FFT based approaches in micromechanics: fundamentals, methods and applications

Lucarini, Sergio; Upadhyay, Manas Vijay; Segurado, J.

doi:10.1088/1361-651x/ac34e1

Cited by 54 publications

(30 citation statements)

References 215 publications

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“…Several FFT-based computational homogenization schemes exist [12,13]. An interested reader may therefore find a comparison and placement of our approach in the context of contemporary literature useful.…”

Section: Comparison With Related Fft-based Schemesmentioning

confidence: 99%

“…These features attracted great interest in the community of computational mechanics of materials, as documented in two recent surveys by Schneider [12] and Lucarini et al [13]. In what follows, we outline the developments most relevant to our work and refer an interested reader to [12,13] for the full story of FFT-based methods.…”

Section: Introductionmentioning

confidence: 95%

“…Proceed to line 18 Newton's method converged matrices, like in (13). Thus, we suggest an efficient algorithm for the assembly of…”

mentioning

confidence: 99%

“…When we apply K ref (i) to vector i 1 , we obtain the first columns of dN n blocks K ref (i) ᾱ1 . From the structure of K ref (i) visible in (13) it is obvious that we need dN n vectors i p to obtain all (dN n ) 2 columns K ref (i) ᾱ β [1, :], where p = ( β − 1)N p + 1 and β ∈ {1, . .…”

mentioning

confidence: 99%

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Optimal FFT-accelerated Finite Element Solver for Homogenization

Ladecký¹,

J.²,

Falsafi³

et al. 2022

Preprint

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We propose a specialized preconditioned FE homogenization scheme that is significantly more efficient than generic FE implementations.• Our formulation offers computational efficiency equivalent to spectral homogenization solvers.• Our formulation is devoid of ringing phenomena intrinsic to spectral methods.• All results are reproducible in an open-source project µSpectre available at https: //muspectre.gitlab.io/muspectre.

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Section: Comparison With Related Fft-based Schemesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

“…Proceed to line 18 Newton's method converged matrices, like in (13). Thus, we suggest an efficient algorithm for the assembly of…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Optimal FFT-accelerated Finite Element Solver for Homogenization

Ladecký¹,

J.²,

Falsafi³

et al. 2022

Preprint

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“…Particularly successful are strategies based on the fast Fourier transform (FFT) [6,7], which operate on a regular grid and exploit the quality of modern FFT implementations. We refer to the recent review articles [8][9][10] for a discussion of the latest developments.…”

Section: State Of the Artmentioning

confidence: 99%

Training deep material networks to reproduce creep loading of short fiber-reinforced thermoplastics with an inelastically-informed strategy

et al. 2022

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Deep material networks (DMNs) are a recent multiscale technology which enable running concurrent multiscale simulations on industrial scale with the help of powerful surrogate models for the micromechanical problem. Classically, the parameters of the DMNs are identified based on linear elastic precomputations. Once the parameters are identified, DMNs may process inelastic material models and were shown to reproduce micromechanical full-field simulations with the original microstructure to high accuracy. The work at hand was motivated by creep loading of thermoplastic components with fiber reinforcement. In this context, multiple scales appear, both in space (due to the reinforcements) and in time (short- and long-term effects). We demonstrate by computational examples that the classical training strategy based on linear elastic precomputations is not guaranteed to produce DMNs whose long-term creep response accurately matches high-fidelity computations. As a remedy, we propose an inelastically informed early stopping strategy for the offline training of the DMNs. Moreover, we introduce a novel strategy based on a surrogate material model, which shares the principal nonlinear effects with the true model but is significantly less expensive to evaluate. For the problem at hand, this strategy enables saving significant time during the parameter identification process. We demonstrate that the novel strategy provides DMNs which reliably generalize to creep loading.

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Recent Advances in Machine Learning‐Assisted Multiscale Design of Energy Materials

Mortazavi

2024

Advanced Energy Materials

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This review highlights recent advances in machine learning (ML)‐assisted design of energy materials. Initially, ML algorithms were successfully applied to screen materials databases by establishing complex relationships between atomic structures and their resulting properties, thus accelerating the identification of candidates with desirable properties. Recently, the development of highly accurate ML interatomic potentials and generative models has not only improved the robust prediction of physical properties, but also significantly accelerated the discovery of materials. In the past couple of years, ML methods have enabled high‐precision first‐principles predictions of electronic and optical properties for large systems, providing unprecedented opportunities in materials science. Furthermore, ML‐assisted microstructure reconstruction and physics‐informed solutions for partial differential equations have facilitated the understanding of microstructure–property relationships. Most recently, the seamless integration of various ML platforms has led to the emergence of autonomous laboratories that combine quantum mechanical calculations, large language models, and experimental validations, fundamentally transforming the traditional approach to novel materials synthesis. While highlighting the aforementioned recent advances, existing challenges are also discussed. Ultimately, ML is expected to fully integrate atomic‐scale simulations, reverse engineering, process optimization, and device fabrication, empowering autonomous and generative energy system design. This will drive transformative innovations in energy conversion, storage, and harvesting technologies.

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FFT based approaches in micromechanics: fundamentals, methods and applications

Cited by 54 publications

References 215 publications

Optimal FFT-accelerated Finite Element Solver for Homogenization

Optimal FFT-accelerated Finite Element Solver for Homogenization

Training deep material networks to reproduce creep loading of short fiber-reinforced thermoplastics with an inelastically-informed strategy

Recent Advances in Machine Learning‐Assisted Multiscale Design of Energy Materials

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