The reduced model multiscale method (R3M) for the nonlinear homogenization of hyperelastic media at finite strains

From MaRDI portal
Publication:876454

DOI10.1016/j.jcp.2006.09.019zbMath1163.74048OpenAlexW2064306347MaRDI QIDQ876454

Qi-Chang He, Julien Yvonnet

Publication date: 18 April 2007

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2006.09.019




Related Items (only showing first 100 items - show all)

Proper orthogonal decomposition assisted eigendeformation-based mathematical homogenization method for modeling cracks in 3D polycrystalline microstructuresPre-trained transformer model as a surrogate in multiscale computational homogenization framework for elastoplastic composite materials subjected to generic loading pathsConcurrent multiscale simulations of nonlinear random materials using probabilistic learningA clustering-enhanced potential-based reduced order homogenization framework for nonlinear heterogeneous materialsA micromechanical mean‐field homogenization surrogate for the stochastic multiscale analysis of composite materials failureA direct \(\mathrm{FE}^2\) method for concurrent multilevel modeling of piezoelectric materials and structuresStatistically compatible hyper-reduction for computational homogenizationAn introduction to kernel and operator learning methods for homogenization by self-consistent clustering analysisSoft elastic composites: microstructure evolution, instabilities and relaxed response by domain formationDeep learning framework for multiscale finite element analysis based on data-driven mechanics and data augmentationA mechanics-informed deep learning framework for data-driven nonlinear viscoelasticityRecent advances on topology optimization of multiscale nonlinear structuresA high-order three-scale reduced homogenization for nonlinear heterogeneous materials with multiple configurationsGeometry-dependent reduced-order models for the computation of homogenized transfer properties in porous mediaFrom virtual clustering analysis to self-consistent clustering analysis: a mathematical studyA model reduction method for the post-buckling analysis of cellular microstructuresDirect \(\mathrm{FE}^2\) for concurrent multilevel modeling of heterogeneous thin plate structuresAn investigation on the coupling of data-driven computing and model-driven computingA nonlinear manifold-based reduced order model for multiscale analysis of heterogeneous hyperelastic materialsEigenstrain based reduced order homogenization for polycrystalline materialsEfficient computational homogenization of simple elastoplastic microstructures using a shear band approachAutomatised selection of load paths to construct reduced-order models in computational damage micromechanics: from dissipation-driven random selection to Bayesian optimizationMathematical foundations of FEM-cluster based reduced order analysis method and a spectral analysis algorithm for improving the accuracyReduced order variational multiscale enrichment method for thermo-mechanical problemsHigh-performance model reduction techniques in computational multiscale homogenizationA reduced multiscale model for nonlinear structural topology optimizationSelf-consistent clustering analysis for multiscale modeling at finite strainsMulti-dimensional wavelet reduction for the homogenisation of microstructuresDiscrete eigenseparation-based reduced order homogenization method for failure modeling of composite materialsAcceleration of the spectral stochastic FEM using POD and element based discrete empirical approximation for a micromechanical model of heterogeneous materials with random geometryEfficient two-scale simulations of engineering structures using the Hashin-Shtrikman type finite element methodMicrostructure-informed reduced modes synthesized with Wang tiles and the generalized finite element methodHomogenization of large deforming fluid-saturated porous structuresMultiscale design of nonlinear materials using reduced-order modelingAn enhanced grain-boundary framework for computational homogenization and micro-cracking simulations of polycrystalline materialsMultiple spatio-temporal scale modeling of composites subjected to cyclic loadingCertification of projection-based reduced order modelling in computational homogenisation by the constitutive relation errorSurrogate modeling of multiscale models using kernel methodsHierarchically parallel coupled finite strain multiscale solver for modeling heterogeneous layersAccelerated offline setup of homogenized microscopic model for multi‐scale analyses using neural network with knowledge transfer<scp>A</scp> second‐order reduced multiscale method for nonlinear shell structures with orthogonal periodic configurationsComputational homogenization of nonlinear elastic materials using neural networksTopology optimization of multiscale elastoviscoplastic structuresThe finite element square reduced (FE2R ) method with GPU acceleration: towards three-dimensional two-scale simulationsStochastic modeling of the Ogden class of stored energy functions for hyperelastic materials: the compressible caseGeometric learning for computational mechanics. II: Graph embedding for interpretable multiscale plasticityMultiscale modeling of linear elastic heterogeneous structures via localized model order reductionArtificial neural network based correction for reduced order models in computational fluid mechanicsSurrogate modeling for the homogenization of elastoplastic composites based on RBF interpolationPOD-based reduced order model for the prediction of global and local elastic responses of fibre-reinforced polymer considering varying fibre distributionA reduced order model for geometrically parameterized two-scale simulations of elasto-plastic microstructures under large deformationsAn adaptive wavelet-based collocation method for solving multiscale problems in continuum mechanicsA numerical study of different projection-based model reduction techniques applied to computational homogenisationMultiscale modeling of prismatic heterogeneous structures based on a localized hyperreduced-order methodMultiscale modeling of laminated thin-shell structures with direct \(\mathrm{FE}^2\)A method of two-scale analysis with micro-macro decoupling scheme: application to hyperelastic composite materialsBridging proper orthogonal decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problemsA nested dynamic multi-scale approach for 3D problems accounting for micro-scale multi-physicsA multilevel computational strategy for handling microscopic and macroscopic instabilitiesA mortar based approach for the enforcement of periodic boundary conditions on arbitrarily generated meshesNumerically explicit potentials for the homogenization of nonlinear elastic heterogeneous materialsUncertainty quantification in computational stochastic multiscale analysis of nonlinear elastic materialsDomain decomposition techniques for the efficient modeling of brittle heterogeneous materialsAn adaptive sub-incremental strategy for the solution of homogenization-based multi-scale problems\(\mathrm{FE}^2\) multiscale in linear elasticity based on parametrized microscale models using proper generalized decompositionA domain decomposition strategy for reduced order models. Application to the incompressible Navier-Stokes equationsA simple computational homogenization method for structures made of linear heterogeneous viscoelastic materialsReduced-order subscales for POD modelsWavelet based reduced order models for microstructural analysesA recurrent neural network-accelerated multi-scale model for elasto-plastic heterogeneous materials subjected to random cyclic and non-proportional loading pathsCell division in deep material networks applied to multiscale strain localization modelingLearning constitutive models from microstructural simulations via a non-intrusive reduced basis methodA deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materialsAn inverse micro-mechanical analysis toward the stochastic homogenization of nonlinear random compositesFEM-cluster based reduction method for efficient numerical prediction of effective properties of heterogeneous material in nonlinear rangeFiber orientation interpolation for the multiscale analysis of short fiber reinforced composite partsIntegration efficiency for model reduction in micro-mechanical analysesEffective pressure-sensitive elastoplastic behavior of particle-reinforced composites and porous media under isotropic loadingData science for finite strain mechanical science of ductile materialsA residual-driven local iterative corrector scheme for the multiscale finite element methodAuxetic orthotropic materials: numerical determination of a phenomenological spline-based stored density energy and its implementation for finite element analysisA GFEM-based reduced-order homogenization model for heterogeneous materials under volumetric and interfacial damageMultiscale computational homogenization: review and proposal of a new enhanced-first-order methodTwo-stage data-driven homogenization for nonlinear solids using a reduced order modelTransient multi-scale analysis with micro-inertia effects using direct FE\(^2\) methodMultiresolution clustering analysis for efficient modeling of hierarchical material systemsMultiscale structural topology optimization with an approximate constitutive model for local material microstructureA deep energy method for finite deformation hyperelasticityFunctional approximation and projection of stored energy functions in computational homogenization of hyperelastic materials: a probabilistic perspectiveReduced order modeling strategies for computational multiscale fractureDimensional hyper-reduction of nonlinear finite element models via empirical cubatureMicro-to-macro transition accounting for general imperfect interfacesSelf-consistent clustering analysis: an efficient multi-scale scheme for inelastic heterogeneous materialsThe Coarse Mesh Condensation Multiscale Method for parallel computation of heterogeneous linear structures without scale separationData-driven multiscale finite element method: from concurrence to separationA framework for data-driven analysis of materials under uncertainty: countering the curse of dimensionalityModel adaptivity on effective elastic properties coupled with adaptive FEMA matrix DEIM technique for model reduction of nonlinear parametrized problems in cardiac mechanicsModel order reduction of nonlinear homogenization problems using a Hashin-Shtrikman type finite element methodMicrostructural material database for self-consistent clustering analysis of elastoplastic strain softening materials



Cites Work


This page was built for publication: The reduced model multiscale method (R3M) for the nonlinear homogenization of hyperelastic media at finite strains