An FFT‐based method for computing weighted minimal surfaces in microstructures with applications to the computational homogenization of brittle fracture
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DOI: 10.1002/nme.6270
Abstract: 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… read more here.
Keywords: homogenization; method computing; fft based; fracture ... See more keywords
On non‐stationary polarization methods in FFT‐based computational micromechanics
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DOI: 10.1002/nme.6812
Abstract: Polarization‐type methods are among the fastest solution methods for FFT‐based computational micromechanics. However, their performance depends critically on the choice of the reference material. Only for finitely contrasted materials, optimum‐selection strategies are known. This work… read more here.
Keywords: fft based; computational micromechanics; polarization; methods fft ... See more keywords
Robust and Efficient FFT‐Based Solvers for Unit‐Cell Problems With Voids and Pores Under Displacement Boundary Conditions
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DOI: 10.1002/nme.70124
Abstract: There is a variety of microstructured materials that involve voids and pores, for example, high‐porosity foams, mechanical metamaterials, or composites involving defects due to damage and cracking, respectively. Computational methods based on the fast Fourier… read more here.
Keywords: fft based; unit; robust efficient; voids pores ... See more keywords
Element‐Based Internal Variable Formulations for Finite Element Discretizations in FFT‐Based Homogenization Methods
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DOI: 10.1002/nme.70170
Abstract: Although finite elements were made available for FFT‐based computational homogenization methods, they are seldomly used for inelastic computations because traditionally the constitutive law is evaluated at each quadrature point of the element, making the storage… read more here.
Keywords: fft based; element; finite element; homogenization methods ... See more keywords
Efficient and accurate two-scale FE-FFT-based prediction of the effective material behavior of elasto-viscoplastic polycrystals
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DOI: 10.1007/s00466-017-1476-2
Abstract: Recently, two-scale FE-FFT-based methods (e.g., Spahn et al. in Comput Methods Appl Mech Eng 268:871–883, 2014; Kochmann et al. in Comput Methods Appl Mech Eng 305:89–110, 2016) have been proposed to predict the microscopic and… read more here.
Keywords: two scale; fft based; elasto viscoplastic; scale fft ... See more keywords
On polarization-based schemes for the FFT-based computational homogenization of inelastic materials
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DOI: 10.1007/s00466-019-01694-3
Abstract: We revisit the polarization-based schemes introduced to FFT-based computational homogenization by Eyre–Milton, Michel–Moulinec–Suquet and Monchiet–Bonnet. When applied to nonlinear problems, these polarization-based methods suffer from two handicaps. Firstly, the optimal choice of algorithmic parameters is… read more here.
Keywords: based computational; computational homogenization; based schemes; polarization based ... See more keywords
A dynamical view of nonlinear conjugate gradient methods with applications to FFT-based computational micromechanics
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DOI: 10.1007/s00466-020-01849-7
Abstract: For fast Fourier transform (FFT)-based computational micromechanics, solvers need to be fast, memory-efficient, and independent of tedious parameter calibration. In this work, we investigate the benefits of nonlinear conjugate gradient (CG) methods in the context… read more here.
Keywords: fft based; computational micromechanics; conjugate gradient; based computational ... See more keywords
Imposing Dirichlet boundary conditions directly for FFT-based computational micromechanics
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DOI: 10.1007/s00466-024-02469-1
Abstract: We discuss how Dirichlet boundary conditions can be directly imposed for the Moulinec–Suquet discretization on the boundary of rectangular domains in iterative schemes based on the fast Fourier transform (FFT) and computational homogenization problems in… read more here.
Keywords: conditions directly; fft based; dirichlet boundary; boundary conditions ... See more keywords
A novel, FFT-based one-dimensional blood flow solution method for arterial network
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DOI: 10.1007/s10237-019-01146-0
Abstract: In the present work, we propose an FFT-based method for solving blood flow equations in an arterial network with variable properties and geometrical changes. An essential advantage of this approach is in correctly accounting for… read more here.
Keywords: blood flow; fft based; method; arterial network ... See more keywords
FFT-based homogenisation accelerated by low-rank tensor approximations
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DOI: 10.1016/j.cma.2020.112890
Abstract: Fast Fourier transform (FFT) based methods has turned out to be an effective computational approach for numerical homogenisation. Particularly, Fourier-Galerkin methods are computational methods for partial differential equations that are discretised with trigonometric polynomials. Its… read more here.
Keywords: fft based; accelerated low; tensor; low rank ... See more keywords
Fast FFT based solver for rate-dependent deformations of composites and nonwovens
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DOI: 10.1016/j.ijsolstr.2016.12.014
Abstract: Abstract This paper presents the application of a fast FFT based solver of the Lippmann-Schwinger equations in elasticity to compute the effective viscoelastic material behavior of composites and nonwovens. The fundamentals of the solver are… read more here.
Keywords: fft based; fast fft; solver rate; based solver ... See more keywords