arXiv subjects

Laurent Ponson

Publications and source records attributed to Laurent Ponson.

At least 19 recordsLinked to original sources

arXiv2026

Beyond linear stability: Heterogeneity-induced fingering of crack fronts

We investigate the stability of elastic interfaces beyond the linear regime by considering penny-shaped crack fronts propagating through toughness heterogeneities. Using fracture mechanics simulations, we drive crack fronts through arrays of obstacles with tunable toughness contrast. At low contrast, the crack front stiffness remains finite and stabilizes front perturbations. Above a critical threshold, however, the stiffness vanishes and the front destabilizes into long fingers that evolve into daughter cracks propagating between obstacles while the original crack remains pinned. Near threshold, the crack front response displays the characteristic square-root scaling behavior of classical saddle-node bifurcations. Yet, our analysis reveals a fundamentally different mechanism: the stable energy-minimizing crack-front configuration disappears without colliding with an unstable counterpart. Instead, the instability originates from a global loss of Griffith-compatible equilibria governed by the nonlocal interactions along the crack front. Beyond fracture mechanics, these findings point toward a broader class of collective global bifurcations in nonlocal elastic interfaces and may help rationalize the brittle-to-quasibrittle transition in heterogeneous solids.

cond-mat.mtrl-sci↗

arXiv2023

Wrapping and unwrapping multifractal fields

We develop a powerful yet simple method that generates multifractal fields with fully controlled scaling properties. Adopting the Multifractal Random Walk (MRW) model of Bacry et al. (2001), synthetic multifractal fields are obtained from the fractional integration of non-Gaussian fluctuations, built by a non-linear transformation of log-correlated Gaussian fields. The resulting fields are parameterized by their roughness exponent $H$, intermittency $\lambda$ and multifractal range $\xi_\omega$. We retrieve all the salient features of the MRW, namely a quadratic scaling exponent spectrum $\zeta_q$, fat-tail statistics of fluctuations, and spatial correlations of local volatility. Such features can be finely tuned, allowing for the generation of ideal multifractals mimicking real multi-affine fields. The construction procedure is then used the other way around to unwrap experimental data -- here the roughness map of a fractured metallic alloy. Our analysis evidences subtle differences with synthetic fields, namely anisotropic filamental clusters reminiscent of dissipation structures found in fluid turbulence.

cond-mat.stat-mech↗

arXiv2023

How criticality meets bifurcation in compressive failure of disordered solids

Continuum mechanics describes compressive failure as a standard bifurcation in the response of a material to an increasing load: damage, which initially grows uniformly in the material, localizes within a thin band at failure. Yet, experiments recording the acoustic activity preceding localization evidence power-law distributed failure precursors of increasing size, suggesting that compressive failure is a critical phenomenon. We examine here this apparent contradiction by probing the spatial organization of the damage activity and its evolution until localization during compression experiments of 2D cellular solids. The intermittent damage evolution measured in our experiments is adequately described by a non-stationary depinning equation derived from damage mechanics and reminiscent of critical phenomena. In this description, precursors are damage cascades emerging from the interplay between the material's disorder and the long-range stress redistributions following individual damage events. Yet, the divergence of their characteristic size close to failure, which we observe in our experiments, is not the signature of a transition towards criticality. Instead, the system remains at a fixed distance to the critical point at all stages of the damage evolution. The divergence results from the progressive loss of stability of the material as it is driven towards localization. Thus, our study shows that compressive failure is a standard bifurcation for which the material disorder plays a marginal role. It also shows that precursory activity constitute by-products of the evolution towards localization and can serve to build a predictive method to assess the residual lifetime of structures.

cond-mat.stat-mech↗

arXiv2022

Damage spreading in quasi-brittle disordered solids: II. What the statistics of precursors teach us about compressive failure

We investigate numerically and theoretically the precursory intermittent activity characterizing the preliminary phase of damage accumulation prior to failure of quasi-brittle solids. We use a minimal but thermodynamically consistent model of damage growth and localization developed by Berthier et al. (2017). The approach accounts for both microstructural disorder and non-local interactions and permits inferring a complete scaling description of the spatio-temporal structure of failure precursors. By developing a theoretical model of damage growth in disordered elasto-damageable specimen, we demonstrate that these scaling relations emerge from the physics of elastic manifolds driven in disordered media, while the divergence of these quantities close to failure is reminiscent of the loss of stability of the specimen at the localization threshold. Our study sorts out a long-standing debate on the nature of the compressive failure point and the origin of the universal statistics of the precursors preceding it. Our analysis rules out a critical-point scenario in which the divergence of the precursor size close to failure is signature of a second-order phase transition governed by the microstructural disorder. Instead, we show that while the jerky evolution of damage prior to failure results from the presence of material disorder, the latter does not significantly change the nature of the localization process, which is an instability well described by standard bifurcation theory of homogeneous systems. Finally, we harness our detailed understanding of the precursory statistics to design a methodology to estimate the residual lifetime of a structure from the statistical analysis of precursors. This method relevant for structural health monitoring is shown to perform rather accurately on our data.

cond-mat.stat-mech↗

arXiv2021

Effective toughness of heterogeneous materials with rate-dependent fracture energy

We investigate dynamic fracture of heterogeneous materials experimentally by measuring displacement fields as a rupture propagates through a periodic array of obstacles of controlled fracture energy. Our measurements demonstrate the applicability of the classical equation of motion of cracks at a discontinuity of fracture energy: the crack speed jumps at the entrance and exit of an obstacle, as predicted by the crack-tip energy balance within the brittle fracture framework. The speed jump amplitude is governed by the fracture energy contrast and by the combination of rate-dependency of fracture energy and inertia of the medium, which allows the crack to cross a fracture energy discontinuity at constant energy release rate. This discontinuous dynamics and the rate-dependence cause higher effective toughness, which governs the coarse-grained behavior of these cracks.

cond-mat.soft↗

arXiv2021

Adaptation of the tapered double cantilever beam test for the measurement of fracture energy and its variations with crack speed

In this work we present the design of a new test geometry inspired by the Tapered Double Cantilever Beam (TDCB) specimen that is shown to provide an improved characterization of the fracture properties of brittle solids. First, we show that our new design results in an exponential increase of the specimen compliance with crack length, leading to an extremely stable crack growth during the test. We determine an analytical description of this behavior, which provides a simple procedure to extract the fracture energy without depending on finite element calculations. Validation tests are done on polymethylmethacrylate (PMMA) specimens. We use both finite element simulations and our analytical model to interpret the data. We find a very good agreement between the toughness determined by both methods. The stable nature of crack growth in our improved TDCB specimens results in a precise control of the crack speed. This feature is employed to go one step further and characterize the variations of toughness with crack speed. We propose an original optimization procedure for the determination of the material parameters characterizing the kinetic law describing the toughness rate dependency. Overall, the approach proposed together with the newly designed test geometry offer unprecedented possibilities for the full and accurate characterization of the fracture behavior of brittle materials such as rocks, sandstone, mortar etc.

cond-mat.mtrl-sci↗

arXiv2020

Universal scaling of the velocity field in crack front propagation

The propagation of a crack front in disordered materials is jerky and characterized by bursts of activity, called avalanches. These phenomena are the manifestation of an out-of-equilibrium phase transition originated by the disorder. As a result avalanches display universal scalings which are however difficult to characterize in experiments at finite drive. Here we show that the correlation functions of the velocity field along the front allow to extract the critical exponents of the transition and to identify the universality class of the system. We employ these correlations to characterize the universal behavior of the transition in simulations and in an experiment of crack propagation. This analysis is robust, efficient and can be extended to all systems displaying avalanche dynamics.

cond-mat.stat-mech↗

arXiv2019

Configurational stability of a crack propagating in a material with mode-dependent fracture energy -- Part II: Drift of fracture facets in mixed-mode I+II+III

In earlier papers (Leblond et.al., 2011, 2019), we presented linear stability analyses of the coplanar propagation of a crack loaded in mixed-mode I+III, based on a "double'' propagation criterion combining Griffith (1920)'s energetic condition and Goldstein and Salganik (1974)'s principle of local symmetry. The difference between the two papers was that in the more recent one, the local value of the critical energy-release-rate was no longer considered as a constant, but heuristically allowed to depend upon the ratio of the local mode III to mode I stress intensity factors. This led to a much improved, qualitatively acceptable agreement of theory and experiments, for the "threshold'' value of the ratio of the unperturbed mode III to mode I stress intensity factors, above which coplanar propagation becomes unstable. In this paper, the analysis is extended to the case where a small additional mode II loading component is present in the initially planar configuration of the crack, generating a small, general kink of this crack from the moment it is applied. The main new effect resulting from presence of such a loading component is that the instability modes present above the threshold must drift along the crack front during its propagation. This prediction may be useful for future theoretical interpretations of a number of experiments where such a drifting motion was indeed observed.

cond-mat.soft↗

arXiv2018

Configurational stability of a crack propagating in a material with mode-dependent fracture energy - Part I: Mixed-mode I+III

In a previous paper (Leblond et al., 2011), we proposed a theoretical interpretation of the experimentally well known instability of coplanar crack propagation in mode I+III. The interpretation relied on a stability analysis based on analytical expressions of the stress intensity factors for a crack slightly perturbed both within and out of its original plane, due to Gao and Rice (1986) and Movchan et al. (1998), coupled with a double propagation criterion combining Griffith's energetic condition and principle of local symmetry. Under such assumptions instability modes were indeed evidenced for values of the mode mixity ratio of the mode III to mode I stress intensity factors applied remotely larger than some threshold depending only on Poisson's ratio. Unfortunately, the predicted thresholds were much larger than those generally observed for typical values of this material parameter. While the subcritical character of the nonlinear bifurcation from coplanar to fragmented fronts has been proposed as a possible explanation for this discrepancy (Chen et al., 2015), we propose here an alternative explanation based on the introduction of a constitutive relationship between the fracture energy and the mode mixity ratio, which is motivated by experimental observations. By reexamining the linear stability analysis of a planar propagating front, we show that such a relationship suffices, provided that it is strong enough, to lower significantly the threshold value of the mode mixity ratio for instability so as to bring it in a range more consistent with experiments. Interesting formulae are also derived for the distributions of the perturbed stress intensity factors and energy release rate, in the special case of perturbations of the crack surface and front obeying the principle of local symmetry and having reached a stationary state.

cond-mat.soft↗

arXiv2017

Elastic interactions in damage models of brittle failure

The failure of brittle solids involves, before macroscopic rupture, power-law distributed avalanches of local rupture events whereby microcracks nucleate and grow, which are also observed in for an elastic interface evolving in a non-homogeneous medium. For this reason, it is tempting to relate failure to the depinning of an elastic interface. Here we compute the elastic kernel of the interface representing the damage field of a brittle solid. In the case of a damage model of rupture under compression, which implements the Mohr-Coulomb criterion at the local scale, we show that the elastic kernel is unstable, and hence is very different from the kernels of usual interfaces. We show that the unstable modes are responsible for the localization of damage along a macroscopic fault observed in numerical simulations. At low disorder, the most unstable mode gives the orientation of the macroscopic fault that we measure in numerical simulations. The orientation of the fault changes when the level of disorder is increased, suggesting a complex interplay of the unstable modes and the disorder.

cond-mat.soft↗

arXiv2017

Fault orientation in damage failure under compression

The Mohr-Coulomb criterion is widely used in geosciences to relate the state of stress at failure to the observed orientation of the resulting faults. This relation is based on the assumption that the fault occurs along a plane that maximizes the Coulomb stress. Here, we test this hypothesis using an elastic, progressive damage model that implements the Mohr-Coulomb criterion at the local scale. We find that the orientation of the fault is not given by the Mohr-Coulomb criterion. Instead, for minimal disorder, it corresponds to the most unstable mode of damage in the model, which we determine through a linear stability analysis of the homogeneously damaged state. Our simulations show that microstructural disorder significantly affects the orientation of the fault, which, however, remains always far from the Mohr-Coulomb prediction.

physics.geo-ph↗

arXiv2014

Turbulent fracture surfaces: A footprint of damage percolation?

We show that a length scale xi can be extracted from the spatial correlations of the "steep cliffs" that appear on fracture surface. Above xi, the slope amplitudes are uncorrelated and the fracture surface is mono-affine. Below xi, long-range spatial correlation lead to a multi-fractal behavior of the surface, reminiscent of turbulent flows. Our results support a unifying conjecture for the geometry of fracture surfaces: for scales > ξthe surface is the trace left by an elastic line propagating in a random medium, while for scales < ξthe highly correlated patterns on the surface result from the merging of interacting damage cavities.

cond-mat.mtrl-sci↗

arXiv2013

Wave mitigation in ordered networks of granular chains

We study the propagation of stress waves through ordered 2D networks of granular chains. The quasi-particle continuum theory employed captures the acoustic pulse splitting, bending, and recombination through the network and is used to derive its effective acoustic properties. The strong wave mitigation properties of the network predicted theoretically are confirmed through both numerical simulations and experimental tests. In particular, the leading pulse amplitude propagating through the system is shown to decay exponentially with the propagation distance and the spatial structure of the transmitted wave shows an exponential localization along the direction of the incident wave. The length scales that characterized these exponential decays are studied and determined as a function of the geometrical properties of the network. These results open avenues for the design of efficient impact mitigating structures and provide new insights into the mechanisms of wave propagation in granular matter.

nlin.PS↗

arXiv2013

From microstructural features to effective toughness in disordered brittle solids

The relevant parameters at the microstructure scale that govern the macroscopic toughness of disordered brittle materials are investigated theoretically. We focus on planar crack propagation and describe the front evolution as the propagation of a long-range elastic line within a plane with random distribution of toughness. Our study reveals two regimes: in the collective pinning regime, the macroscopic toughness can be expressed as a function of a few parameters only, namely the average and the standard deviation of the local toughness distribution and the correlation lengths of the heterogeneous toughness field; in the individual pinning regime, the passage from micro to macroscale is more subtle and the full distribution of local toughness is required to be predictive. Beyond the failure of brittle solids, our findings illustrate the complex filtering process of microscale quantities towards the larger scales into play in a broad range of systems governed by the propagation of an elastic interface in a disordered medium.

cond-mat.dis-nn↗

arXiv2013

Correlating toughness and roughness in ductile fracture

Three dimensional calculations of ductile crack growth under mode I plane strain, small scale yielding conditions are carried out using an elastic-viscoplastic constitutive relation for a progres- sively cavitating plastic solid with two populations of void nucleating second phase particles. Full field solutions are obtained for three dimensional material microstructures characterized by ran- dom distributions of void nucleating particles. Crack growth resistance curves and fracture surface roughness statistics are calculated using standard procedures. The range of void nucleating particle volume fractions considered give rise to values of toughness, JIC, that vary by a factor of four. For all volume fractions considered, the computed fracture surfaces are self-affine over a size range of about two orders of magnitude with a roughness exponent of 0.54 $\pm$ 0.03. For small void nucleating particle volume fractions, the mean large particle spacing serves as a single dominant length scale. In this regime, the correlation length of the fracture surface corresponding to the cut-off of the self-affine behavior is found to be linearly related to JIC thus quantitatively correlating toughness and fracture surface roughness.

cond-mat.soft↗

arXiv2012

Toughening and asymmetry in peeling of heterogeneous adhesives

The effective adhesive properties of heterogeneous thin films are characterized through a combined experimental and theoretical investigation. By bridging scales, we show how variations of elastic or adhesive properties at the microscale can significantly affect the effective peeling behavior of the adhesive at the macroscale. Our study reveals three elementary mechanisms in heterogeneous systems involving front propagation: (i) patterning the elastic bending stiffness of the film produces fluctuations of the driving force resulting in dramatically enhanced resistance to peeling; (ii) optimized arrangements of pinning sites with large adhesion energy are shown to control the effective system resistance, allowing the design of highly anisotropic and asymmetric adhesives; (iii) heterogeneities of both types result in front motion instabilities producing sudden energy releases that increase the overall adhesion energy. These findings open potentially new avenues for the design of thin films with improved adhesion properties, and motivate new investigation of other phenomena involving front propagation.

cond-mat.soft↗

arXiv2010

Nonlinear Waves in Disordered Diatomic Granular Chains

We investigate the propagation and scattering of highly nonlinear waves in disordered granular chains composed of diatomic (two-mass) units of spheres that interact via Hertzian contact. Using ideas from statistical mechanics, we consider each diatomic unit to be a "spin", so that a granular chain can be viewed as a spin chain composed of units that are each oriented in one of two possible ways. Experiments and numerical simulations both reveal the existence of two different mechanisms of wave propagation: In low-disorder chains, we observe the propagation of a solitary pulse with exponentially decaying amplitude. Beyond a critical level of disorder, the wave amplitude instead decays as a power law, and the wave transmission becomes insensitive to the level of disorder. We characterize the spatio-temporal structure of the wave in both propagation regimes and propose a simple theoretical interpretation for such a transition. Our investigation suggests that an elastic spin chain can be used as a model system to investigate the role of heterogeneities in the propagation of highly nonlinear waves.

nlin.PS↗

arXiv2009

Crack opening profile in DCDC specimen

The opening profile of the cracks produced in the Double Cleavage Drilled Compression (DCDC) specimens for brittle materials is investigated. The study is achieved by combining Finite Element simulations of a DCDC linear elastic medium with experimental measurements by crack opening interferometry on pure silica glass samples. We show that the shape of the crack can be described by a simple expression as a function of the geometrical parameters of the sample and the external loading conditions. This result can be used to measure accurately in real time relevant quantities during DCDC experiments, such as the crack length or the stress intensity factor applied to the specimen.

cond-mat.mtrl-sci↗