arXiv subjects

Kirsten Martens

Publications and source records attributed to Kirsten Martens.

At least 37 records · Page 2Linked to original sources

arXiv2018

Creep dynamics of athermal amorphous materials: a mesoscopic approach

Yield stress fluids display complex dynamics, in particular when driven into the transient regime between the solid and the flowing state. Inspired by creep experiments on dense amorphous materials, we implement mesocale elasto-plastic descriptions to analyze such transient dynamics in athermal systems. Both our mean-field and space-dependent approaches consistently reproduce the typical experimental strain rate responses to different applied steps in stress. Moreover, they allow us to understand basic processes involved in the strain rate slowing down (creep) and the strain rate acceleration (fluidization) phases. The fluidization time increases in a power-law fashion as the applied external stress approaches a static yield stress. This stress value is related to the stress over-shoot in shear start-up experiments, and it is known to depend on sample preparation and age. By calculating correlations of the accumulated plasticity in the spatially resolved model, we reveal different modes of cooperative motion during the creep dynamics.

cond-mat.soft↗

arXiv2018

Precursors of fluidisation in the creep response of a soft glass

Using extensive numerical simulations, we study the fluidisation process of dense amorphous materials subjected to an external shear stress, using a three-dimensional colloidal glass model. In order to disentangle possible boundary effects from finite size effects in the process of fluidisation, we implement a novel geometry-constrained protocol with periodic boundary conditions. We show that this protocol is well controlled and that the longtime fluidisation dynamics is, to a great extent, independent of the details of the protocol parameters. Our protocol, therefore, provides an ideal tool to investigate the bulk dynamics prior to yielding and to study finite size effects regarding the fluidisation process. Our study reveals the existence of precursors to fluidisation observed as a peak in the strain-rate fluctuations, that allows for a robust definition of a fluidisation time. Although the exponents in the power-law creep dynamics seem not to depend significantly on the system size, we reveal strong finite size effects for the onset of fluidisation.

physics.comp-ph↗

arXiv2018

Deformation and flow of amorphous solids: An updated review of mesoscale elastoplastic models

The deformation and flow of disordered solids, such as metallic glasses and concentrated emulsions, involves swift localized rearrangements of particles that induce a long-range deformation field. To describe these heterogeneous processes, elastoplastic models handle the material as a collection of 'mesoscopic' blocks alternating between an elastic behavior and plastic relaxation, when they are too loaded. Plastic relaxation events redistribute stresses in the system in a very anisotropic way. We review not only the physical insight provided by these models into practical issues such as strain localization, creep and steady-state rheology, but also the fundamental questions that they address with respect to criticality at the yielding point and the statistics of avalanches of plastic events. Furthermore, we discuss connections with concurrent mean-field approaches and with related problems such as the plasticity of crystals and the depinning of an elastic line.

cond-mat.dis-nn↗

arXiv2018

Mean-field scenario for the athermal creep dynamics of yield-stress fluids

We develop an elasto-plastic description for the transient dynamics prior to steady flow of athermally yielding materials. Our mean-field model not only reproduces the experimentally observed non-linear time dependence of the shear-rate response to an external shear-stress, but also allows for the determination of the different physical processes involved in the onset of the re-acceleration phase after the initial critical slowing down and a distinct well defined fluidization phase. The evidenced power-law dependence of the fluidization time on the distance of the applied to an age dependent static yield stress is not universal but strongly dependent on initial conditions.

cond-mat.soft↗

arXiv2017

Nontrivial rheological exponents in sheared yield stress fluids

In this work we discuss possible physical origins for non-trivial exponents in the athermal rheology of soft materials at low but finite driving rates. A key ingredient in our scenario is the presence of a self-consistent mechanical noise that stems from the spatial superposition of long-range elastic responses to localized plastically deforming regions. We study analytically a mean-field model, in which this mechanical noise is accounted for by a stress diffusion term coupled to the plastic activity. Within this description we show how a dependence of the shear modulus and/or the local relaxation time on the shear rate introduces corrections to the usual mean-field prediction, concerning the Herschel-Bulkley-type rheological response of exponent 1/2. This feature of the mean-field picture is then shown to be robust with respect to structural disorder and partial relaxation of the local stress. We test this prediction numerically on a mesoscopic lattice model that implements explicitly the long-range elastic response to localized shear transformations, and we conclude on how our scenario might be tested in rheological experiments.

cond-mat.soft↗

arXiv2017

Nonlinear Rheology in a Model Biological Tissue

Mechanical signaling plays a key role in biological processes like embryo development and cancer growth. One prominent way to probe mechanical properties of tissues is to study their response to externally applied forces. Using a particle-based model featuring random apoptosis and environment-dependent division rates, we evidence a crossover from linear flow to a shear-thinning regime with increasing shear rate. To rationalize this non-linear flow we derive a theoretical mean-field scenario that accounts for the interplay of mechanical and active noise in local stresses. These noises are respectively generated by the elastic response of the cell matrix to cell rearrangements and by the internal activity.

cond-mat.soft↗

arXiv2015

Driving rate dependence of avalanche statistics and shapes at the yielding transition

We study stress time series caused by plastic avalanches in athermally sheared disordered materials. Using particle-based simulations and a mesoscopic elasto-plastic model, we analyze size and shear-rate dependence of the stress-drop durations and size distributions together with their average temporal shape. We find critical exponents different from mean-field predictions, and a clear asymmetry for individual avalanches. We probe scaling relations for the rate dependency of the dynamics and we report a crossover towards mean-field results for strong driving.

cond-mat.soft↗

arXiv2015

Probing relevant ingredients in mean-field approaches for the athermal rheology of yield stress materials

Although the notion of mechanical noise is expected to play a key role in the non-linear rheology of athermally sheared amorphous systems, its characterization has so far remained elusive. Here, we show using molecular dynamic simulations that in spite of the presence of strong spatio-temporal correlations in the system, the local stress exhibits normal diffusion under the effect of the mechanical noise in the finite driving regime. The diffusion constant appears to be proportional to the mean plastic activity. Our data suggests that the corresponding proportionality constant is density independent, and can be directly related to the specific form of the rheological flow curve, pointing the way to a generic way of modeling mechanical noise in mean-field equations.

cond-mat.soft↗

arXiv2015

On the relevance of disorder in athermal amorphous materials under shear

We show that, at least at a mean-field level, the effect of structural disorder in sheared amorphous media is very dissimilar depending on the thermal or athermal nature of their underlying dynamics. We first introduce a toy model, including explicitly two types of noise (thermal versus athermal). Within this interpretation framework, we argue that mean-field athermal dynamics can be accounted for by the so-called H{é}braud-Lequeux (HL) model, in which the mechanical noise stems explicitly from the plastic activity in the sheared medium. Then, we show that the inclusion of structural disorder, by means of a distribution of yield energy barriers, has no qualitative effect in the HL model, while such a disorder is known to be one of the key ingredients leading kinematically to a finite macroscopic yield stress in other mean-field descriptions, such as the Soft-Glassy-Rheology model. We conclude that the statistical mechanisms at play in the emergence of a macroscopic yield stress, and a complex stationary dynamics at low shear rate, are different in thermal and athermal amorphous systems.

cond-mat.soft↗

arXiv2014

Relaxation in yield stress systems through elastically interacting activated events

We study consequences of long-range elasticity in thermally assisted dynamics of yield stress materials. Within a two-dimensinal mesoscopic model we calculate the mean-square displacement and the dynamical structure factor for tracer particle trajectories. The ballistic regime at short time scales is associated with a compressed exponential decay in the dynamical structure factor, followed by a subdiffusive crossover prior to the onset of diffusion. We relate this crossover to spatiotemporal correlations and thus go beyond established mean field predictions.

cond-mat.soft↗

arXiv2014

Rheology of athermal amorphous solids: Revisiting simplified scenarios and the concept of mechanical noise temperature

We study the rheology of amorphous solids in the limit of negligible thermal fluctuations. On the basis of general arguments, the flow curve is shown to result from an interplay between the time scales of the macroscopic driving and the (cascades of) local particle rearrangements. Such rearrangements are known to induce a redistribution of the elastic stress in the system. Although mechanical noise, i.e., the local stress fluctuations arising from this redistribution, is widely believed to activate new particle rearrangements, we provide evidence that casts severe doubt on the analogy with thermal fluctuations: mechanical and thermal fluctuations lead to asymptotically different statistics for barrier crossing. These ideas are illustrated and supported by a simple coarse-grained model whose ingredients are directly connected with the physical processes relevant for the flow.

cond-mat.soft↗

arXiv2014

Universal and non-universal features in coarse-grained models of flow in disordered solids

We study the two-dimensional (2D) shear flow of amorphous solids within variants of an elastoplastic model, paying particular attention to spatial correlations and time fluctuations of, e.g., local stresses. The model is based on the local alternation between an elastic regime and plastic events during which the local stress is redistributed. The importance of a fully tensorial description of the stress and of the inclusion of (coarse-grained) convection in the model is investigated; scalar and tensorial models yield very similar results, while convection enhances fluctuations and breaks the spurious symmetry between the flow and velocity gradient directions, for instance when shear localisation is observed. Besides, correlation lengths measured with diverse protocols are discussed. One class of such correlation lengths simply scale with the spacing between homogeneously distributed, simultaneous plastic events. This leads to a scaling of the correlation length with the shear rate as $\dotγ^{\frac{-1}{2}}$ in 2D in the athermal regime, regardless of the details of the model. The radius of the cooperative disk, defined as the near-field region in which plastic events induce a stress redistribution that is not amenable to a mean-field treatment, notably follows this scaling. On the other hand, the cooperative volume measured from the four-point stress susceptibility and its dependence on the system size and the shear rate are model-dependent.

cond-mat.soft↗

arXiv2012

Nonlinear wavelength selection in surface faceting under electromigration

We report on the control of the faceting of crystal surfaces by means of surface electromigration. When electromigration reinforces the faceting instability, we find perpetual coarsening with a wavelength increasing as $t^{1/2}$. For strongly stabilizing electromigration, the surface is stable. For weakly stabilizing electromigration, a cellular pattern is obtained, with a nonlinearly selected wavelength. The selection mechanism is not caused by an instability of steady-states, as suggested by previous works in the literature. Instead, the dynamics is found to exhibit coarsening {\it before} reaching a continuous family of stable non-equilibrium steady-states.

cond-mat.mtrl-sci↗

arXiv2012

Spontaneous formation of permanent shear bands in a mesoscopic model of flowing disordered matter

This study proposes a coherent scenario of the formation of permanent shear bands in the flow of yield stress materials. It is a well accepted point of view that flow in disordered media is occurring via local plastic events, corresponding to small size rearrangements, that yield a long range stress redistribution over the system. Within a minimalistic mesoscopic model that incorporates these local dynamics, we study the spatial organisation of the local plastic events. The most important parameter in this study is the typical restructuring time needed to regain the original structure after a local rearrangement. In agreement with a recent mean field study [Coussot \textit{et al., Eur. Phys. J. E}, 2010, \textbf{33}, 183] we observe a spontaneous formation of permanent shear bands, when this restructuring time is large compared to the typical stress release time in a rearrangement. The bands consist of a large number of plastic events within a solid region that remains elastic. This heterogeneous flow behaviour is different in nature from the transient dynamical heterogeneities that one observes in the small shear rate limit in flow without shear-banding [Martens \textit{et al., Phys. Rev. Lett.}, 2011, \textbf{106}, 156001]. We analyse in detail the dependence of the shear bands on system size, shear rate and restructuring time. Further we rationalise the scenario within a mean field version of the spatial model, that produces a non monotonous flow curve for large restructuring times. This explains the instability of the homogeneous flow below a critical shear rate, that corresponds to the minimum of the curve. Our study therefore strongly supports the idea that the characteristic time scales involved in the local dynamics are at the physical origin of permanent shear bands.

cond-mat.soft↗

arXiv2011

Influence of flux balance on the generalized chemical potential in mass transport models

In equilibrium systems, the conservation of the number of particles (or mass) leads to the equalization of the chemical potential throughout the system. Using a non-equilibrium generalization of the notion of chemical potential, we investigate the influence of disorder and of the balance of mass fluxes on the generalized chemical potential in the framework of stochastic mass transport models. We focus specifically on the issue of local mesurements of the chemical potential. We find that while local dynamical disorder does not affect the measurement process, the presence of large-scale geometrical heterogeneities (branching geometry) leads to unequal local measurement results in different points of the system. We interpret these results in terms of mass flux balance, and argue that the conditions for the global definition of the chemical potential still hold, but that local measurements fail to capture the global theoretical value.

cond-mat.stat-mech↗

arXiv2011

Connecting diffusion and dynamical heterogeneities in actively deformed amorphous systems

We present an extensive numerical study of dynamical heterogeneities and their influence on diffusion in an athermal mesoscopic model for actively deformed amorphous solids. At low strain rates the stress dynamics are governed by cooperative regions of plastic events. On the basis of scaling arguments as well as an extensive numerical study of an athermal elasto-plastic model, we show that there is a direct link between the self-diffusion coefficient and the size of cooperative regions at low strain rates. Both depend strongly on rate and on system size. A measure of the mean square displacement of passive tracers in deformed amorphous media thus gives information about the microscopic rheology, such as the geometry of the cooperative regions and their scaling with strain rate and system size.

cond-mat.mtrl-sci↗

arXiv2010

Entropy-based characterizations of the observable-dependence of the fluctuation-dissipation temperature

The definition of a nonequilibrium temperature through generalized fluctuation-dissipation relations relies on the independence of the fluctuation-dissipation temperature from the observable considered. We argue that this observable independence is deeply related to the uniformity of the phase-space probability distribution on the hypersurfaces of constant energy. This property is shown explicitly on three different stochastic models, where observable-dependence of the fluctuation-dissipation temperature arises only when the uniformity of the phase-space distribution is broken. The first model is an energy transport model on a ring, with biased local transfer rules. In the second model, defined on a fully connected geometry, energy is exchanged with two heat baths at different temperatures, breaking the uniformity of the phase-space distribution. Finally, in the last model, the system is connected to a zero temperature reservoir, and preserves the uniformity of the phase-space distribution in the relaxation regime, leading to an observable-independent temperature.

cond-mat.stat-mech↗

arXiv2010

Dependence of the fluctuation-dissipation temperature on the choice of observable

On general grounds, a nonequilibrium temperature can be consistently defined from generalized fluctuation-dissipation relations only if it is independent of the observable considered. We argue that the dependence on the choice of observable generically occurs when the phase-space probability distribution is non-uniform on constant energy shells. We relate quantitatively this observable dependence to a fundamental characteristics of nonequilibrium systems, namely the Shannon entropy difference with respect to the equilibrium state with the same energy. This relation is illustrated on a mean-field model in contact with two heat baths at different temperatures.

cond-mat.stat-mech↗