activated flow even below $Σ_c$. Here, we study the steady state thermal flow of amorphous solids using a mesoscopic elasto-plastic model. In the Hebraud-Lequex (HL) model we provide an analytical solution of the thermally activated flow at low temperature. We then propose a general scaling law that also describes the transition rounding. Finally, we find that the scaling law holds in numerical simulations of the HL model, a 2D elasto-plastic model, and in previously published molecular dynamics simulations of 2D Lennard-Jones glass.

cond-mat.soft↗

arXiv2020

Improving the initial guess for the Newton-Raphson protocol in time-dependent simulations

A general linearisation procedure for the consistent tangent of a small-strain visco-plastic material model is presented in this note. The procedure is based on multi-variable linearisation around a so-called 'reference state'. In particular, the linerarisation of the time integration scheme is found to yield an extra term compared to classical expressions, which only appears because the material response is time-dependent. It has the effect of yielding a very accurate initial guess for the Newton-Raphson protocol based on the ongoing viscous flow. It is shown, using a modern variational FFT-based solver, that the extra term reduces both the CPU time and the number of Newton-Raphson iterations by around a factor two.

math.NA↗

arXiv2019

How collective asperity detachments nucleate slip at frictional interfaces

Sliding at a quasi-statically loaded frictional interface can occur via macroscopic slip events, which nucleate locally before propagating as rupture fronts very similar to fracture. We introduce a novel microscopic model of a frictional interface that includes asperity-level disorder, elastic interaction between local slip events, and inertia. For a perfectly flat and homogeneously loaded interface, we find that slip is nucleated by avalanches of asperity detachments of extension larger than a critical radius $A_c$ governed by a Griffith criterion. We find that after slip, the density of asperities at a local distance to yielding $x_σ$ presents a pseudo-gap $P(x_σ) \sim (x_σ)^θ$, where $θ$ is a non-universal exponent that depends on the statistics of the disorder. This result makes a link between friction and the plasticity of amorphous materials where a pseudo-gap is also present. For friction, we find that a consequence is that stick-slip is an extremely slowly decaying finite size effect, while the slip nucleation radius $A_c$ diverges as a $θ$-dependent power law of the system size. We discuss how these predictions can be tested experimentally.

cond-mat.dis-nn↗

arXiv2019

Energy-based comparison between the Fourier--Galerkin method and the finite element method

The Fourier-Galerkin method (in short FFTH) has gained popularity in numerical homogenisation because it can treat problems with a huge number of degrees of freedom. Because the method incorporates the fast Fourier transform (FFT) in the linear solver, it is believed to provide an improvement in computational and memory requirements compared to the conventional finite element method (FEM). Here, we systematically compare these two methods using the energetic norm of local fields, which has the clear physical interpretation as being the error in the homogenised properties. This enables the comparison of memory and computational requirements at the same level of approximation accuracy. We show that the methods' effectiveness relies on the smoothness (regularity) of the solution and thus on the material coefficients. Thanks to its approximation properties, FEM outperforms FFTH for problems with jumps in material coefficients, while ambivalent results are observed for the case that the material coefficients vary continuously in space. FFTH profits from a good conditioning of the linear system, independent of the number of degrees of freedom, but generally needs more degrees of freedom to reach the same approximation accuracy. More studies are needed for other FFT-based schemes, non-linear problems, and dual problems (which require special treatment in FEM but not in FFTH).

math.NA↗

arXiv2019

Theory for the density of interacting quasi-localised modes in amorphous solids

Quasi-localised modes appear in the vibrational spectrum of amorphous solids at low-frequency. Though never formalised, these modes are believed to have a close relationship with other important local excitations, including shear transformations and two-level systems. We provide a theory for their frequency density, $D_{L}(ω)\simω^α$, that establishes this link for systems at zero temperature under quasi-static loading. It predicts two regimes depending on the density of shear transformations $P(x)\sim x^θ$ (with $x$ the additional stress needed to trigger a shear transformation). If $θ>1/4$, $α=4$ and a finite fraction of quasi-localised modes form shear transformations, whose amplitudes vanish at low frequencies. If $θ<1/4$, $α=3+ 4 θ$ and all quasi-localised modes form shear transformations with a finite amplitude at vanishing frequencies. We confirm our predictions numerically.

cond-mat.soft↗

arXiv2018

Elasto-plastic description of brittle failure in amorphous materials

The response of amorphous materials to an applied strain can be continuous, or instead display a macroscopic stress drop when a shear band nucleates. Such discontinuous response can be observed if the initial configuration is very stable. We study theoretically how such brittleness emerges in athermal, quasi-statically driven, materials as their initial stability is increased. We show that this emergence is well reproduced by elasto-plastic models and is predicted by a mean field approximation, where it corresponds to a continuous transition. In mean field, failure can be forecasted from the avalanche statistics. We show that this is not the case for very brittle materials in finite dimensions due to rare weak regions where a shear band nucleates. Their critical radius is predicted to follow $a_c\sim (Σ-Σ_b)^{-2}$, where $Σ$ is the stress and $Σ_b$ the stress a shear band can carry.

cond-mat.soft↗

arXiv2016

A finite element perspective on non-linear FFT-based micromechanical simulations

Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the Lippmann-Schwinger type integral equation. Their computational efficiency results from handling the kernel of this equation by the Fast Fourier Transform (FFT). However, the kernel is derived from an auxiliary homogeneous linear problem, which renders the extension of FFT-based schemes to non-linear problems conceptually difficult. This paper aims to establish a link between FE- and FFT-based methods, in order to develop a solver applicable to general history- and time-dependent material models. For this purpose, we follow the standard steps of the FE method, starting from the weak form, proceeding to the Galerkin discretization and the numerical quadrature, up to the solution of non-linear equilibrium equations by an iterative Newton-Krylov solver. No auxiliary linear problem is thus needed. By analyzing a two-phase laminate with non-linear elastic, elasto-plastic, and visco-plastic phases, and by elasto-plastic simulations of a dual-phase steel microstructure, we demonstrate that the solver exhibits robust convergence. These results are achieved by re-using the non-linear FE technology, with the potential of further extensions beyond small-strain inelasticity considered in this paper.

physics.comp-ph↗