A numerical method for computing the overall response of nonlinear composites with complex microstructure

Abstract

The local and overall responses of nonlinear composites are classically investigated by the Finite Element Method. We propose an alternate method based on Fourier series which avoids meshing and which makes direct use of microstructure images. It is based on the exact expression of the Green function of a linear elastic and homogeneous comparison material. First, the case of elastic nonhomogeneous constituents is considered and an iterative procedure is proposed to solve the Lippman-Schwinger equation which naturally arises in the problem. Then, the method is extended to non-linear constituents by a step-by-step integration in time. The accuracy of the method is assessed by varying the spatial resolution of the microstructures. The flexibility of the method allows it to serve for a large variety of microstructures. (C) 1998 Elsevier Science S.A.

Cited by in corpus (68)

• A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials
• Fourier-based schemes for computing the mechanical response of composites with accurate local fields
• Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients
• Exploring the 3D architectures of deep material network in data-driven multiscale mechanics
• An FFT-based Galerkin Method for Homogenization of Periodic Media
• Computational Homogenization of Polycrystals
• Fourier-based schemes with modified Green operator for computing the electrical response of heterogeneous media with accurate local fields
• Finite strain FFT-based non-linear solvers made simple
• A finite element perspective on non-linear FFT-based micromechanical simulations
• Simulation of the Hall-Petch effect in FCC polycrystals by means of strain gradient crystal plasticity and FFT homogenization
• Discrete dislocation dynamics simulations of dislocation-${\theta }^{\prime }$ precipitate interaction in Al-Cu alloys
• An FE-DMN method for the multiscale analysis of fiber reinforced plastic components
• A Fourier-accelerated volume integral method for elastoplastic contact
• Filtering material properties to improve FFT-based methods for numerical homogenization
• On the accuracy of spectral solvers for micromechanics based fatigue modeling
• DBFFT: A displacement based FFT approach for non-linear homogenization of the mechanical behavior
• Nonlocal Effective Electromagnetic Wave Characteristics of Composite Media: Beyond the Quasistatic Regime
• Guaranteed upper-lower bounds on homogenized properties by FFT-based Galerkin method
• Materials knowledge system for nonlinear composites
• Infinite-contrast periodic composites with strongly nonlinear behavior: Effective-medium theory versus full-field simulations
• A micromechanical analysis of intergranular stress corrosion cracking of an irradiated austenitic stainless steel
• Atomic-scale modeling of twinning disconnections in zirconium
• A Supervised Machine Learning Approach for Accelerating the Design of Particulate Composites: Application to Thermal Conductivity
• An algorithm for stress and mixed control in Galerkin based FFT homogenization
• An FFT framework for simulating non-local ductile failure in heterogeneous materials
• A coalescence criterion for porous single crystals
• An FFT-based method for computing the effective crack energy of a heterogeneous material on a combinatorially consistent grid
• Cell division in deep material networks applied to multiscale strain localization modeling
• Towards Quantum Computational Mechanics
• Exploration of the Microstructure Space in TiAlZrN Ultra-Hard Nanostructured Coatings
• A probabilistic virtual process chain to quantify process-induced uncertainties in Sheet Molding Compounds
• Yield criterion and finite strain behavior of random porous isotropic materials
• Effective Elastic Wave Characteristics of Composite Media
• Learning constitutive models from microstructural simulations via a non-intrusive reduced basis method
• FFT-based homogenisation accelerated by low-rank tensor approximations
• Computational homogenization of higher-order continua
• An FFT-based framework for predicting corrosion-driven damage in fractal porous media
• A Spectral-based Physics-informed Finite Operator Learning for Prediction of Mechanical Behavior of Microstructures
• Numerical analysis of several FFT-based schemes for computational homogenization
• A reduced order model for geometrically parameterized two-scale simulations of elasto-plastic microstructures under large deformations
• AutoMat -- Automatic Differentiation for Generalized Standard Materials on GPUs
• Statistically equivalent surrogate material models and the impact of random imperfections on elasto-plastic response
• Extension of a phase-field KKS model to predict the microstructure evolution in LPBF AlSi10Mg alloy submitted to non isothermal processes
• Numerical simulation of model problems in plasticity based on field dislocation mechanics
• Fracture initiation in multi-phase materials: a systematic three-dimensional approach using a FFT-based solver
• Multiscale modeling of fiber reinforced materials via non-matching immersed methods
• Recurrent Localization Networks applied to the Lippmann-Schwinger Equation
• Analytical Parameterization of Self-Consistent Polycrystal Mechanics: Fast Calculation of Upper Mantle Anisotropy
• Computation of effective elastic moduli of rocks using hierarchical homogenization
• Learning constitutive models from microstructural simulations via a non-intrusive reduced basis method: Extension to geometrical parameterizations
• Numerical investigation into coarse-scale models of diffusion in complex heterogeneous media
• Effective Response of Heterogeneous Materials using the Recursive Projection Method
• Micropolar elastoplasticity using a fast Fourier transform-based solver
• A Framework for FFT-based Homogenization on Anisotropic Lattices
• Quantification of 3D spatial correlations between state variables and distances to the grain boundary network in full-field crystal plasticity spectral method simulations
• A stable and accurate X-FFT solver for linear elastic homogenization problems in 3D
• A new open source framework for multiscale modeling of fibrous materials on heterogeneous supercomputers
• Universal Fourier Neural Operators for periodic homogenization problems in linear elasticity
• Simulation-Free Determination of Microstructure Representative Volume Element Size via Fisher Scores
• Adaptation and validation of FFT methods for homogenization of lattice based materials
• Lamination-based efficient treatment of weak discontinuities for non-conforming finite element meshes
• 3D image based stochastic micro-structure modelling of foams for simulating elasticity
• A statistical framework for generating microstructures of two-phase random materials: application to fatigue analysis
• Variational modeling adapted to the medium with gradient properties
• A non-local model for the description of twinning in polycrystalline materials in the context of infinitesimal strains: application to a magnesium alloy
• A variance reduction strategy for numerical random homogenization based on the equivalent inclusion method
• QAFE${}^2$: Quantum accelerated multiscale finite element analysis
• Approximation of Periodic PDE Solutions with Anisotropic Translation Invariant Spaces