A FFT solver for variational phase-field modeling of brittle fracture

Chen, Yang; Vasiukov, Dmytro; Gélebart, Lionel; Park, Chung

doi:10.1016/j.cma.2019.02.017

Cited by 71 publications

(71 citation statements)

References 54 publications

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“…Quasi‐Newton methods, such as Anderson acceleration and the Barzilai‐Borwein method, have attracted considerable attention for FFT‐based micromechanics. In contrast to the classical Newton method, these schemes do not require computing the Hessian.…”

Section: Discussionmentioning

confidence: 99%

“…One such algorithm is Anderson acceleration which was recently applied by Shantraj et al and Chen et al in the context of FFT‐based micromechanics. A general discussion of the scheme and its implementation is found, for example, in Walker and Ni or Kelley .…”

Section: Newton and Quasi‐newton Methods In Fft‐based Micromechanicsmentioning

confidence: 99%

“…Note that for the given algorithm Anderson acceleration is applied for every iteration. In contrast, Chen et al only accelerate every third iteration and apply Moulinec‐Suquet's basic scheme otherwise.…”

Section: Newton and Quasi‐newton Methods In Fft‐based Micromechanicsmentioning

confidence: 99%

“…Their popularity rests on their computational efficiency, the ability to treat nonlinear material behavior and the compatibility to imaging techniques such as microcomputed tomography. Owing to these advantages, FFT‐based solvers have found widespread application in various fields, including the homogenization of polycrystals at small and finite strains, damage and fracture mechanics, fatigue prediction, electromechanically coupled materials, and concurrent multiscale simulations …”

Section: Introductionmentioning

confidence: 99%

“…The algorithm is included in the software DAMASK as the nonlinear GMRES method. More recently, Chen et al successfully adapted the Anderson acceleration to simulate damage initiation and brittle fracture . Originally developed to accelerate general fixed‐point iterations, Anderson acceleration was linked to Quasi‐Newton schemes by Fang and Saad .…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On Quasi‐Newton methods in fast Fourier transform‐based micromechanics

Wicht

Schneider

Böhlke

2019

Numerical Meth Engineering

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SUMMARY This work is devoted to investigating the computational power of Quasi‐Newton methods in the context of fast Fourier transform (FFT)‐based computational micromechanics. We revisit FFT‐based Newton‐Krylov solvers as well as modern Quasi‐Newton approaches such as the recently introduced Anderson accelerated basic scheme. In this context, we propose two algorithms based on the Broyden‐Fletcher‐Goldfarb‐Shanno (BFGS) method, one of the most powerful Quasi‐Newton schemes. To be specific, we use the BFGS update formula to approximate the global Hessian or, alternatively, the local material tangent stiffness. Both for Newton and Quasi‐Newton methods, a globalization technique is necessary to ensure global convergence. Specific to the FFT‐based context, we promote a Dong‐type line search, avoiding function evaluations altogether. Furthermore, we investigate the influence of the forcing term, that is, the accuracy for solving the linear system, on the overall performance of inexact (Quasi‐)Newton methods. This work concludes with numerical experiments, comparing the convergence characteristics and runtime of the proposed techniques for complex microstructures with nonlinear material behavior and finite as well as infinite material contrast.

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Section: Discussionmentioning

confidence: 99%

Section: Newton and Quasi‐newton Methods In Fft‐based Micromechanicsmentioning

confidence: 99%

Section: Newton and Quasi‐newton Methods In Fft‐based Micromechanicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On Quasi‐Newton methods in fast Fourier transform‐based micromechanics

Wicht

Schneider

Böhlke

2019

Numerical Meth Engineering

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High‐performance computational homogenization of Stokes–Brinkman flow with an Anderson‐accelerated FFT method

Chen

2023

Numerical Methods in Fluids

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Fluid flow problems in bi‐porous media have strong implications in a variety of industrial applications, such as nuclear waste disposal and composites manufacturing. Despite various numerical solutions proposed in the literature, the prediction of dual‐scale flow remains a challenging task due to the requirement of fine meshes to resolve the complex microstructures of bi‐porous media. This paper introduces a new numerical solver based on fast Fourier transform (FFT) for the Stokes–Brinkman problem to predict fluid flow in bi‐porous media with local anisotropy. The novel FFT solver is derived from a velocity‐form of the problem, in contrast to the stress‐form proposed by a recent work. The Anderson acceleration technique is applied for the first time to the Stokes–Brinkman problem, leading to a substantial (orders of magnitude) improvement of the convergence rate. A range of detailed numerical examples are provided to validate the method against the analytical and literature results. Parametric studies are also demonstrated to aid in the selection of model parameters to achieve optimum numerical performance. With a 3D unit cell of a woven textile fabric, we demonstrate that the proposed method is capable of handling high‐resolution simulations with strongly heterogeneous microstructures. Combined with a parallelized implementation over high‐performance computing systems, our method demonstrates a new state‐of‐the‐art in numerical solvers for the Stokes‐Brinkman problem, in terms of computation capacity.

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An FFT‐based method for computing weighted minimal surfaces in microstructures with applications to the computational homogenization of brittle fracture

Schneider

2019

Numerical Meth Engineering

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Summary Cell formulae for the effective crack resistance of a heterogeneous medium obeying Francfort‐Marigo's formulation of linear elastic fracture mechanics have been proved recently, both in the context of periodic and stochastic homogenization. This work proposes a numerical strategy for computing the effective, possibly anisotropic, crack resistance of voxelized microstructures using the fast Fourier transform (FFT). Based on Strang's continuous minimum cut—maximum flow duality, we explore a primal‐dual hybrid gradient method for computing the effective crack resistance, which may be readily integrated into an existing FFT‐based code for homogenizing thermal conductivity. We close with demonstrative numerical experiments.

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A FFT solver for variational phase-field modeling of brittle fracture

Cited by 71 publications

References 54 publications

On Quasi‐Newton methods in fast Fourier transform‐based micromechanics

On Quasi‐Newton methods in fast Fourier transform‐based micromechanics

High‐performance computational homogenization of Stokes–Brinkman flow with an Anderson‐accelerated FFT method

An FFT‐based method for computing weighted minimal surfaces in microstructures with applications to the computational homogenization of brittle fracture

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