Computational homogenization of nonlinear elastic materials using neural networks
From MaRDI portal
Publication:2952866
DOI10.1002/nme.4953zbMath1352.74266OpenAlexW1606775516MaRDI QIDQ2952866
Qi-Chang He, Ba-Anh Le, Julien Yvonnet
Publication date: 30 December 2016
Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/nme.4953
neural networkshigh-dimensional approximationnonlinear homogenizationmultiscale methodscomputational homogenization
Related Items
Constitutive artificial neural networks: a fast and general approach to predictive data-driven constitutive modeling by deep learning ⋮ Recent advances on topology optimization of multiscale nonlinear structures ⋮ Learning constitutive relations using symmetric positive definite neural networks ⋮ An investigation on the coupling of data-driven computing and model-driven computing ⋮ A nonlinear manifold-based reduced order model for multiscale analysis of heterogeneous hyperelastic materials ⋮ Data-driven tissue mechanics with polyconvex neural ordinary differential equations ⋮ Accelerating the distance-minimizing method for data-driven elasticity with adaptive hyperparameters ⋮ A nonlinear data-driven reduced order model for computational homogenization with physics/pattern-guided sampling ⋮ Propagation of uncertainty in the mechanical and biological response of growing tissues using multi-fidelity Gaussian process regression ⋮ Bayesian inference of non-linear multiscale model parameters accelerated by a deep neural network ⋮ Nonlinear multiscale simulation of elastic beam lattices with anisotropic homogenized constitutive models based on artificial neural networks ⋮ Nonlinear multiscale modeling of thin composite shells at finite deformations ⋮ Variational framework for distance-minimizing method in data-driven computational mechanics ⋮ A machine learning based plasticity model using proper orthogonal decomposition ⋮ Accelerated offline setup of homogenized microscopic model for multi‐scale analyses using neural network with knowledge transfer ⋮ Material modeling for parametric, anisotropic finite strain hyperelasticity based on machine learning with application in optimization of metamaterials ⋮ A micromechanics‐based recurrent neural networks model for path‐dependent cyclic deformation of short fiber composites ⋮ Geometric learning for computational mechanics. II: Graph embedding for interpretable multiscale plasticity ⋮ A mechanics‐informed artificial neural network approach in data‐driven constitutive modeling ⋮ Molecular dynamics inferred transfer learning models for finite‐strain hyperelasticity of monoclinic crystals: Sobolev training and validations against physical constraints ⋮ <scp>Data</scp>‐physics driven reduced order homogenization ⋮ Machine learning based asymptotic homogenization and localization: Predictions of key local behaviors of multiscale configurations bearing microstructural varieties ⋮ Machine learning-enabled self-consistent parametrically-upscaled crystal plasticity model for Ni-based superalloys ⋮ Micromechanics-based surrogate models for the response of composites: a critical comparison between a classical mesoscale constitutive model, hyper-reduction and neural networks ⋮ Computational modeling and data‐driven homogenization of knitted membranes ⋮ Automatic generation of interpretable hyperelastic material models by symbolic regression ⋮ Two-stage 2D-to-3d reconstruction of realistic microstructures: implementation and numerical validation by effective properties ⋮ \(\mathrm{FE^{ANN}}\): an efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining ⋮ A data-driven harmonic approach to constructing anisotropic damage models with a minimum number of internal variables ⋮ On the micromechanics of deep material networks ⋮ A reduced order model for geometrically parameterized two-scale simulations of elasto-plastic microstructures under large deformations ⋮ A monolithic hyper ROM \(\mathrm{FE}^2\) method with clustered training at finite deformations ⋮ Pre-trained transformer model as a surrogate in multiscale computational homogenization framework for elastoplastic composite materials subjected to generic loading paths ⋮ Concurrent multiscale simulations of nonlinear random materials using probabilistic learning ⋮ Review of solution methodologies for structural analysis of composites ⋮ A time-adaptive FE\(^2\)-approach within the method of vertical lines ⋮ Deep learning framework for multiscale finite element analysis based on data-driven mechanics and data augmentation ⋮ On-the-fly construction of surrogate constitutive models for concurrent multiscale mechanical analysis through probabilistic machine learning ⋮ A framework for neural network based constitutive modelling of inelastic materials ⋮ A mechanics-informed deep learning framework for data-driven nonlinear viscoelasticity ⋮ Data-driven nonparametric identification of material behavior based on physics-informed neural network with full-field data ⋮ Modular machine learning-based elastoplasticity: generalization in the context of limited data ⋮ A structural-based computational model of tendon-bone insertion tissues ⋮ Systematic study of homogenization and the utility of circular simplified representative volume element ⋮ Model-data-driven constitutive responses: application to a multiscale computational framework ⋮ A recurrent neural network-accelerated multi-scale model for elasto-plastic heterogeneous materials subjected to random cyclic and non-proportional loading paths ⋮ Micromechanics-based material networks revisited from the interaction viewpoint; robust and efficient implementation for multi-phase composites ⋮ An efficient monolithic solution scheme for FE\(^2\) problems ⋮ Cell division in deep material networks applied to multiscale strain localization modeling ⋮ Learning constitutive models from microstructural simulations via a non-intrusive reduced basis method ⋮ A neural network-aided Bayesian identification framework for multiscale modeling of nanocomposites ⋮ An FE-DMN method for the multiscale analysis of short fiber reinforced plastic components ⋮ Surrogate modeling of elasto-plastic problems via long short-term memory neural networks and proper orthogonal decomposition ⋮ A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials ⋮ Meta-modeling game for deriving theory-consistent, microstructure-based traction-separation laws via deep reinforcement learning ⋮ On the mathematical foundations of the self-consistent clustering analysis for non-linear materials at small strains ⋮ Fiber orientation interpolation for the multiscale analysis of short fiber reinforced composite parts ⋮ Latent map Gaussian processes for mixed variable metamodeling ⋮ Predicting the mechanical properties of biopolymer gels using neural networks trained on discrete fiber network data ⋮ Data science for finite strain mechanical science of ductile materials ⋮ A DNN-based data-driven modeling employing coarse sample data for real-time flexible multibody dynamics simulations ⋮ Smart constitutive laws: inelastic homogenization through machine learning ⋮ Machine learning materials physics: multi-resolution neural networks learn the free energy and nonlinear elastic response of evolving microstructures ⋮ Geometric deep learning for computational mechanics. I: Anisotropic hyperelasticity ⋮ Finite element solver for data-driven finite strain elasticity ⋮ A kernel method for learning constitutive relation in data-driven computational elasticity ⋮ Bi-directional evolutionary structural optimization on advanced structures and materials: a comprehensive review ⋮ Two-stage data-driven homogenization for nonlinear solids using a reduced order model ⋮ Anisotropic hyperelastic constitutive models for finite deformations combining material theory and data-driven approaches with application to cubic lattice metamaterials ⋮ Machine learning based multiscale calibration of mesoscopic constitutive models for composite materials: application to brain white matter ⋮ A deep energy method for finite deformation hyperelasticity ⋮ Functional approximation and projection of stored energy functions in computational homogenization of hyperelastic materials: a probabilistic perspective ⋮ Local approximate Gaussian process regression for data-driven constitutive models: development and comparison with neural networks ⋮ A physics-constrained data-driven approach based on locally convex reconstruction for noisy database ⋮ Data-driven multiscale finite element method: from concurrence to separation ⋮ Deep material network with cohesive layers: multi-stage training and interfacial failure analysis ⋮ A framework for data-driven analysis of materials under uncertainty: countering the curse of dimensionality ⋮ Microstructural material database for self-consistent clustering analysis of elastoplastic strain softening materials ⋮ Exploring the 3D architectures of deep material network in data-driven multiscale mechanics ⋮ Interaction-based material network: a general framework for (porous) microstructured materials ⋮ Clustering discretization methods for generation of material performance databases in machine learning and design optimization ⋮ A data-driven computational homogenization method based on neural networks for the nonlinear anisotropic electrical response of graphene/polymer nanocomposites ⋮ Derivation of heterogeneous material laws via data-driven principal component expansions ⋮ Phase distribution and properties identification of heterogeneous materials: a data-driven approach ⋮ Recurrent neural networks (RNNs) with dimensionality reduction and break down in computational mechanics; application to multi-scale localization step ⋮ Learning constitutive relations from indirect observations using deep neural networks ⋮ Data-driven multiscale method for composite plates ⋮ Learning constitutive models from microstructural simulations via a non-intrusive reduced basis method: extension to geometrical parameterizations ⋮ Multiscale modelling and material design of woven textiles using Gaussian processes ⋮ Automated constitutive modeling of isotropic hyperelasticity based on artificial neural networks
Cites Work
- Unnamed Item
- Approximation by neural networks with sigmoidal functions
- Multiparametric analysis within the proper generalized decomposition framework
- Uncertainty quantification in computational stochastic multiscale analysis of nonlinear elastic materials
- PGD-based \textit{computational vademecum} for efficient design, optimization and control
- Numerically explicit potentials for the homogenization of nonlinear elastic heterogeneous materials
- A simple computational homogenization method for structures made of linear heterogeneous viscoelastic materials
- The reduced model multiscale method (R3M) for the nonlinear homogenization of hyperelastic media at finite strains
- A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids
- A numerical method for homogenization in nonlinear elasticity
- An adaptive method for homogenization in orthotropic nonlinear elasticity
- Weighted trigonometric approximation and inner-outer functions on higher dimensional Euclidean spaces
- Nonuniform transformation field analysis
- General foundations of high-dimensional model representations
- Multiscale structural topology optimization with an approximate constitutive model for local material microstructure
- Reliability-based structural optimization using neural networks and Monte Carlo simulation
- Effective properties of composite materials with periodic microstructure: A computational approach
- Structural optimization using evolution strategies and neural networks
- Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy
- Elastic properties of reinforced solids: Some theoretical principles
- Nonincremental proper generalized decomposition solution of parametric uncoupled models defined in evolving domains
- Hierarchically parallel coupled finite strain multiscale solver for modeling heterogeneous layers
- High dimensional model representation for piece‐wise continuous function approximation
- On the overall properties of nonlinearly viscous composites
- Multi‐scale constitutive modelling of heterogeneous materials with a gradient‐enhanced computational homogenization scheme
- A finite element method for crack growth without remeshing
- Approximation by superpositions of a sigmoidal function
- A class of general algorithms for multi-scale analyses of heterogeneous media