arXiv subjects

Javier Segurado

Publications and source records attributed to Javier Segurado.

13 recordsLinked to original sources

arXiv2026

An FFT-based solver with general boundary conditions for stationary diffusion problems based on Chebyshev collocation

An efficient and robust FFT-based solver is proposed for diffusion-type problems with general Neumann and Dirichlet boundary conditions, based on a Chebyshev collocation framework. The method combines Chebyshev polynomial approximations with FFT-based operators to provide a matrix-free implementation of the discrete differential operator at the Chebyshev-Gauss-Lobatto points. The linear system of equations resulting from the Chebyshev discretization is solved using LGMRES. To overcome convergence problems on fine grids, a hierarchical refinement strategy based on modal prolongation is proposed, enabling the solution of very large 3D problems. The methodology is applicable to homogeneous and heterogeneous domains, as well as to linear and nonlinear constitutive equations. The accuracy of the proposed method is analyzed by solving the Poisson equation in homogeneous 1D and 3D domains with general boundary conditions, using manufactured analytical solutions as references. Convergence to the analytical solution is achieved in a few iterations, with smaller errors than those obtained using DCT/DST approaches. Discretizations of up to $256^3$ are achieved thanks to the hierarchical refinement strategy. In the case of heterogeneous domains, the accuracy and efficiency obtained are similar to those of a standard periodic FFT approach. It is found that the computational complexity of the method preserves the FFT scaling, of order $n\log n$, in all the cases studied.

math.NA↗

arXiv2025

Effective toughness estimation by FFT based phase field fracture: application to composites and polycrystals

An estimate of the effective toughness of heterogeneous materials is proposed based on the Phase Field Fracture model implemented in an FFT homogenization solver. The estimate is based on the simulation of the deformation of representative volume elements of the microstructure, controlled by a constant energy dissipation rate using an arc-length type control. The definition of the toughness corresponds to the total energy dissipated after the total fracture of the RVE -- which can be accurately obtained thanks to the dissipation control -- divided by the RVE transverse area (length in 2D). The proposed estimate accounts for both the effect of heterogeneity in toughness and elastic response on the overall fracture energy and allows as well to account for phases with anisotropic elastic and fracture response (fracture by cleavage). To improve toughness predictions, crack-tip enrichment is used to model initial cracks. The method is applied to obtain the effective toughness of composites and elastic polycrystals in a series of examples. In the two types of materials, it is found that both heterogeneity in elastic response and fracture energy contribute to increase the effective toughness. Microscopically, it is found that toughening mechanisms are related to the passage of the crack through tougher phases and deviation of the crack path. It is also found that the latter is the controlling mechanism for cases with marked heterogeneity and high anisotropy, eventually provoking toughening saturation for sufficiently high values of heterogeneity or anisotropy.

cond-mat.mtrl-sci↗

arXiv2025

Multiscale modeling of hydrogen diffusion in iron considering the effect of dislocations

Modeling hydrogen diffusion and its absorption in traps is a fundamental first step towards the understanding and prediction of hydrogen embrittlement. In this study, a multiscale approach which includes DFT simulations, OkMC, and phase-field dislocations, is developed to study the movement of hydrogen atoms in alpha-iron crystals containing dislocations. At the nanoscale the interaction energies of hydrogen on different sites of the iron lattice are studied using DFT. At the microscale, this information is used to feed a lattice object kinetic Monte Carlo code (OKMC) which aims to evolve the arrangement of a large set of hydrogen atoms into the iron lattice considering point defects and the presence of dislocations. At the continuum level, an array of dislocations is introduced using a phase-field approach to accurately consider their elastic fields and core regions. The OKMC model includes both the chemical energies of H and vacancies and the elastic interactions between these point defects and the dislocations. The elastic interaction is obtained by an FFT-based approach which allows a very efficient computation of the elastic microfields created by the defects in an anisotropic medium. The framework has been used to obtain the diffusivity tensor of hydrogen as a function of the external stress state, temperature, and the presence of dislocations. It has been found that dislocations strongly affect the diffusivity tensor by breaking its isotropy and reducing its value by the effect of the microstresses around the dislocations.

cond-mat.mtrl-sci↗

arXiv2024

A crack-length control technique for phase field fracture in FFT homogenization

Modeling the propagation of cracks at the microscopic level is fundamental to understand the effect of the microstructure on the fracture process. Nevertheless, microscopic propagation is often unstable and when using phase field fracture poor convergence is found or, in the case of using staggered algorithms, leads to the presence of jumps in the evolution of the cracks. In this work, a novel method is proposed to perform micromechanical simulations with phase field fracture imposing monotonic increases of crack length and allowing the use of monolithic implementations, being able to resolve all the snap-backs during the unstable propagation phases. The method is derived for FFT based solvers in order to exploit its very high numerical performance n micromechanical problems, but an equivalent method is also developed for Finite Elements (FE) showing the equivalence of both implementations. It is shown that the stress-strain curves and the crack paths obtained using the crack control method are superposed in stable propagation regimes to those obtained using strain control with a staggered scheme. J-integral calculations confirm that during the propagation process in the crack control method, the energy release rate remains constant and equal to an effective fracture energy that has been determined as function of the discretization for FFT simulations. Finally, to show the potential of the method, the technique is applied to simulate crack propagation through the microstructure of composites and porous materials providing an estimation of the effective fracture toughness.

cond-mat.mtrl-sci↗

arXiv2024

An FFT based chemo-mechanical framework with fracture: application to mesoscopic electrode degradation

An FFT based method is proposed to simulate chemo-mechanical problems at the microscale including fracture, specially suited to predict crack formation during the intercalation process in batteries. The method involves three fields fully coupled, concentration, deformation gradient and damage. The mechanical problem is set in a finite strain framework and solved using Fourier Galerkin for non-linear problems in finite strains. The damage is modeled with Phase Field Fracture using a stress driving force. This problem is solved in Fourier space using conjugate gradient with an ad-hoc preconditioner. The chemical problem is modeled with the second Fick's law and physically based chemical potentials, is integrated using backward Euler and is solved by Newton-Raphson combined with a conjugate gradient solver. Buffer layers are introduced to break the periodicity and emulate Neumann boundary conditions for incoming mass flux. The framework is validated against Finite Elements the results of both methods are very close in all the cases. Finally, the framework is used to simulate the fracture of active particles of graphite during ion intercalation. The method is able to solve large problems at a reduced computational cost and reproduces the shape of the cracks observed in real particles.

cond-mat.mtrl-sci↗

arXiv2024

A stochastic discrete slip approach to microplasticity: Application to submicron W pillars

A stochastic discrete slip approach is proposed to model plastic deformation in submicron domains. The model is applied to the study of submicron pillar ($D~\leq~1\mu m$) compression experiments on tungsten (W), a prototypical metal for applications under extreme conditions. Slip events are geometrically resolved in the specimen and considered as eigenstrain fields producing a displacement jump across a slip plane. This novel method includes several aspects of utmost importance to small-scale plasticity, i.e. source truncation effects, surface nucleation effects, starvation effects, slip localization and an inherently stochastic response. Implementation on an FFT-spectral solver results in an efficient computational 3-D framework. Simulations of submicron W pillars ($D~\leq~1\mu m$) under compression show that the method is capable of capturing salient features of sub-micron scale plasticity. These include the natural competition between pre-existing dislocations and surface nucleation of new dislocations. Our results predict distinctive flow stress power-law dependence exponents as well as a size-dependence of the strain-rate sensitivity exponent. The results are thoroughly compared with experimental literature.

cond-mat.mtrl-sci↗

arXiv2024

An FFT based approach to account for elastic interactions in OkMC: Application to dislocation loops in iron

Object kinetic Montecarlo (OkMC) is a fundamental tool for modeling defect evolution in volumes and times far beyond atomistic models. The elastic interaction between defects is classically considered using a dipolar approximation but this approach is limited to simple cases and can be inaccurate for large and close interacting defects. In this work a novel framework is proposed to include "exact" elastic interactions between defects in OkMC valid for any type of defect and anisotropic media. In this method, the elastic interaction energy of a defect is computed by volume integration of its elastic strain multiplied by the stress created by all the other defects, being both fields obtained numerically using a FFT solver. The resulting interaction energies reproduce analytical elastic solutions and show the limited accuracy of dipole approaches for close and large defects. The OkMC framework proposed is used to simulate the evolution in space and time of self-interstitial atoms and dislocation loops in iron. It is found that including the anisotropy has a quantitative effect in the evolution of all the type of defects studied. Regarding dislocation loops, it is observed that using the "exact" interaction energy result in higher interactions than using the dipole approximation for close loops.

cond-mat.mtrl-sci↗

arXiv2022

Microstructure sensitive fatigue life prediction model for SLM fabricated Hastelloy-X

A microstructure-sensitive fatigue life prediction framework based on CP-FFT is proposed to study SLM fabricated Hastelloy-X. The microstructure enters in the model through the shape, size and orientation distributions of grains in the RVEs, which are generated from experimental EBSD data. The framework has been applied to specimens built in two different directions with different polycrystalline microstructures and is able to accurately predict their fatigue life, using just two experiments for calibration. The model reproduces the better fatigue performance found experimentally at high stresses for samples built in transverse direction, identifying the origin of this anisotropy in grain aspect ratios.

cond-mat.mtrl-sci↗

arXiv2020

A multiplicative finite strain crystal plasticity formulation based on additive elastic corrector rates: Theory and numerical implementation

The purpose of continuum plasticity models is to efficiently predict the behavior of structures beyond their elastic limits. The purpose of multiscale materials science models, among them crystal plasticity models, is to understand the material behavior and design the material for a given target. The current successful continuum hyperelastoplastic models are based in the multiplicative decomposition from crystal plasticity, but significant differences in the computational frameworks of both approaches remain, making comparisons not straightforward. In previous works we have presented a theory for multiplicative continuum elastoplasticity which solved many long-standing issues, preserving the appealing structure of additive infinitesimal Wilkins algorithms. In this work we extend the theory to crystal plasticity. We show that the new formulation for crystal plasticity is parallel and comparable to continuum plasticity, preserving the attractive aspects of the framework: (1) simplicity of the kinematics reaching a parallelism with the infinitesimal framework; (2) possibility of very large elastic strains and unrestricted type of hyperelastic behavior; (3) immediate plain backward-Euler algorithmic implementation of the continuum theory avoiding algorithmically motivated exponential mappings, yet preserving isochoric flow; (4) absence of Mandel-type stresses in the formulation; (5) objectiveness and weak-invariance by construction due to the use of flow rules in terms of elastic corrector rates. We compare the results of our crystal plasticity formulation with the classical formulation from Kalidindi and Anand based on quadratic strains and an exponential mapping update of the plastic deformation gradient.

cond-mat.mtrl-sci↗

arXiv2019

DBFFT: A displacement based FFT approach for non-linear homogenization of the mechanical behavior

Most of the FFT methods available for homogenization of the mechanical response use the strain/deformation gradient as unknown, imposing their compatibility using Green's functions or projection operators. This implies the allocation of redundant information and, when the method is based in solving a linear equation, the rank-deficiency of the resulting system. In this work we propose a fast, robust and memory-efficient FFT homogenization framework in which the displacement field on the Fourier space is the unknown: the displacement based FFT (DBFFT) algorithm. The framework allows any general non-linear constitutive behavior for the phases and direct strain, stress and mixed control of the macroscopic load. In the linear case, the method results in a linear system defined in terms of linear operators in the Fourier space and that does not require a reference medium. The system has an associated full rank Hermitian matrix and can be solved using iterative Krylov solvers and allows the use of preconditioners. A preconditioner is proposed to improve the efficiency of the system resolution. Finally, some numerical examples including elastic, hyperelastic and viscoplastic materials are solved to check the accuracy and efficiency of the method. The computational cost reduction respect the Galerkin-FFT was around 30%.

cs.CE↗

arXiv2019

Effect of Grain Orientation and Local Strains on Void Growth and Coalescence in Titanium

Ductile fracture has been extensively studied in metals with weak mechanical anisotropy such as copper and aluminum. The fracture of more anisotropic metals, especially those with a hexagonal crystal structure (e.g. titanium), remains far less understood. This paper investigates the ductile fracture process in commercially pure titanium (CP-Ti) with particular emphasis on the influence of grain orientation and local state of strain on void growth. An experimental approach was developed to directly relate the growth of a void in three dimensions to its underlying grain orientation. Grain orientation was obtained by electron back scattered diffraction on void-containing CP-Ti sheets prior to their diffusion bonding. Changes in void dimensions were measured during in-situ straining within an x-ray tomography system. The strong influence of the embedded grain orientation and that of its neighbors on void growth rate and coalescence has been experimentally quantified. Finite element crystal plasticity simulations that take into account both grain orientation and the local strain state were found to predict the experimental void growth. Grains where basal slip dominates show the largest void growth rates because they are closer to a plane strain condition that favors void growth and coalescence.

cond-mat.mtrl-sci↗

arXiv2019

Development of a thermo-mechanically coupled crystal plasticity modeling framework: application to polycrystalline homogenization

Accurate predictions of thermo-mechanically coupled process in metals can lead to a reduction of cost and an increase of productivity in manufacturing processes such as forming. For modeling these coupled processes with the finite element method, accurate descriptions of both the mechanical and the thermal responses of the material, as well as their interaction, are needed. Conventional material modeling employs empirical macroscopic constitutive relations but does not account for the actual thermo-mechanical mechanisms occurring at the microscopic level. However, the consideration of the latter might be crucial to obtain accurate predictions and a complete understanding of the underlying physics. In this work we describe a fully coupled implicit thermo-mechanical framework for crystal plasticity simulations. This framework includes thermal strains, temperature dependency of the crystal behavior and heat generation by dissipation due to plastic slip and allows the use of large deformation steps thanks to the implicit integration of the governing equations. Its use within computational homogenization simulations allows to bridge the plastic deformation and temperature gradients at the macroscopic scale with the microscopic slip at the grain scale. A series of numerical examples are presented to validate the approach.

cond-mat.mtrl-sci↗

arXiv2018

On the accuracy of spectral solvers for micromechanics based fatigue modeling

A framework based on FFT is proposed for micromechanical fatigue modeling of polycrystals as alternative to the Finite Element method (FEM). The variational FFT approach is used with a crystal plasticity model for the cyclic behavior of the grains introduced through a FEM material subroutine, in particular an Abaqus umat. The framework also includes an alternative projection operator based on discrete differentiation to improve the microfield fidelity allowing to include second phases. The accuracy and efficiency of the FFT framework for microstructure sensitive fatigue prediction are assessed by comparing with FEM. The macroscopic cyclic response of a polycrystal obtained with both methods were indistinguishable, irrespective of the number of cycles. The microscopic fields presented small differences that decrease when using the discrete projection operator, which indeed allowed simulating accurately microstructures containing very stiff particles. Finally, the maximum differences in the fatigue life estimation from the microfields respect FEM were around 15% . In summary, this framework allows predicting fatigue life with a similar accuracy than using FEM but strongly reducing the computational cost.

physics.comp-ph↗