arXiv subjects

Laura De Lorenzis

Publications and source records attributed to Laura De Lorenzis.

At least 19 recordsLinked to original sources

arXiv2026

An associated model of Coulomb friction based on the real area of contact

Coulomb friction is a non-associated law: it contains a threshold that depends on the contact pressure, i.e. a stress that is not conjugate to any internal variable, hence it admits no dissipation potential in the sense of generalized standard materials (GSM), and the incremental frictional contact problem is not a minimization problem. In this paper, we propose an alternative friction model that retains Coulomb-like behavior while being associated and fully GSM-compatible. Key to our formulation is the introduction of a new internal variable motivated by the microscopic contact state of rough surfaces, whose evolution is driven by the plastic deformation of the asperities. Under a non-decreasing contact pressure and below a threshold pressure, the model recovers Coulomb friction up to an asperity-scale penetration depth. This depth is physically meaningful and can be calibrated to reproduce known tribology results. Under decreasing contact pressures, the model exhibits a memory effect due to irreversible plastic deformation of the asperities, whereas above the pressure threshold it yields a saturation of the frictional traction. We present both penalty and Lagrange multiplier formulations of the model. A 2D finite element implementation of the penalty approach confirms excellent agreement with the classical Coulomb predictions across two benchmark tests.

physics.app-ph↗

arXiv2026

On phase-field regularization in dynamic fracture with brittle and cohesive formulations

Phase-field models of fracture are widely used for simulating crack nucleation and propagation, yet the role of the phase-field regularization in the dynamic regime is not fully understood and depends critically on how the damage variable is coupled to the displacement field. In this paper, we analyze three alternative formulations: the brittle model with stiffness degradation, its variant with stiffness+density degradation, and our recently proposed phase-field regularization of cohesive fracture, which we extend to elastodynamics. By studying the interaction of a tensile and a compressive elastic wave with a phase-field crack in a one-dimensional bar, we determine for which models and under which conditions the phase-field regularization preserves the features of the wave-crack interaction expected for a sharp crack, and we theoretically explain which variables control the behavior. For the new cohesive model extended to dynamics, we further derive an analytical dynamic cohesive opening law. Finally, we study the dynamic behavior including branching of a two-dimensional notched plate at two loading intensities.

cs.CE↗

arXiv2026

Iterative convergence in phase-field brittle fracture computations: exact line search is all you need

Variational phase-field models of brittle fracture pose a local constrained minimization problem of a non-convex energy functional. In the discrete setting, the problem is most often solved by alternate minimization, exploiting the separate convexity of the energy with respect to the two unknowns. This approach is theoretically guaranteed to converge, provided each of the individual subproblems is solved successfully. However, strong non-linearities of the energy functional may lead to failure of iterative convergence within one or both subproblems. We analyze and visualize the energy along Newton directions to illustrate why Newton's method without line search fails. Motivated by this, we propose to employ an exact line search algorithm based on bisection, which (under certain conditions) can guarantee global convergence of Newton's method for each subproblem and consequently the successful determination of critical points of the energy through the alternate minimization scheme. Through several benchmark tests computed with various strain energy decompositions and two strategies for the enforcement of the irreversibility constraint in two and three dimensions, we demonstrate the robustness of the approach and assess its efficiency in comparison with other commonly used line search algorithms. With the outlined approach, we are able to compute the especially demanding Brazilian test featuring contact in 3D with the star-convex model.

cs.CE↗

arXiv2026

Variational phase-field modeling of fracture and fatigue in shape memory alloys: a one-dimensional study

We propose a novel variational phase-field model for fracture and fatigue in pseudoelastic shape memory alloys (SMAs). The model, developed in a one-dimensional setting, builds upon the Auricchio-Petrini constitutive formulation for SMAs and couples damage evolution with phase transformation. We study analytically and numerically the homogeneous and localization responses of a bar under both monotonic and cyclic loading, and we investigate various macroscopic behaviors by tuning the constitutive parameters. A key feature of the model is the introduction of a transformation strain limit, beyond which the material is fully martensitic and behaves elastically. This leads to a distinctive behavior in which the region of localized damage widens, yielding a delay of fracture. The capability of the model to predict the fatigue performance is assessed by simulating the uniaxial response of Ni-Ti multi-wire samples under different loading conditions. The results show that the model discriminates between safe and critical loading scenarios, capturing the experimental trend of increased fatigue resistance with higher mean strain at a fixed strain amplitude. Ongoing efforts are aimed at further evaluating its reliability for quantitative fatigue life prediction.

physics.app-ph↗

arXiv2026

Imposing Boundary Conditions on Neural Operators via Learned Function Extensions

Neural operators have emerged as powerful surrogates for the solution of partial differential equations (PDEs), yet their ability to handle general, highly variable boundary conditions (BCs) remains limited. Existing approaches often fail when the solution operator exhibits strong sensitivity to boundary forcings. We propose a general framework for conditioning neural operators on complex non-homogeneous BCs through function extensions. Our key idea is to map boundary data to latent pseudo-extensions defined over the entire spatial domain, enabling any standard operator learning architecture to consume boundary information. The resulting operator, coupled with an arbitrary domain-to-domain neural operator, can learn rich dependencies on complex BCs and input domain functions at the same time. To benchmark this setting, we construct 18 challenging datasets spanning Poisson, linear elasticity, and hyperelasticity problems, with highly variable, mixed-type, component-wise, and multi-segment BCs on diverse geometries. Our approach achieves state-of-the-art accuracy, outperforming baselines by large margins, while requiring no hyperparameter tuning across datasets. Overall, our results demonstrate that learning boundary-to-domain extensions is an effective and practical strategy for imposing complex BCs in existing neural operator frameworks, enabling accurate and robust scientific machine learning models for a broader range of PDE-governed problems.

cs.LG↗

arXiv2026

Discovery of Hyperelastic Constitutive Laws from Experimental Data with EUCLID

We assess the performance of EUCLID, Efficient Unsupervised Constitutive Law Identification and Discovery, a recently proposed framework for automated discovery of constitutive laws, on experimental data. Mechanical tests are performed on natural rubber specimens spanning simple to complex geometries, from which we collect both global, force elongation, and local, full-field displacement, measurements. Using these data, we obtain constitutive laws via two routes, the conventional identification of unknown parameters in a priori selected material models, and EUCLID, which automates model selection and parameter identification within a unified model-discovery pipeline. We compare the two methodologies using global versus local data, analyze predictive accuracy, and examine generalization to unseen geometries. Moreover, we quantify the experimental noise, investigate the coverage of the material state space achieved by each approach and discuss the relative performance of different datasets and different a priori chosen models versus EUCLID.

physics.comp-ph↗

arXiv2025

Automated Constitutive Model Discovery by Pairing Sparse Regression Algorithms with Model Selection Criteria

The automated discovery of constitutive models from data has recently emerged as a promising alternative to the traditional model calibration paradigm. In this work, we present a fully automated framework for constitutive model discovery that systematically pairs three sparse regression algorithms Least Absolute Shrinkage and Selection Operator (LASSO), Least Angle Regression (LARS), and Orthogonal Matching Pursuit (OMP)) with three model selection criteria: $K$-fold cross-validation (CV), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC). This pairing yields nine distinct algorithms for model discovery and enables a systematic exploration of the trade-off between sparsity, predictive performance, and computational cost. While LARS serves as an efficient path-based solver for the $\ell_1$-constrained problem, OMP is introduced as a tractable heuristic for $\ell_0$-regularized selection. The framework is applied to both isotropic and anisotropic hyperelasticity, utilizing both synthetic and experimental datasets. Results reveal that all nine algorithm-criterion combinations perform consistently well in discovering isotropic and anisotropic materials, yielding highly accurate constitutive models. These findings broaden the range of viable discovery algorithms beyond $\ell_1$-based approaches such as LASSO.

cs.LG↗

arXiv2025

Variational phase-field modeling of cohesive fracture with flexibly tunable strength surface

Variational phase-field models of brittle fracture are powerful tools for studying Griffith-type crack propagation in complex scenarios. However, as approximations of Griffith's theory-which does not incorporate a strength criterion-these models lack flexibility in prescribing material-specific strength surfaces. Consequently, they struggle to accurately capture crack nucleation under multiaxial stress conditions. In this paper, inspired by Alessi et al. (2014), we propose a variational phase-field model that approximates cohesive fracture. The model accommodates an arbitrary (convex) strength surface, independent of the regularization length scale, and allows for flexible tuning of the cohesive response. Our formulation results in sharp cohesive cracks and naturally enforces a sharp non-interpenetration condition, thereby eliminating the need for additional energy decomposition strategies. It inherently satisfies stress softening and produces "crack-like" residual stresses by construction. To ensure strain hardening, the ratio of the regularization length to the material's cohesive length must be sufficiently small; however, if crack nucleation is desired, this ratio must also be large enough to make the homogeneous damaged state unstable. We investigate the model in one and three dimensions, establishing first- and second-order stability results. The theoretical findings are validated through numerical simulations using the finite element method, employing standard discretization and solution techniques.

physics.app-ph↗

arXiv2025

Gamma convergence for a phase-field cohesive energy

Reproducing the key features of fracture behavior under multiaxial stress states is essential for accurate modeling. Experimental evidence indicates that three intrinsic material properties govern fracture nucleation in elastic materials: elasticity, strength, and fracture toughness. Among these, strength remains the most often misunderstood, as it is not a single scalar quantity but rather a full surface in stress space. The flexibility in defining this strength envelope in phase-field models poses significant challenges, especially under complex loading conditions. Existing models in the literature often fail to capture both the qualitative shape and the quantitative fit of experimentally observed strength surfaces. To address this limitation, recent work introduces a new energy functional within a cohesive phase-field framework, specifically designed to control the shape of elastic domains. This model introduces an internal variable to describe the inelastic response. Notably, the strength is decoupled from the internal length, that is not interpreted as a material length scale, as often done in literature, but rather as a purely variational tool. The proposed functional allows for a rigorous variational framework, enabling the use of tools from the calculus of variations. We investigate the Gamma-convergence of the model to a sharp cohesive fracture energy in the one- and two-dimensional (anti-plane) setting, using a finite element discrete formulation and exploiting the strong localization of the damage variable. Notably, unlike classical models where the elastic and fracture energies converge independently, this model exhibits a coupling of all energy terms. We also present numerical simulations exploring the sensitivity of the model to mesh anisotropy, offering insight into both its theoretical robustness and its practical implementation.

math.NA↗

arXiv2025

A variational phase-field model for anisotropic fracture accounting for multiple cohesive lengths

We propose a novel variational phase-field model for fracture in anisotropic materials. The model is specifically designed to allow a more flexible calibration of crack nucleation than existing anisotropic fracture formulations, while avoiding the introduction of multiple damage variables. In addition to the classical components of anisotropic phase-field models based on a single damage variable -- namely, anisotropic elasticity and the extension of the fracture energy density via a second-order structural tensor -- the proposed approach introduces fracture anisotropy through a cohesive degradation function with potentially distinct cohesive lengths along the principal material directions. For this reason, we refer to it as multi-cohesive model. This feature enables independent control of the critical stresses governing crack nucleation in each material direction. We analyze the homogeneous solution and its second-order stability, and we compare the resulting strength surfaces with those of two representative anisotropic phase-field models available in the literature. Finally, numerical simulations in two and three dimensions demonstrate the capability of the proposed model to independently control crack nucleation and propagation in anisotropic fracture problems of increasing complexity.

physics.app-ph↗

arXiv2025

A variationally consistent and asymptotically convergent phase-field model for solute precipitation and dissolution

We propose a novel phase-field model for solute precipitation and dissolution in liquid solutions. Unlike in previous studies with similar scope, in our model the two non-linear coupled governing equations of the problem, which deliver the solute ion concentration and the phase-field variable, are derived in a variationally consistent way starting from a free energy functional of Modica-Mortola type. The phase-field variable is assumed to follow the non-conservative Allen-Cahn evolution law, whereas the solute ion concentration obeys the conservative Cahn-Hilliard equation. We also assess the convergence of the new model to the corresponding sharp-interface model via the method of matched asymptotic expansions, and derive a novel expression of the reaction rate of the sharp-interface model. Through a finite element discretization, we present several numerical examples in two and three dimensions.

physics.comp-ph↗

arXiv2025

A topology optimisation framework to design test specimens for one-shot identification or discovery of material models

The increasing availability of full-field displacement data from imaging techniques in experimental mechanics is determining a gradual shift in the paradigm of material model calibration and discovery, from using several simple-geometry tests towards a few, or even one single test with complicated geometry. The feasibility of such a "one-shot" calibration or discovery heavily relies upon the richness of the measured displacement data, i.e., their ability to probe the space of the state variables and the stress space (whereby the stresses depend on the constitutive law being sought) to an extent sufficient for an accurate and robust calibration or discovery process. The richness of the displacement data is in turn directly governed by the specimen geometry. In this paper, we propose a density-based topology optimisation framework to optimally design the geometry of the target specimen for calibration of an anisotropic elastic material model. To this end, we perform automatic, high-resolution specimen design by maximising the robustness of the solution of the inverse problem, i.e., the identified material parameters, given noisy displacement measurements from digital image correlation. We discuss the choice of the cost function and the design of the topology optimisation framework, and we analyse a range of optimised topologies generated for the identification of isotropic and anisotropic elastic responses.

cs.CE↗

arXiv2025

Phase-field modeling of elastic microphase separation

We propose a novel phase-field model to predict elastic microphase separation in polymer gels. To this end, we extend the Cahn-Hilliard free-energy functional to incorporate an elastic strain energy and a coupling term. These contributions are naturally obtained from a derivation that starts from an entropic elastic energy density combined with the assumption of weak compressibility, upon second-order approximation around the swollen state. The resulting terms correspond to those of a poroelastic formulation where the coupling energetic term can be interpreted as the osmotic work of the solvent within the polymer matrix. Additionally, a convolution term is included in the total energy to model non-local forces responsible for coarsening arrest. With analytical derivations in 1D and finite element computations in 2D we show that the mechanical deformation controls the composition of the stable phases, the initial characteristic length and time, the coarsening rates and the arrested characteristic length. Moreover, we demonstrate that the proposed coupling is able to predict the arrest of coarsening at a length scale controlled by the stiffness of the dry polymer. The numerical results show excellent agreement with the experimental evidence in terms of phase-separated morphology and scaling of the characteristic length with the stiffness of the dry polymer.

cond-mat.mtrl-sci↗

arXiv2025

Predicting Crack Nucleation and Propagation in Brittle Materials Using Deep Operator Networks with Diverse Trunk Architectures

Phase-field modeling reformulates fracture problems as energy minimization problems and enables a comprehensive characterization of the fracture process, including crack nucleation, propagation, merging, and branching, without relying on ad-hoc assumptions. However, the numerical solution of phase-field fracture problems is characterized by a high computational cost. To address this challenge, in this paper, we employ a deep neural operator (DeepONet) consisting of a branch network and a trunk network to solve brittle fracture problems. We explore three distinct approaches that vary in their trunk network configurations. In the first approach, we demonstrate the effectiveness of a two-step DeepONet, which results in a simplification of the learning task. In the second approach, we employ a physics-informed DeepONet, whereby the mathematical expression of the energy is integrated into the trunk network's loss to enforce physical consistency. The integration of physics also results in a substantially smaller data size needed for training. In the third approach, we replace the neural network in the trunk with a Kolmogorov-Arnold Network and train it without the physics loss. Using these methods, we model crack nucleation in a one-dimensional homogeneous bar under prescribed end displacements, as well as crack propagation and branching in single edge-notched specimens with varying notch lengths subjected to tensile and shear loading. We show that the networks predict the solution fields accurately, and the error in the predicted fields is localized near the crack.

physics.comp-ph↗

arXiv2025

Fracture in concrete: X-ray tomography with in-situ testing, digital volume correlation and phase-field modeling

We test and simulate the mesoscopic cracking behavior of specimens made of a standard concrete mixture. To this end, we combine stable wedge-splitting fracture experiments performed during X-ray tomography, their analysis with digital volume correlation providing the full three-dimensional displacement field, and phase-field cohesive fracture modeling. In our computations, we apply the measured boundary conditions and model the actual heterogeneous material structure at the mesoscopic scale. Within the phase-field model, we explicitly distinguish among (thus individually represent) the mesostructural features of distinct material phases with size above a threshold of 1 mm, while we homogenize pores and finer aggregates below this threshold within the cementitious mortar matrix, with material parameters characterized accordingly. We compare experimental and numerical results in terms of both local and global quantities.

cond-mat.mes-hall↗

arXiv2024

An adaptive acceleration scheme for phase-field fatigue computations

Phase-field models of fatigue are capable of reproducing the main phenomenology of fatigue behavior. However, phase-field computations in the high-cycle fatigue regime are prohibitively expensive, due to the need to resolve spatially the small length scale inherent to phase-field models and temporally the loading history for several millions of cycles. As a remedy, we propose a fully adaptive acceleration scheme based on the cycle jump technique, where the cycle-by-cycle resolution of an appropriately determined number of cycles is skipped while predicting the local system evolution during the jump. The novelty of our approach is a cycle-jump criterion to determine the appropriate cycle-jump size based on a target increment of a global variable which monitors the advancement of fatigue. We propose the definition and meaning of this variable for three general stages of the fatigue life. In comparison to existing acceleration techniques, our approach needs no parameters and bounds for the cycle-jump size, and it works independently of the material, specimen or loading conditions. Since one of the monitoring variables is the fatigue crack length, we introduce an accurate, flexible and efficient method for its computation, which overcomes the issues of conventional crack tip tracking algorithms and enables the consideration of several cracks evolving at the same time. The performance of the proposed acceleration scheme is demonstrated with representative numerical examples, which show a speedup reaching four orders of magnitude in the high-cycle fatigue regime with consistently high accuracy.

cs.CE↗

arXiv2024

Calibration and Validation of a Phase-Field Model of Brittle Fracture within the Damage Mechanics Challenge

In the context of the Damage Mechanics Challenge, we adopt a phase-field model of brittle fracture to blindly predict the behavior up to failure of a notched three-point-bending specimen loaded under mixed-mode conditions. The beam is additively manufactured using a geo-architected gypsum based on the combination of bassanite and a water-based binder. The calibration of the material parameters involved in the model is based on a set of available independent experimental tests and on a two-stage procedure. In the first stage an estimate of most of the elastic parameters is obtained, whereas the remaining parameters are optimized in the second stage so as to minimize the discrepancy between the numerical predictions and a set of experimental results on notched three-point-bending beams. The good agreement between numerical predictions and experimental results in terms of load-displacement curves and crack paths demonstrates the predictive ability of the model and the reliability of the calibration procedure.

cs.CE↗

arXiv2024

MeltpoolINR: Predicting temperature field, melt pool geometry, and their rate of change in laser powder bed fusion

We present a data-driven, differentiable neural network model designed to learn the temperature field, its gradient, and the cooling rate, while implicitly representing the melt pool boundary as a level set in laser powder bed fusion. The physics-guided model combines fully connected feed-forward neural networks with Fourier feature encoding of the spatial coordinates and laser position. Notably, our differentiable model allows for the computation of temperature derivatives with respect to position, time, and process parameters using autodifferentiation. Moreover, the implicit neural representation of the melt pool boundary as a level set enables the inference of the solidification rate and the rate of change in melt pool geometry relative to process parameters. The model is trained to learn the top view of the temperature field and its spatiotemporal derivatives during a single-track laser powder bed fusion process, as a function of three process parameters, using data from high-fidelity thermo-fluid simulations. The model accuracy is evaluated and compared to a state-of-the-art convolutional neural network model, demonstrating strong generalization ability and close agreement with high-fidelity data.

physics.app-ph↗