Creep under a sustained load can persist for long times yet culminate in abrupt yielding or rupture, implying a finite lifetime even when the material appears solid. Here, we formulate lifetime prediction as Bayesian inference over an evolving activation-energy landscape. A time-dependent distribution of activation barriers controls deformation: stress lowers barriers, while irreversible rearrangements deplete the weakest sites and reshape the low-barrier tail. Using early-time acoustic emission data, Bayesian inference estimates the evolving barrier statistics in each sample and yields posterior predictive distributions for the time-to-failure. This approach provides uncertainty-aware lifetime forecasts that link microscopic barrier evolution to macroscopic creep dynamics.

Identifying signatures of fatigue crack growth and detecting early warnings in service in Non-Destructive Testing applications remain major challenges for research and industry alike. To address these issues, we propose a waveform-based signal processing technique applied to Acoustic Emission (AE) data. This study explores how a fully unsupervised, data-driven approach can cluster acoustic signals based on their physical emission mechanisms associated with fatigue cracking. Using AE datasets recorded during fatigue crack growth tests on compact tension specimens made of aluminum or steel alloys, we demonstrate that hierarchical clustering of acoustic multiplets-signatures of a unique source-is consistent with the phenomenological classification of multiplets previously established distinguishing multiplets generated by local contacts between crack surfaces from those associated with fatigue crack growth at crack tip. Here we show that we can assign physical emission mechanisms to each multiplet solely based on acoustic information through waveform-based dissimilarity measures - unlike standard AE signal processing techniques. Furthermore, by taking advantage of the multiple levels of analysis offered by hierarchical clustering, we significantly improve multiplets detection by reducing dependency on user-parameters. This improvement opens the possibility of developing a more automated Non-Destructive Testing architecture for fatigue cracking signatures detection, thus reducing computational complexity.

The mechanical characteristics of fibers (of various materials), as well as of fiber bundles, are of primary importance for the design and the mechanical behavior of textiles, or of fibrous and composite materials. These characteristics are classically determined from strain-rate-controlled tensile testing, generally assuming a negligible role of thermal activation on damage and fracturing processes. Under this assumption, the distribution of individual fiber strengths can be deduced from a downscaling of the macroscopic mechanical behavior at the bundle scale. There is, however, considerable experimental evidence of strain-rate and temperature effects on the mechanical behavior of individual fibers or bundles, which can also creep under constant applied load. This indicates a strong role of thermal activation on these processes. Here, these effects are analyzed from a fiber-bundle model with equal load sharing, in which thermal activation of fiber breakings is introduced from a kinetic Monte Carlo algorithm adapted for time-varying stresses. This allows one to rationalize these rate or temperature effects, such as a decrease in bundle strength, strain at peak stress, and apparent Young's modulus with decreasing strain rate and/or increasing temperature. This also shows that the classical downscaling procedure used to estimate the distribution of individual fiber strengths from the mechanical behavior at the bundle scale should be considered with caution. If mechanical testing of the bundle is performed under conditions favoring the role of thermal activation (e.g. low applied strain rate), this procedure can strongly underestimate the intrinsic (athermal) Weibull's parameters of the fiber strength's distribution. The same model is also used to explore size (number of fibers) effects on bundle mechanical response.

Unlike meteorological hazards, tectonic earthquakes remain hardly predictable, reinforcing their deadly character. This relates to an out-of-equilibrium, intermittent dynamic associated with a strong time asymmetry, with few and non-systematic foreshocks sometimes preceding large earthquakes, while aftershocks are ubiquitous and have been known for a long time. However, 130 years after Omori, the physical origin of this time asymmetry and of aftershocks remains highly debated. Here, we model earthquake interactions and natural seismicity from a spring-slider model based on a minimal number of fundamental mechanisms, namely elastic stress transfer and reaction rate theory applied to the simplest form of static friction. This allows introducing a microscopic timescale as well as temperature in a physically meaningful way, and to strikingly reproduce many aspects of seismicity and earthquake interactions. This includes (a) a power law distribution of seismic moments, (b) an Omori's as well as productivity laws for aftershocks, (c) a clustering of aftershocks nearby the edge of the mainshock rupture zone and (d) a strong time asymmetry of the seismic cycle.

The precipitation of magnesite and dolomite from aqueous media is challenging kinetically because several hydrated or hydroxylated Mg-carbonate phases can retard or inhibit the formation of these "enigmatic" minerals under so-called mild conditions (T <= 90 degrees C and atmospheric pressure). Here, we demonstrate that Fe-magnesite can be synthesized at 60 degrees C in only 2 days via indirect carbonation of peridotite, following an amorphous-to-nesquehonite-to-magnesite transformation route. In this reactive configuration, the magnesite production time is significantly reduced from 2 days to only 6 h when the temperature is increased to 90 degrees C. The discovery of these mild conditions for magnesite production is a promising result because currently these temperatures can be reached by free-carbon energies. We also assess the incorporation of a fabricated magnesite-rich material at 90 degrees C as a partial cement substitute in concrete manufacturing. Preliminary results show that substituting 15 wt % of cement with magnesite-rich material could significantly reduce the CO2 footprint with minimal impact on the concrete's mechanical-textural properties, including Young's modulus, strength, and macro-porosity. In practice, this circular carbon approach could provide a dual advantage-reduced clinker production and permanent CO2 storage-and present a significant opportunity to lower the carbon footprint of cement production.

Analyzing how fracture networks develop from preexisting isolated fault segments in immature faults may provide knowledge of the preparation process leading to fault growth and dynamic rupture. We reproduce this process experimentally using triaxial compression experiments coupled with time-lapse in-situ synchrotron X-ray tomography in Westerly granite core samples (10 mm diameter, 20 mm height) that contain two parallel notches oriented at 30 degrees with respect to the axis of the cylinder. We conducted the experiments at room temperature with a constant confining pressure of 20 MPa. We image microfracture development, characterize the microphysical processes of damage and fault growth in an intact rock bridge between the notches, and analyze the evolution of fractures oriented at 0 degrees-17 degrees (extensile) and 17 degrees-32 degrees (shear) as the rock approached failure. We also elucidate the strain localization process in the deforming rock using digital volume correlation. Our study offers a detailed comparison of microfracture and strain field development during fault growth. Results indicate that the rock bridge between the notches becomes damaged with a damage rate and a fracture rate diverging as the rock approaches macroscopic failure. Immediately preceding failure, shear fractures dominate the fracture networks. DVC analysis showed that the deformation process is mixed-mode, accommodated by dilation and shear strain, with the shear strains being more localized than the dilation. Furthermore, regions of high dilative strain host both extensile and shear fractures. These findings provide valuable insights into the fault growth process within an intact rock bridge between two fault segments in nature, demonstrating how mixed-mode deformation facilitates fault maturation.

Stressed under a constant load, materials creep with a final acceleration of deformation and for any given applied stress and material, the creep failure time can strongly vary. We investigate creep on sheets of paper and confront the statistics with a simple fiber bundle model of creep failure in a disordered landscape. In the experiments, acoustic emission event times t_j were recorded, and both this data and simulation event series reveal sample-dependent history effects with log-normal statistics and non-Markovian behavior. This leads to a relationship between t_j and the failure time t_f with a power law relationship, evolving with time. These effects and the predictability result from how the energy gap distribution develops during creep.

Slow earthquakes are transient events detected with geodetic (slow slip) and/or seismic (low-frequency earthquakes and tremors) observations that release energy over a period of hours to months, i.e., much longer than regular earthquakes. These events are observed in several subduction at a specific range of depths and with their properties, such as strength, duration, recurrence interval, and predominance of either slip or seismic components varying along the subduction interface. In this study, we investigate slow earthquakes based on numerical modeling by applying a combined Maxwell viscoelastic and damaging rheology. Unlike conventional rate and state modeling practices utilizing infinitely thin fault assumptions with fault friction laws, our approach incorporates a finite fault thickness through a damage mechanism and suitable failure criteria. Our model directly predicts a geodetically observable slow displacement, while rock damaging rate is considered as a proxy to seismic tremors. We run a set of numerical simulations to systematically explore the effects of model parameters such as viscosity, yield stress, and healing time on slow slip and tremors. We then incorporate along-fault variations in temperature, pore pressure, and permeability rate to infer changes in viscosity, yield stress, and healing time. The model successfully reproduces the observed synchronous episodes of slow slip and tremors in the initial stage. We show that decreasing strength and healing time results in reducing the recurrence intervals between these episodes and the amplitude of slow slip. Conversely, decreasing viscosity leads to a larger recurrence time and increased amplitude. After introducing the along-fault variability of main mechanical parameters, the model successfully predicts tremor concentration in the downdip zone which can be explained by the influence of high pore pressure in the yield stress profile as a function of depth. The capacity of the model to reproduce some patterns seen in observations underscores its capacity to capture the physics of slow earthquakes, emphasizing its potential to improve our understanding of seismic phenomena in subduction zones.

Using discrete element simulations based on molecular dynamics, we investigate the mechanical behavior of two-dimensional sheared, dry, frictional granular media in the "dense" and "critical" regimes. We find that this behavior is partitioned between transient stages and a final stationary stage. While the latter is macroscopically consistent with the predictions of the viscous μ(I) rheology, both the macroscopic behavior during the transient stages and the overall microscopic behavior suggest a more complex picture. Indeed, the simulated granular medium exhibits a finite elastic stiffness throughout its entire shear deformation history, although topological rearrangements of the grains at the microscale translate into a partial degradation of this stiffness, which can be interpreted as a form of elastic damage. When letting the system relax under constant volume at different stages of shear deformation, the relaxation of stresses follows a compressed exponential, also highlighting the role of elastic interactions in the medium, with residual stresses that depend on the level of elastic damage. The relations we establish between elastic and relaxation properties point to a complex rheology, characterized by a damage-dependent transition between a viscoelastoplastic and a viscous behavior.

Since the discovery of fatigue phenomena, scientific research has constantly sought to understand and anticipate the failure of materials due to fatigue to mitigate unforeseen accidents and malfunctions in various technical fields. Numerous studies using acoustic emission (AE) - a key method in non-destructive testing - have shown a correlation between acoustic activity and fatigue damage. However, these measurements suffer from the non-specific nature of AE signals, which may be due to various physical sources. To investigate further the mechanisms of AE emission associated with fatigue, we study the groups of acoustic signals generated by fatigue cracking in metals. These so-called acoustic multiplets are characterized by highly correlated waveforms, are repeatedly triggered over many successive loading cycles at nearby stress levels and originate from a single location. These acoustic signatures produced during the propagation of fatigue cracks in alloys are automatically detected by a dedicated algorithm, grouped into multiplets and analyzed to understand the physical mechanisms from which they originate. By synchronizing their detection with digital image correlation measurements of fracture mechanics quantities, the investigation of this acoustic emission phenomenon shows that two mechanisms are at the origin of the multiplets: repeated local friction over fracture surfaces, and incremental crack propagation in the Paris regime, probably due to the reactivation of crack tip plasticity at each cycle. These two multiplet types serve as acoustic signatures, distinctly indicating the existence and propagation of a fatigue crack.

Non-destructive detection of fatigue crack propagation in industrial parts remains nowadays a key challenge in various engineering fields. Acoustic emission (AE) signals specific to incremental fatigue crack growth can be detected, cycle after cycle, as precursors to final fatigue rupture. These so-called acoustic multiplets are characterized by strongly similar waveforms, triggered at almost the same load during the fatigue cycle, and arising from the same source.Detecting such multiplets provides information about the crack growth process and for industrial parts in service, allows an early warning of potential failure. We developed a method based on a density-based data clustering algorithm (DBSCAN) working with a dissimilarity metric derived from the cross-correlation of AE waveforms to automatically classify acoustic multiplets in fatigue and other fields. Automatized processes described here allow to use the algorithm both on laboratory and industrial fatigue cases, and are designed to work in-operando. Our methodology is tested on AE signals recorded during different laboratory fatigue tests. This demonstrates the robustness of the algorithm to detect different multiplets for different materials, test conditions, specimen geometries, or acoustic sensors.

It is now well established that, upon decreasing system sizes down to a few m or below, the nature of plasticity of metallic materials is changing. Two important features of this small-sizes plasticity are two size effects, which can be summed up as “smaller is stronger” and “smaller is wilder”, this last observation meaning that the jerkiness of plastic deformation becomes prominent at small enough system sizes. In FCC and HCP materials, this is now rather well understood within the framework of obstacle-controlled plasticity, from the key role of a scaling ratio between the system size L and an internal scale l mainly dictated by dislocation patterning in pure materials, or by the nature of extrinsic disorder in alloys. The situation is more complex in BCC materials, for which screw dislocation motion becomes lattice-controlled, i.e. is thermally activated, below a transition temperature T_a . Therefore, in small-sized BCC systems, temperature, size and strain-rate effects combine to give rise to a complex landscape. We show, from an analysis of the literature as well as micropillar compression tests on Molybdenum performed with different sample sizes, under different temperatures and different applied strain-rates, that (i) near or above T_a , the plasticity of pure BCC metals is athermal and obstacle-controlled, much like at bulk scales, therefore mimicking that of pure FCC metals; (ii) below T_a and for sample sizes larger than ∼ 1 m, BCC plasticity becomes lattice-controlled, this damping dislocation avalanches and thus reducing wildness; but (iii) for very small systems, still below T_a , the role of screw dislocations on plasticity vanishes, i.e. is no more lattice-controlled, opening again the door for wild plastic fluctuations and jerkiness.

Unlike e.g. meteorological hazards, tectonic earthquakes remain hardly predictable, reinforcing their deadly character. This is related to a strong time asymmetry, with few and nonsystematic foreshocks sometimes preceding large earthquakes, while aftershocks are ubiquitous and have been known for a long time. However, 130 years after Omori, the physical origin of this time asymmetry and of aftershocks remains highly debated. Slider-blocks models have been proposed to explain earthquakes physics and statistics. If these models can reproduce a Gutenberg-Richer distribution of slip magnitudes, they are unable to simulate aftershocks and time asymmetry except if introducing viscous relaxation in a deterministic way. Here, we model earthquake interactions and natural seismicity from a minimal number of fundamental mechanisms, namely elastic stress transfer and reaction rate theory applied to the simplest form of static friction. This allows introducing temperature in a physically meaningful way, and to strikingly reproduce many aspects of seismicity and earthquake interactions, including time asymmetry.

We revisit the problem of describing creep in heterogeneous materials by an effective temperature by considering more realistic (and complex) non-mean-field elastic redistribution kernels. We show first, from theoretical considerations, that, if elastic stress redistribution and memory effects are neglected, the average creep failure time follows an Arrhenius expression with an effective temperature explicitly increasing with the quenched heterogeneity. Using a thermally activated progressive damage model of compressive failure, we show that this holds true when taking into account elastic interactions and memory effects, however, with an effective temperature T_{eff} depending as well on the nature of the (nondemocratic) elastic interaction kernel. We observe that the variability of creep lifetimes, for given external conditions of load and temperature, is roughly proportional to the mean lifetime and therefore depends as well on T, on quenched heterogeneity, and the elastic kernel. Finally, we discuss the implications of this effective temperature effect on the interpretation of macroscopic creep tests to estimate an activation volume at the microscale.

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Analyzing how fracture networks develop from preexisting isolated fault segments may provide knowledge of the preparation process leading to fault growth and dynamic rupture. We reproduce this process experimentally in granite core samples that contain preexisting notches. We characterize the microphysical processes of damage and fault growth in two cylindrical Westerly granite samples (10 mm diameter, 20 mm height) that contain two parallel notches oriented at 30o with respect to the axis of the cylinder, that separate an intact rock bridge. We performed triaxial compression experiments at room temperature with a constant confining pressure of 20 MPa. We image microfracture development between the notches using dynamic in situ X-ray tomography at the European Synchrotron Radiation Facility. During compressive loading, we acquired a series of tomograms of the samples, from which we extracted and quantified the statistical properties of the fractures. We analyzed the development of rock damage and the evolution of fractures oriented at 0o-17o (extensile) and 17o-32o (shear) as the rock approaches failure. We also calculated digital volume correlation to elucidate the strain localization process in the deforming rock. Our results indicate that immediately preceding failure, shear fractures dominate the fracture networks. The rock bridge between the notches becomes damaged with a damage rate and a fracture rate diverging as the rock approaches macroscopic failure. DVC analysis showed that the deformation process is mixed-mode, accommodated by dilation and shear strain. The shear strains are more localized than the dilation. Furthermore, the data reveal that regions with high dilative strain host both extensile and shear fractures.

In order to address the challenge of exploring new signals and recognizing sources based on both statistics and physics, a relevant time series representation tool, known as a deep scattering network, has been developed. A deep scattering network is a deep convolutional neural network that implements a cascade of convolutions with wavelet filters, a modulus function, and pooling operations. The advantage for unsupervised classification of time series is that deep scattering spectra are locally invariant to translation and preserve transient phenomena such as attack and amplitude modulation. We show that an AE adapted scattering network, combined with reduction model and clustering algorithm, is an efficient tool to perform unsupervised investigation of continuous acoustic data by applying our method on AE streaming recorded during fatigue testing: low amplitude acoustic multiplets non registered by common AE procedure has been clustered successfully and the content of the continuous acoustic background can be automatically grouped into classes of similar physical mechanisms, e.g. frictions, plasticity or electronic and mechanical noise.

The overwhelming amount of seismic, geodesic and in-situ observations accumulated over the last 30 years clearly indicate that, from a mechanical point of view, faults should be considered as both damageable elastic solids in which highly localized features emerge as a result of very short-term brittle processes and materials experiencing ductile strains distributed in large volumes and over long time scales. The interplay of both deformation mechanisms, brittle and ductile, give rise to transient phenomena associating slow slip and tremors, known as slow earthquakes, which dissipate a significant amount of stress in the fault system. The physically-based numerical models developed to improve our comprehension of the mechanical and dynamical behaviour of faults must therefore have the capacity to treat simultaneously both deformation mechanisms and to cover a wide range of time scales in a numerically efficient manner. This capability is essential, both for simulating accurately their deformation cycles and for improving our interpretation of the available observations.In this paper, we present a numerically efficient visco-elasto-brittle numerical framework that can simulate transient deformations akin to that observed in the context of subduction zones, over the wide range of time scales relevant for slow earthquakes. We implement the model in idealized simple shear simulations and explore the sensitivity of its behavior to the value of its main mechanical parameters.

We study an experimental model of a fault consisting in a stationary shear band in a compressed granular sample. To obtain those bands, we perform a biaxial compression of a granular sample constituted of glass beads during which we observe the spontaneous formation of shear planes along the Mohr-Coulomb directions in the sample. We study the post-failure regime during which all the deformation occurs along the stationary shear bands. Using an interferometric method of measurement of micro-deformations based on multiple scattering, we obtain full-field measurements of the local incremental deformation in the sample. The deformation measured are typically of $10^{-5}$ with a resolution of about 300 microns (3 bead diameters). Our technics gives access to the strain fluctuations inside the shear band and we show that the macroscopic mean deformation in the bands is the result of the accumulation of local, intermittent, shear events. The size distribution of those shear events follows the Gutenberg-Richter law. We observe clustering of those events following Omori's law and we apply a declustering method to reveal the causal structure underlying our sequences of events (Houdoux et al. 2021). In my talk, I will focus on recent experimental results regarding the dependence of the series statistics on the driving velocity. We have studied sequences of aftershocks for different compression velocities and we have shown that surprinsingly the aftershock sequences we observe are deformation-dependent and not time-dependent. We discuss such a deformation memory effect in the framework of an Olami-Feder-Christensen model.Houdoux et al. Commun Earth Environ 2, 90 (2021)