arXiv subjects

Jean-François Molinari

Publications and source records attributed to Jean-François Molinari.

At least 19 recordsLinked to original sources

arXiv2026

A matrix-free, differentiable PyTorch solver for phase-field fracture: Formulation, benchmarks, and inverse analysis

A matrix-free, open-source PyTorch solver is presented for phase-field fracture on central processing units (CPUs) and graphics processing units (GPUs) without custom compiled extensions. In the explicit dynamic pathway, finite-element operations are formulated as element-wise tensor contractions with scatter-based accumulation, removing global sparse mechanics-stiffness assembly from the core time-stepping loop. Both Ambrosio-Tortorelli regularisations (AT1 and AT2), multiple energy decompositions (spectral, volumetric-deviatoric, and star-convex), and plane strain or plane stress assumptions are supported. The explicit mechanics kernels are compatible with PyTorch's automatic differentiation engine (autograd), while the implicit, bound-constrained damage solve is wrapped in a custom backward rule. This rule implements implicit differentiation through the conjugate-gradient (CG) linear solve and keeps memory independent of the internal CG iteration count. The same implementation runs unmodified across macOS, Linux, and Windows, and has been run on meshes of order $10^6$ nodes on a single NVIDIA A100 GPU. The solver is compared against four dynamic fracture cases (straight crack propagation, shear-induced kinking, dynamic branching, and crack-hole interaction in perforated plates) and two quasi-static cases (single-edge notched tension and a notched-holed plate). As a differentiability demonstration, the scalar fracture energy $G_c$ is recovered from observed crack patterns using PyTorch gradients through the forward solve and limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimisation. Recovery of $G_c$ with relative error below $10^{-3}$ is achieved after three accepted L-BFGS states for glass and two for alumina. The implementation can be extended and combined with differentiable optimisation and machine-learning components.

cs.CE↗

arXiv2026

The semi-explicit nonsmooth Newmark time integrator for robust unilateral contact in dynamic fragmentation simulations

Numerical simulations of solids undergoing dynamic fragmentation, a problem characterized by dynamic fracture and dense contacts, require accurately capturing the transition from a solid continuum to interacting fragments. We use the finite-element method with the extrinsic cohesive zone model for fracture. For contact, conventional penalty-based methods often exhibit numerical instabilities in dynamic collision-rich settings. To address this, we adapt and validate a novel semi-explicit time-integration scheme: the Nonsmooth Newmark (NSN) method for unilateral contact. Based on Nonsmooth Contact Dynamics, this formulation strongly enforces contact constraints at the velocity level. Within this scheme, bulk dynamics and fracture are integrated explicitly, while contact is integrated implicitly. Benchmark tests demonstrate that the NSN scheme achieves accuracy comparable to established nonsmooth methods and outperforms penalty-based approaches by orders of magnitude. Although it incurs a higher per-step computational cost, its enhanced stability permits significantly larger time steps, yielding overall efficiency comparable to purely explicit approaches on 1D benchmarks. We applied this framework to 1D fragmentation in both free and confined expansions. Results reveal confinement shifts the fracture energy budget from local fragment kinetic energy to larger-scale global system kinetic energy. Counterintuitively, compared to fully elastic contact, adding contact dissipation reduces fracture energy yet increases the final fragment count. This contact dissipation reduces vibration within damaged fragments, allowing cleaner stress-wave propagation and better damage localization to drive full separation. These results establish the NSN scheme as a robust tool for generating high-fidelity fragmentation statistics.

physics.comp-ph↗

arXiv2026

Inverse Design of Metainterfaces for Static Friction Control: Beyond the Hertzian Limit

Programming the static friction of mechanical interfaces is critical for soft robotics, haptics, and precision gripping. Static friction is governed by the real contact area, and standard rough surfaces exhibit a linear area-load scaling inherent to classical Archard and Greenwood-Williamson models, severely restricting their functional range. Here, we propose a framework for the inverse design of tribological metainterfaces engineered for programmable contact behaviors. By utilizing general axisymmetric asperities, we unlock nonlinear macroscopic responses unattainable by standard Hertzian contacts. To solve the inverse problem, we embed a fully differentiable contact mechanics engine within a neural network and a quadratic optimizer. We leverage regularized physical gradients to automatically discover non-standard topographies that reproduce complex target friction laws, with only a few asperities in unit cells. The predicted designs are strictly validated against high-fidelity Boundary Element Method (BEM) simulations. This framework bridges data-driven optimization and rigorous physics, offering a scale-invariant pathway for discovering functional tribological surfaces.

cond-mat.soft↗

arXiv2026

Mapping the limits of equilibrium in sheared granular liquid crystals

Athermal elongated particles are well-known to follow Jeffery orbits when sheared in viscous fluids. It is less clear if similar orbits appear in dense granular flows. We show that when sheared for long enough, sufficiently elongated frictionless granular rods, rather than following noisy Jeffery-like orbits, exist in a quasi-equilibrium state, whose orientational statistics are quantitatively described by classical liquid crystal theory, where the noise is provided by collisions due to shear. At the same time, we demonstrate a systematic breakdown of this equilibrium analogy at two distinct limits: at low aspect ratios, where the equilibrium theory incorrectly predicts an isotropic state, and as inter-particle friction is introduced, where the system moves from steric screening to frictional gearing. Even within this frictionally geared state, the rotational dynamics remain distinct from classical Jeffery orbits. We link this frictional breakdown directly to the system being driven far from equilibrium, as quantified by an effective Ericksen number that compares non-equilibrium rotational driving to steric ordering. Our results provide a quantitative map of the transition from a quasi-equilibrium to a far-from-equilibrium steady state in a dense, driven system, defining the limits of applicability for thermal liquid crystal theory in athermal matter.

cond-mat.soft↗

arXiv2025

Origins of phase-field crack widening in dynamic fragmentation explained

We investigate dynamic crack propagation and fragmentation with the phase-field fracture approach. The method was chosen for its ability to yield crack paths that are independent of the underlying mesh, thanks to the damage regularization zone. In dynamics, we observe a progressive widening of this regularization zone and attribute it to an unphysical trapping of elastic waves. We show that the damage zones do not represent free boundaries accurately and that wave interactions induce additional damage. We reveal how mass erosion, by conserving the elastic wave speed in the damaged regions, can be used to efficiently reduce the spurious diffusion of damage. Furthermore, we provide numerical evidence that dynamically propagating cracks in the phase-field formulation, both with and without mass erosion, converge to the predictions of linear elastic fracture mechanics. For vanishing regularization length, the crack speed and energy release rate become independent of the phase-field regularization length, provided that this length scale is small enough and the mesh fine enough to resolve the process zone.

physics.comp-ph↗

arXiv2025

Stability of Extrinsic Cohesive-Zone Model with Penalty-Based Contact in Explicit Dynamic Fragmentation Simulations

Dynamic fragmentation simulations are essential for predicting material response at high strain rates, yet explicit dynamic simulations that combine an extrinsic cohesive-zone model (CZM) with penalty-based contact often exhibit severe instabilities. In a two-dimensional benchmark, we observe exponential energy growth and resulting artificial fragmentation under standard contact penalty settings and time step choices, which motivates a systematic analysis of instability sources. Three mechanisms are isolated and quantified: (i) diverging initial cohesive stiffness, which constrains the stable time step; (ii) discontinuous stiffness jumps at the cohesive-contact interface; and (iii) discontinuity introduced by cohesive softening. Analytical error estimates, phase-space diagnostics, and energy growth metrics reveal that repeated cohesive-contact switching can accumulate small per-step energy errors into long-term energy drift. Within the explored parameter space, maintaining stability requires time steps well below the usual limit. To mitigate these energy artifacts, we assess an adaptive penalty strategy that ties the contact stiffness to the evolving cohesive stiffness. This modification eliminates the discontinuity and restores energy conservation, but it allows larger interpenetration, making it suitable as a diagnostic rather than a definitive remedy. Overall, our study identifies the root causes of unphysical energy drift and demonstrates that penalty-based contact is not a viable approach for long-term, energy-consistent fragmentation simulations with physically meaningful fragment statistics.

physics.comp-ph↗

arXiv2025

Shear flow of frictional spheroids: Comparison between elongated and flattened particles

The rheology of dense granular shear flows is influenced by friction and particle shape. We investigate numerically the impact of non-spherical particle geometries under shear on packing fraction, stress ratios, velocity fluctuations, force distribution, and dissipation mechanisms, for a wide range of inertial numbers, friction coefficients and aspect ratios. We obtain a regime diagram for the dissipation which shows that lentil-like (oblate) particles exhibit an extended sliding regime compared to rice-like (prolate) particles with the same degree of eccentricity. Additionally, we identify non-monotonic behaviour of slightly aspherical particles at low friction, linking it to their higher fluctuating rotational kinetic energy. We find that angular velocity fluctuations are generally reduced when particles align with the flow, except in highly frictional rolling regimes, where fluctuations collapse onto a power-law distribution and motion becomes less correlated. Moreover, for realistic friction coefficients power dissipation tends to concentrate along the major axis aligned with the flow, where slip events are more frequent. We also show that flat particles develop stronger fabric anisotropy than elongated ones, influencing macroscopic stress transmission. These findings provide new insights into the role of particle shape in granular mechanics, with implications for both industrial and geophysical applications.

cond-mat.soft↗

arXiv2025

A multiscale model of friction considering the influence of third-body wear particles

Accurately predicting friction in sliding interfaces that contain third body wear particles is critical for engineering applications such as sliding movement in pistons, bearings, or metal forming. We present a hierarchical multiscale framework that links particle scale mechanics to macroscopic friction in a strip draw friction test. At the macroscale, a one dimensional finite element model reproduces the global stress state of the strip draw setup and updates the local wear particle density via Archard's law. The local friction force at each node is then computed from mesoscale simulation results. At the mesoscale, a coupled discrete element boundary element approach resolves load sharing between rough surfaces and rigid oblate spheroidal wear particles. The mesoscale solution returns to the macroscale solver a friction coefficient that depends on normal pressure, sliding velocity, surface geometry, and particle density, thereby closing the loop between scales. The simulated friction coefficient matches strip draw experiments, capturing both the observed decrease in friction with increasing normal pressure and the influence of tool pad size.

physics.app-ph↗

arXiv2024

A Parallelized 3D Geomechanical Solver for Fluid-induced Fault Slip in Poroelastic Media

We present a fully implicit formulation of coupled fluid flow and geomechanics for fluid injection/withdrawal in fractured reservoirs in the context of CO2storage. Utilizing a Galerkin finite-element approach, both flow and poroelasticity equations are discretized on a shared three-dimensional mesh. The fluid flow is assumed to be single-phase. The hydraulic behaviour of fractures is represented through a double-nodes flow element, which allows to efficiently model longitudinal and transversal fracture permeabilities. In addressing the mechanical subproblem, fractures are explicitly modelled using cohesive elements to account for contact, friction and opening phenomena. The nonlinear set of equations is solved implicitly through an iterative partitioned conjugate gradient procedure, extending its traditional application to continuous problems to those involving explicit discontinuities such as faults and fractures. The model's accuracy is verified against analytical solutions for different geomechanical problems, notably for the growth of a frictional slip rupture along a fault due to fluid injection. Such a particularly challenging benchmark for a critically stressed fault is here reproduced for the first time by a finite-element based scheme. The capabilities of the developed parallel solver are then illustrated through a scenario involving CO2 injection into a faulted aquifer. The original solver code, tutorials, and data visualization routines are publicly accessible.

physics.geo-ph↗

arXiv2024

Do Slip-Weakening Laws Shapes Influence Rupture Dynamics?

To model rupture dynamics, a friction law must be assumed. Commonly used constitutive laws for modeling friction include slip-weakening laws which are characterized by a drop from static to dynamic frictional stress. Within this framework, the prevailing understanding asserts that the frictional behavior is solely controlled by the fracture energy -- the area beneath the frictional stress versus the cumulative slip curve. In particular, it is claimed that the curve's shape itself has no influence on the system's response. Here we perform fully dynamic rupture simulations to challenge prevailing beliefs by demonstrating that the constitutive law shape exerts an intimate control over rupture profiles. For a consistent fracture energy but varying constitutive law shapes, the velocity profile is different: each abrupt slope transition leads to the localization of a distinct velocity peak. For example, in the case of a bilinear slip-weakening law featuring two different slopes, the rupture exhibits two distinct velocity peaks. This phenomenon arises from the transition between a constant weakening rate to another. However, this distinction does not seem to influence how a rupture responds to a stress barrier or the cumulative radiated energy emitted. These results are derived through two separate numerical schemes (spectral boundary integral and finite element methods) ensuring their independence from the computational approach employed.

physics.geo-ph↗

arXiv2024

A finite geometry, inertia assisted coarsening-to-complexity transition in homogeneous frictional systems

The emergence of statistical complexity in frictional systems, manifested in broad distributions of various observables, is not yet understood. We study this problem in velocity-driven, homogeneous (no quenched disorder) unstable frictional systems of height $H$. The latter are described at the continuum scale within a realistic rate-and-state friction interfacial constitutive framework, where elasto-frictional instabilities emerge from rate-weakening friction. For large $H$, such frictional systems were recently shown to undergo continuous coarsening until settling into a spatially periodic traveling solution. We show that when the system's height-to-length ratio becomes small, coarsening is less effective and the periodic solution is dynamically avoided. Instead, and consistently with previous reports, the system settles into a stochastic, statistically stationary state. The latter features slip bursts, classified into predominantly non-propagating small bursts and propagating large bursts, which are non-trivially distributed. The statistical distributions emerge from dynamically self-generated heterogeneity, where both the non-equilibrium history of the interface and wave reflections from finite boundaries, mediated by material inertia, play central roles. Specifically, the dynamics and statistics of large bursts reveal a timescale $\sim\!H/c_{\rm s}$, where $c_{\rm s}$ is the shear wave-speed. We discuss the robustness of our findings against variations of the frictional parameters, most notably affecting the magnitude of frictional rate-weakening, as well as against different interfacial state evolution laws. Finally, we demonstrate a reverse transition in which statistical complexity disappears in favor of the spatially periodic traveling solution. Overall, our results elucidate how relatively simple physical ingredients can give rise to the emergence of slip complexity.

cond-mat.mtrl-sci↗

arXiv2023

Fluid-mediated impact of soft solids

A viscous, lubrication-like response can be triggered in a thin film of fluid squeezed between a rigid and flat surface and the tip of an incoming projectile. We develop a comprehensive theory for this viscous approach stage of fluid-mediated normal impact, applicable to soft impactors. Under the assumption of mediating fluid being incompressible, the impacting solid displays two limit regimes: one dominated by elasticity and the other by inertia. The transition between the two is predicted by a dimensionless parameter, which can be interpreted as the ratio between two time scales that are the time that it takes for the surface waves to warn the leading edge of the impactor of the forthcoming impact, and the characteristic duration of the final viscous phase of the approach. Additionally, we assess the role of solid compressibility and elucidate why nearly-incompressible solids feature (a) substancial "gliding" prior to contact at the transition between regimes, (b) the largest size of entrapped bubble between the deformed tip of the impactor and the flat surface, and (c) a sudden drop in entrapped bubble radius past the transition between regimes. Finally, we argue that the above time scale ratio (a dimensionless number) can govern the different dynamics reported experimentally for a fluid droplet as a function of its viscosity and surface tension.

cond-mat.soft↗

arXiv2023

Role of minimum adhesive wear particle size in third-body layer properties

We employ a novel discrete element method (DEM) force formulation to simulate adhesive wear and assess the effects of material and loading parameters on the properties of the third-body layer (TBL) formed during sliding motion. The study emphasizes the role of a material's critical length scale d* in the rheology of the TBL. This critical length scale is already known for controlling the size of smallest wear particles. We observe the emergence of a several wear regimes involving wear particle creation and aggregation, with limited effect from d* on TBL properties. Instead, material strength and surface energy have a profound influence. This study opens up new avenues for exploration of larger systems, three-dimensional setups, and other loading conditions.

cond-mat.soft↗

arXiv2023

Roughness evolution induced by third-body wear

Surface roughness is a key factor when it comes to friction and wear, as well as to other physical properties. These phenomena are controlled by mechanisms acting at small scales, in which the topography of apparently-flat surfaces is revealed. Roughness in natural surfaces has been reported to conform to self-affine statistics in a wide variety of settings (ranging from earthquake physics to micro-electro-mechanical devices), meaning that the height profile can be described using a spectrum where the amplitude is proportional to its wavelength raised to a constant power, which is related to a statistical parameter named Hurst exponent. We analyze the roughness evolution in atomistic surfaces during molecular dynamics simulations of wear. Both pairs of initially-flat and initially-rough surfaces in contact are worn by a third body formed by particles trapped between them during relative sliding. During the first sliding stages, the particles trapped between the first bodies scratch the surfaces. Once the former become coated with atoms from the latter, the wear process slows down and becomes "adhesive-like". The initial particle sizes are consistent with the minimum size to be expected for the debris, but tend to grow by material removal from the surfaces and to agglomerate. We show that, for the particular configurations under consideration, the surface roughness seems to converge to a steady state characterized by Hurst exponent close to 0.8, independently of the initial conditions.

cond-mat.mtrl-sci↗

arXiv2023

Breakdown of Reye's theory in nanoscale wear

Building on an analogy to ductile fracture mechanics, we quantify the size of debris particles created during adhesive wear. Earlier work suggested a linear relation between tangential work and wear debris volume, assuming that the debris size is proportional to the micro contact size multiplied by the junction shear strength. However, the present study reveals deviations from linearity. These deviations can be rationalized with fracture mechanics and imply that less work is necessary to generate debris than what was assumed. Here, we postulate that the work needed to detach a wear particle is made of the surface energy expended to create new fracture surfaces, and also of plastic work within a fracture process zone of a given width around the cracks. Our theoretical model, validated by molecular dynamics simulations, reveals a super-linear scaling relation between debris volume ($V_d$) and tangential work ($W_t$): $V_d \sim W_t^{3/2}$ in 3D and $V_d \sim W_t^{2}$ in 2D. This study provides a theoretical foundation to estimate the statistical distribution of sizes of fine particles emitted due to adhesive wear processes.

cond-mat.mtrl-sci↗

arXiv2023

Quasi-static crack front deformations in cohesive materials

When a crack interacts with material heterogeneities, its front distorts and adopts complex tortuous configurations that are reminiscent of the energy barriers encountered during crack propagation. As such, the study of crack front deformations is key to rationalize the effective failure properties of micro-structured solids and interfaces. Yet, the impact of a localized dissipation in a finite region behind the crack front, called the process zone, has often been overlooked. In this work, we derive the equation ruling 3D coplanar crack propagation in heterogeneous cohesive materials where the opening of the crack is resisted by some traction in its wake. We show that the presence of a process zone results in two competing effects on the deformation of crack fronts: (i) it makes the front more compliant to small-wavelength perturbations, and (ii) it smooths out local fluctuations of strength and process zone size, from which emerge heterogeneities of fracture energy. Their respective influence on front deformations is shown to strongly impact the stability of perturbed crack fronts, as well as their stationary shapes when interacting with arrays of tough obstacles. Overall, our theory provides a unified framework to predict the variety of front profiles observed in experiments, even when the small-scale yielding hypothesis of linear elastic fracture mechanics breaks down.

cond-mat.mtrl-sci↗

arXiv2022

Mesh d-refinement: a data-based computational framework to account for complex material response

Model-free data-driven computational mechanics (DDCM) is a new paradigm for simulations in solid mechanics. The modeling step associated to the definition of a material constitutive law is circumvented through the introduction of an abstract phase space in which, following a pre-defined rule, physically-admissible states are matched to observed material response data (coming from either experiments or lower-scale simulations). In terms of computational resources, the search procedure that performs these matches is the most onerous step in the algorithm. One of the main advantages of DDCM is the fact that it avoids regression-based, bias-prone constitutive modeling. However, many materials do display a simple linear response in the small-strain regime while also presenting complex behavior after a certain deformation threshold. Motivated by this fact, we present a novel refinement technique that turns regular elements (equipped with a linear-elastic constitutive law) into data-driven ones if they are expected to surpass the threshold known to trigger material non-linear response. We term this technique ``data refinement'', ``d-refinement'' for short. Starting from an initially regular FEM mesh, the proposed algorithm detects where the refinement is needed and iterates until all elements presumed to display non-linearity become data-driven ones. Insertion criteria are discussed. The scheme is well-suited for simulations that feature non-linear response in relatively small portions of the domain while the rest remains linear-elastic. The method is validated against a traditional incremental solver (i.e., Newton-Raphson method) and we show that the d-refinement framework can outperform it in terms of speed at no loss of accuracy. We provide an application that showcases the advantage of the new method: bridging scales in architected metamaterials.

cond-mat.mtrl-sci↗

arXiv2022

Data-driven numerical site response

Prediction of ground motion triggered by earthquakes is a prime concern for both the seismology community and geotechnical earthquake engineering one. The subfield occupied with such a problem is termed site response analysis (SRA), its one-dimensional flavor (1D-SRA) being particularly popular given its simplicity. Despite the simple geometrical setting, a paramount challenge remains when it comes to numerically consider intense shaking in the soft upper soil strata of the crust: how to mathematically model the high-strain, dissipative, potentially rate-dependent soil behavior. Both heuristics models and phenomenological constitutive laws have been developed to meet the challenge, neither of them being exempt of either numerical limitations or physical inadequacies or both. We propose herein to bring the novel data-driven paradigm to bear, thus giving away with the need to construct constitutive behavior models altogether. Data-driven computational mechanics (DDCM) is a novel paradigm in solid mechanics that is gaining popularity; in particular, the multiscale version of it relies on studying the response of the microstructure (in the case of soil, representative volumes containing grains) to populate a dataset that is later used to inform the response at the macroscale. This manuscript presents the first application of multiscale DDCM to 1D-SRA: first, we demonstrate its capacity to handle wave propagation problems using discrete datasets, obtained via sampling grain ensembles using the discrete element method (DEM), in lieu of a constitutive law and then we apply it specifically to analyze the propagation of harmonic waves in a soft soil deposit that overlies rigid bedrock. We validate the implementation via comparison to regular finite elements analyses (FEA) and demonstrate that traditional amplification functions are recovered when using the DDCM.

physics.geo-ph↗