A review of nonlinear FFT-based computational homogenization methods
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Publication:2234259
DOI10.1007/s00707-021-02962-1zbMath1491.74099OpenAlexW3135925085MaRDI QIDQ2234259
Publication date: 18 October 2021
Published in: Acta Mechanica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00707-021-02962-1
convergencefracture mechanicsNewton methodgranular materialcompositecrystaldiscretization schemedual schemenonlinear solution methodnonlinear computational homogenization
Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids (74-02) Homogenization in equilibrium problems of solid mechanics (74Q05) Spectral and related methods applied to problems in solid mechanics (74S25) Homogenization and oscillations in dynamical problems of solid mechanics (74Q10)
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Cites Work
- Linear Convergence and Metric Selection for Douglas-Rachford Splitting and ADMM
- Two classes of multisecant methods for nonlinear acceleration
- Anderson Acceleration for Fixed-Point Iterations
- On the effective viscosity of a periodic suspension - analysis of primal and dual formulations for Newtonian and non-Newtonian solvents
- Representations for the conductivity functions of multicomponent composites
- The Numerical Solution of Parabolic and Elliptic Differential Equations
- On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
- Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface
- Convergence of FFT‐based homogenization for strongly heterogeneous media
- Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints
- An accelerated FFT algorithm for thermoelastic and non-linear composites
- Variational Principles for Inhomogeneous Non-linear Media
- GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- Two-Point Step Size Gradient Methods
- A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials
- AVERAGING DIFFERENTIAL OPERATORS WITH ALMOST PERIODIC, RAPIDLY OSCILLATING COEFFICIENTS
- Splitting Algorithms for the Sum of Two Nonlinear Operators
- Updating Quasi-Newton Matrices with Limited Storage
- Inexact Newton Methods
- A uniform strain hexahedron and quadrilateral with orthogonal hourglass control
- Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
- Solution of Sparse Indefinite Systems of Linear Equations
- The Methods of Cyclic Reduction, Fourier Analysis and the FACR Algorithm for the Discrete Solution of Poisson’s Equation on a Rectangle
- Numerical Optimization
- The Immersed Interface Method for Elliptic Equations with Discontinuous Coefficients and Singular Sources
- On the Gibbs Phenomenon and Its Resolution
- A Fast Iterative Algorithm for Elliptic Interface Problems
- A stabilization technique to avoid hourglassing in finite elasticity
- The Theory of Composites
- FFT‐based homogenization for microstructures discretized by linear hexahedral elements
- On characterizing the set of possible effective tensors of composites: The variational method and the translation method
- Strain-driven homogenization of inelastic microstructures and composites based on an incremental variational formulation
- Choosing the Forcing Terms in an Inexact Newton Method
- Quantitative Homogenization for the Case of an Interface Between Two Heterogeneous Media
- Adaptive restart of accelerated gradient methods under local quadratic growth condition
- Function minimization by conjugate gradients
- A full-field image conversion method for the inverse conductivity problem with internal measurements
- A model problem concerning recoverable strains of shape-memory polycrystals
- Some methods of speeding up the convergence of iteration methods
- Iterative Procedures for Nonlinear Integral Equations
- A Family of Variable-Metric Methods Derived by Variational Means
- The Convergence of a Class of Double-rank Minimization Algorithms
- A new approach to variable metric algorithms
- Conditioning of Quasi-Newton Methods for Function Minimization
- An introduction to continuous optimization for imaging
- Methods of conjugate gradients for solving linear systems
- Random heterogeneous materials. Microstructure and macroscopic properties
- The Chebyshev iteration revisited
- Modeling the propagation of elastic waves using a modified finite difference grid.
- On the micromechanics of deep material networks
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Mixed boundary conditions for FFT-based homogenization at finite strains
- Asymptotic homogenization of periodic thermo-magneto-electro-elastic heterogeneous media
- A Fourier based numerical method for computing the dynamic permeability of periodic porous media
- Fourier-based strength homogenization of porous media
- Filtering material properties to improve FFT-based methods for numerical homogenization
- Efficient fixed point and Newton-Krylov solvers for FFT-based homogenization of elasticity at large deformations
- An optimal variance estimate in stochastic homogenization of discrete elliptic equations
- Elastic behavior of composites containing Boolean random sets of inhomogeneities
- Computational approach for composite materials with coupled constitutive laws
- On the accuracy of spectral solvers for micromechanics based fatigue modeling
- Combining Galerkin approximation techniques with the principle of Hashin and Shtrikman to derive a new FFT-based numerical method for the homogenization of composites
- A comparative study on low-memory iterative solvers for FFT-based homogenization of periodic media
- A multiscale approach for modeling progressive damage of composite materials using fast Fourier transforms
- A dynamical view of nonlinear conjugate gradient methods with applications to FFT-based computational micromechanics
- Infinite-contrast periodic composites with strongly nonlinear behavior: effective-medium theory versus full-field simulations
- The variational approach to fracture
- Multi-scale computational homogenization: trends and challenges
- Effective properties of elastic periodic composite media with fibers
- A FFT-based method to compute the permeability induced by a Stokes slip flow through a porous medium
- Modeling the effective elastic behavior of composites: a mixed finite element and homogenisation approach
- Simulation of damage evolution in discontinuously reinforced metal matrix composites: a phase-field model
- A variational approach to the theory of the elastic behaviour of multiphase materials
- Non-homogeneous media and vibration theory
- A dual algorithm for the solution of nonlinear variational problems via finite element approximation
- Bounds for effective elastic moduli of disordered materials
- Bounds and self-consistent estimates for the overall properties of anisotropic composites
- Introductory lectures on convex optimization. A basic course.
- Intraphase strain heterogeneity in nonlinear composites: A computational approach
- Jacobian-free Newton-Krylov methods: a survey of approaches and applications.
- Determination of the size of the representative volume element for random composites: Statistical and numerical approach.
- Simulation of the multi-scale convergence in computational homogenization approaches
- Numerical experiments in revisited brittle fracture
- A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites.
- Conductivity of composites with multiple polygonal aggregates, theoretical estimates and numerical solutions from polarization series
- Combining FFT methods and standard variational principles to compute bounds and estimates for the properties of elastic composites
- Field statistics in linear viscoelastic composites and polycrystals
- Tight global linear convergence rate bounds for Douglas-Rachford splitting
- An FFT method for the computation of thermal diffusivity of porous periodic media
- Effect of a nonuniform distribution of voids on the plastic response of voided materials: a computational and statistical analysis
- Influences of micro-pores and meso-pores on elastic and plastic properties of porous materials
- A numerical method for computing the overall response of nonlinear composites with complex microstructure
- Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients
- Revisiting brittle fracture as an energy minimization problem
- Deformation patterning in finite-strain crystal plasticity by spectral homogenization with application to magnesium
- A simple and flexible model order reduction method for FFT-based homogenization problems using a sparse sampling technique
- On the mathematical foundations of the self-consistent clustering analysis for non-linear materials at small strains
- An efficient solution scheme for small-strain crystal-elasto-viscoplasticity in a dual framework
- Fiber orientation interpolation for the multiscale analysis of short fiber reinforced composite parts
- Efficient and accurate two-scale FE-FFT-based prediction of the effective material behavior of elasto-viscoplastic polycrystals
- Fourier-accelerated nodal solvers (FANS) for homogenization problems
- A multiscale FE-FFT framework for electro-active materials at finite strains
- A framework for FFT-based homogenization on anisotropic lattices
- Geometric variational principles for computational homogenization
- An incremental-iterative method for modeling damage evolution in voxel-based microstructure models
- A computational multi-scale model for the stiffness degradation of short-fiber reinforced plastics subjected to fatigue loading
- FFT based numerical homogenization method for porous conductive materials
- Computation of macroscopic permeability of doubly porous media with FFT based numerical homogenization method
- Improving the initial guess for the Newton-Raphson protocol in time-dependent simulations
- A FFT solver for variational phase-field modeling of brittle fracture
- Self-consistent clustering analysis for multiscale modeling at finite strains
- FFT-based homogenization of hypoelastic plasticity at finite strains
- An inverse modeling approach for predicting filled rubber performance
- FFT-based homogenisation accelerated by low-rank tensor approximations
- Effective response of heterogeneous materials using the recursive projection method
- Maximum-entropy based estimates of stress and strain in thermoelastic random heterogeneous materials
- Efficient FFT-based upscaling of the permeability of porous media discretized on uniform grids with estimation of RVE size
- Runtime optimization of a memory efficient CG solver for FFT-based homogenization: implementation details and scaling results for linear elasticity
- Energy-based comparison between the Fourier-Galerkin method and the finite element method
- A model order reduction method for computational homogenization at finite strains on regular grids using hyperelastic laminates to approximate interfaces
- An FFT-based spectral solver for interface decohesion modelling using a gradient damage approach
- An FFT-based fast gradient method for elastic and inelastic unit cell homogenization problems
- Finite strain FFT-based non-linear solvers made simple
- Self-consistent clustering analysis: an efficient multi-scale scheme for inelastic heterogeneous materials
- Fast implicit solvers for phase-field fracture problems on heterogeneous microstructures
- The composite voxel technique for inelastic problems
- Numerical simulations and modeling of the effective plastic flow surface of a biporous material with pressurized intergranular voids
- Model order reduction of nonlinear homogenization problems using a Hashin-Shtrikman type finite element method
- FFT-based solver for higher-order and multi-phase-field fracture models applied to strongly anisotropic brittle materials
- Two reduction methods for stochastic FEM based homogenization using global basis functions
- On polarization-based schemes for the FFT-based computational homogenization of inelastic materials
- DBFFT: a displacement based FFT approach for non-linear homogenization of the mechanical behavior
- Homogenization of free discontinuity problems
- An FFT-based Galerkin method for homogenization of periodic media
- Stochastic homogenisation of free-discontinuity problems
- Two-scale FE-FFT- and phase-field-based computational modeling of bulk microstructural evolution and macroscopic material behavior
- Macroscopic behavior and field fluctuations in viscoplastic composites: second-order estimates versus full-field simulations
- Multiplier and gradient methods
- Elastic properties of reinforced solids: Some theoretical principles
- A variational approach to the theory of the elastic behaviour of polycrystals
- Guaranteed upper-lower bounds on homogenized properties by FFT-based Galerkin method
- Use of composite voxels in FFT-based homogenization
- A polarization-based FFT iterative scheme for computing the effective properties of elastic composites with arbitrary contrast
- Analysis of a Fast Fourier Transform Based Method for Modeling of Heterogeneous Materials
- A fast method for solving microstructural problems defined by digital images: a space Lippmann-Schwinger scheme
- Comparison of three accelerated FFT-based schemes for computing the mechanical response of composite materials
- Fourier-based schemes with modified Green operator for computing the electrical response of heterogeneous media with accurate local fields
- Improved guaranteed computable bounds on homogenized properties of periodic media by the Fourier-Galerkin method with exact integration
- Optical properties of deposit models for paints: full-fields FFT computations and representative volume element
- A polarization-based fast numerical method for computing the effective conductivity of composites
