arXiv subjects

I. Romero

Publications and source records attributed to I. Romero.

8 recordsLinked to original sources

arXiv2026

A Correction Method for Crack Area Overestimation in Phase-Field Fracture

Phase-field fracture models are known to overestimate the crack area, a discrepancy that compromises the accuracy of fracture predictions. This issue stems from the diffuse crack representation and numerical artifacts, such as strain localization, where the phase-field variable artificially saturates across finite elements. Existing correction strategies, including mesh-dependent factors and skeletonization algorithms, have significant limitations. Mesh-based corrections are often unreliable for unstructured meshes, while skeletonization can be complex and inaccurate for intricate crack topologies, especially in three dimensions. This paper introduces a novel and robust framework to correct this overestimation. Our approach is founded on the principle of energy equipartition, where the energy contributions from the phase-field and its gradient are equal as the length-scale parameter approaches zero. Since numerical artifacts primarily affect the phase-field term while leaving the gradient term largely unperturbed, we propose that the crack area can be accurately approximated as twice the gradient-dependent energy. This method is inherently mesh-independent and readily applicable to the entire domain, including 3D simulations. The proposed methodology is validated against benchmarks with analytical solutions and compared with established methods like skeletonization to demonstrate its accuracy. It is then applied to complex geometries with curvilinear crack paths and evaluated in a three-dimensional simulation.

cond-mat.mtrl-sci↗

arXiv2026

A regularized method for quadratic optimization problems with finite-dimensional degeneracy

We propose and analyze a perturbative regularization method to approximate quadratic optimization problems with finite-dimensional degeneracy. The original problem is first approximated by a regularized problem depending on a small positive parameter, and then discretized using the finite element method. The resulting families of continuous and discrete functionals $\Gamma$-converge to the functional of the original problem and the corresponding minimizers converge as well. Our method generalizes the approach proposed in Kaleem et al. (2026) for numerically approximating pure Neumann problems, which represents the cornerstone of a sparsity-preserving, numerically efficient alternative to the methods developed in Bochev and Lehoucq (2005), Ivanov et al. (2019) and Roccia et al. (2024). References: A. Kaleem, C. Gebhardt, and I. Romero. On the pure traction problem of linear elasticity: a regularized formulation and its robust approximation. arXiv preprint arXiv:2602.04359, 2026. P. Bochev and R. Lehoucq. On the finite element solution of the pure Neumann problem. SIAM Review, 47:50-66, 2005. M. Ivanov, I. Kremer, and M. Urev. Solving the pure Neumann problem by a finite element method. Numerical Analysis and Applications, 12:359-371, 2019. B. Roccia, C. Alturria, F. Mazzone, and C. Gebhardt. On the homogeneous torsion problem for heterogeneous and orthotropic cross-sections: theoretical and numerical aspects. Applied Numerical Mathematics, 201:579-607, 2024.

math.NA↗

arXiv2025

A Phase-Field Approach to Fracture and Fatigue Analysis: Bridging Theory and Simulation

This article presents a novel, robust and efficient framework for fatigue crack-propagation that combines the principles of Linear Elastic Fracture Mechanics (LEFM) with phase-field fracture (PFF). Contrary to cycle-by-cycle PFF approaches, this work relies on a single simulation and uses standard crack propagation models such as Paris' law for the material response, simplifying its parametrization. The core of the methodology is the numerical evaluation of the derivative of a specimen's compliance with respect to the crack area. To retrieve this compliance the framework relies on a PFF-FEM simulation, controlled imposing a monotonic crack growth. This control of the loading process is done by a new crack-control scheme which allows to robustly trace the complete equilibrium path of a crack, capturing complex instabilities. The specimen's compliance obtained from the PFF simulation enables the integration of Paris' law to predict fatigue life. The proposed methodology is first validated through a series of benchmarks with analytical solutions to demonstrate its accuracy. The framework is then applied to more complex geometries where the crack path is unknown, showing a very good agreement with experimental results of both crack paths and fatigue life.

cond-mat.mtrl-sci↗

arXiv2022

Grain growth competition during melt pool solidification -- Comparing phase-field and cellular automaton models

A broad range of computational models have been proposed to predict microstructure development during solidification processing but they have seldom been compared to each other on a quantitative and systematic basis. In this paper, we compare phase-field (PF) and cellular automaton (CA) simulations of polycrystalline growth in a two-dimensional melt pool under conditions relevant to additive manufacturing (powder-bed fusion). We compare the resulting grain structures using local (point-by-point) measurements, as well as averaged grain orientation distributions over several simulations. We explore the effect of the CA spatial discretization level and that of the melt pool aspect ratio upon the selected grain texture. Our simulations show that detailed microscopic features related to transient growth conditions and solid-liquid interface stability (e.g. the initial planar growth stage prior to its cellular/dendritic destabilization, or the early elimination of unfavorably oriented grains due to neighbor grain sidebranching) can only be captured by PF simulations. The resulting disagreement between PF and CA predictions can only be addressed partially by a refinement of the CA grid. However, overall grain distributions averaged over the entire melt pools of several simulations seem to lead to a notably better agreement between PF and CA, with some variability with the melt pool shape and CA grid. While further research remains required, in particular to identify the appropriate selection of CA spatial discretization and its link to characteristic microstructural length scales, this research provides a useful step forward in this direction by comparing both methods quantitatively at process-relevant length and time scales.

cond-mat.mtrl-sci↗

arXiv2022

Multiscale simulation of powder-bed fusion processing of metallic alloys

We present a computational framework for the simulations of powder-bed fusion of metallic alloys, which combines: (1) CalPhaD calculations of temperature-dependent alloy properties and phase diagrams, (2) macroscale finite element (FE) thermal simulations of the material addition and fusion, and (3) microscopic phase-field (PF) simulations of solidification in the melt pool. The methodology is applied to simulate the selective laser melting (SLM) of an Inconel 718 alloy using realistic processing parameters. We discuss the effect of temperature-dependent properties and the importance of accounting for different properties between the powder bed and the dense material in the macroscale thermal simulations. Using a two-dimensional longitudinal slice of the thermal field calculated via FE simulations, we perform an appropriately-converged PF solidification simulation at the scale of the entire melt pool, resulting in a calculation with over one billion grid points, yet performed on a single cluster node with eight graphics processing units (GPUs). These microscale simulations provide new insight into the grain texture selection via polycrystalline growth competition under realistic SLM conditions, with a level of detail down to individual dendrites.

cond-mat.mtrl-sci↗

arXiv2007

Tunable Plasmon Molecules in Overlapping Nanovoids

Coupled and shape-tailored metallic nanoparticles are known to exhibit hybridized plasmon resonances. This Letter discuss the optical properties of a complementary system formed by overlapped nanovoid dimers buried in gold and filled with silica. This is an alternative route for plasmon engineering that benefits from vanishing radiation losses. Our analysis demonstrates the possibility of designing artificial plasmon molecules on the basis of void plasmon hybridization, which allows fine mode tuning by varying the overlap between voids. The proposed structures could find application to both signal processing through buried optical elements and tunable-plasmon biosensing.

cond-mat.mtrl-sci↗

arXiv2007

Plasmon tunability in metallodielectric metamaterials

The dielectric properties of metamaterials consisting of periodically arranged metallic nanoparticles of spherical shape are calculated by rigorously solving Maxwell's equations. Effective dielectric functions are obtained by comparing the reflectivity of planar surfaces limiting these materials with Fresnel's formulas for equivalent homogeneous media, showing mixing and splitting of individual-particle modes due to inter-particle interaction. Detailed results for simple cubic and fcc crystals of aluminum spheres in vacuum, silver spheres in vacuum, and silver spheres in a silicon matrix are presented. The filling fraction of the metal f is shown to determine the position of the plasmon modes of these metamaterials. Significant deviations are observed with respect to Maxwell-Garnett effective medium theory for large f, and multiple plasmons are predicted to exist in contrast to Maxwell-Garnett theory.

cond-mat.mtrl-sci↗

arXiv2007

Plasmons in nearly touching metallic nanoparticles: singular response in the limit of touching dimers

The response of gold nanoparticle dimers is studied theoretically near and beyond the limit where the particles are touching. As the particles approach each other, a dominant dipole feature is observed that is pushed into the infrared due to interparticle coupling and that is associated with a large pileup of induced charge in the interparticle gap. The redshift becomes singular as the particle separation decreases. The response weakens for very small separation when the coupling across the interparticle gap becomes so strong that dipolar oscillations across the pair are inhibited. Lower-wavelength, higher-order modes show a similar separation dependence in nearly touching dimers. After touching, singular behavior is observed through the emergence of a new infrared absorption peak, also accompanied by huge charge pileup at the interparticle junction, if initial interparticle-contact is made at a single point. This new mode is distinctly different from the lowest mode of the separated dimer. When the junction is made by contact between flat surfaces, charge at the junction is neutralized and mode evolution is continuous through contact. The calculated singular response explains recent experiments on metallic nanoparticle dimers and is relevant in the design of nanoparticle-based sensors and plasmon circuits.

cond-mat.other↗