Surrogate modeling for the homogenization of elastoplastic composites based on RBF interpolation

[1]  J. Fish,et al.  Data‐physics driven reduced order homogenization , 2022, International Journal for Numerical Methods in Engineering.

[2]  Jan N. Fuhg,et al.  Modular machine learning-based elastoplasticity: generalization in the context of limited data , 2022, Computer Methods in Applied Mechanics and Engineering.

[3]  P. Kerfriden,et al.  Physically recurrent neural networks for path-dependent heterogeneous materials: embedding constitutive models in a data-driven surrogate , 2022, Computer Methods in Applied Mechanics and Engineering.

[4]  K. Linka,et al.  A new family of Constitutive Artificial Neural Networks towards automated model discovery , 2022, ArXiv.

[5]  Nikolaos N. Vlassis,et al.  Geometric deep learning for computational mechanics Part II: Graph embedding for interpretable multiscale plasticity , 2022, Computer Methods in Applied Mechanics and Engineering.

[6]  M. Kästner,et al.  FE $${}^\textrm{ANN}$$ ANN : an efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining , 2022, Computational Mechanics.

[7]  Wing Kam Liu,et al.  Mechanistically informed data-driven modeling of cyclic plasticity via artificial neural networks , 2022, Computer Methods in Applied Mechanics and Engineering.

[8]  K. Terada,et al.  Substitution approach for decoupled two-scale analysis of materially nonlinear composite plates , 2021 .

[9]  V. Tagarielli,et al.  A computational framework to establish data-driven constitutive models for time- or path-dependent heterogeneous solids , 2021, Scientific Reports.

[10]  K. Terada,et al.  A decoupling scheme for two‐scale finite thermoviscoelasticity with thermal and cure‐induced deformations , 2020, International Journal for Numerical Methods in Engineering.

[11]  L. Lorenzis,et al.  Unsupervised discovery of interpretable hyperelastic constitutive laws , 2020, Computer Methods in Applied Mechanics and Engineering.

[12]  K. Terada,et al.  $${\text {FE}}^r$$ FE r method with surrogate localization model for hyperelastic com , 2020 .

[13]  Julian N. Heidenreich,et al.  On the potential of recurrent neural networks for modeling path dependent plasticity , 2020 .

[14]  Qian Xiang,et al.  Exploring Elastoplastic Constitutive Law of Microstructured Materials Through Artificial Neural Network—A Mechanistic-Based Data-Driven Approach , 2020 .

[15]  Ludovic Noels,et al.  A recurrent neural network-accelerated multi-scale model for elasto-plastic heterogeneous materials subjected to random cyclic and non-proportional loading paths , 2020 .

[16]  T. Okabe,et al.  Multiscale analysis and experimental validation of crack initiation in quasi-isotropic laminates , 2020, International Journal of Solids and Structures.

[17]  K. Terada,et al.  Decoupled two-scale viscoelastic analysis of FRP in consideration of dependence of resin properties on degree of cure , 2020 .

[18]  P. Wriggers,et al.  A machine learning based plasticity model using proper orthogonal decomposition , 2020, Computer Methods in Applied Mechanics and Engineering.

[19]  M Mozaffar,et al.  Deep learning predicts path-dependent plasticity , 2019, Proceedings of the National Academy of Sciences.

[20]  F. Ghavamian,et al.  Accelerating multiscale finite element simulations of history-dependent materials using a recurrent neural network , 2019 .

[21]  J. Kato,et al.  Finite thermo‐elastic decoupled two‐scale analysis , 2019, International Journal for Numerical Methods in Engineering.

[22]  Felix Fritzen,et al.  Two-stage data-driven homogenization for nonlinear solids using a reduced order model , 2018 .

[23]  Julien Yvonnet,et al.  Homogenization methods and multiscale modeling : Nonlinear problems , 2017 .

[24]  Marc G. D. Geers,et al.  A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials , 2017, J. Comput. Phys..

[25]  Felix Fritzen,et al.  The finite element square reduced (FE2R) method with GPU acceleration: towards three‐dimensional two‐scale simulations , 2016 .

[26]  Pierre Suquet,et al.  A model-reduction approach in micromechanics of materials preserving the variational structure of constitutive relations , 2016 .

[27]  K. Terada,et al.  Characterization of time-varying macroscopic electro-chemo-mechanical behavior of SOFC subjected to Ni-sintering in cermet microstructures , 2015 .

[28]  Sonia Marfia,et al.  Reduced order modeling in nonlinear homogenization , 2015 .

[29]  Takashi Kyoya,et al.  Applicability of micro–macro decoupling scheme to two-scale analysis of fiber-reinforced plastics , 2014 .

[30]  Felix Fritzen,et al.  GPU accelerated computational homogenization based on a variational approach in a reduced basis framework , 2014 .

[31]  Kenjiro Terada,et al.  A method of two-scale analysis with micro-macro decoupling scheme: application to hyperelastic composite materials , 2013 .

[32]  Felix Fritzen,et al.  Reduced basis hybrid computational homogenization based on a mixed incremental formulation , 2013 .

[33]  Sonia Marfia,et al.  A nonuniform TFA homogenization technique based on piecewise interpolation functions of the inelastic field , 2013 .

[34]  F. Chinesta,et al.  A Short Review in Model Order Reduction Based on Proper Generalized Decomposition , 2018 .

[35]  Adrien Leygue,et al.  An overview of the proper generalized decomposition with applications in computational rheology , 2011 .

[36]  V. G. Kouznetsova,et al.  Multi-scale computational homogenization: Trends and challenges , 2010, J. Comput. Appl. Math..

[37]  B. Schrefler,et al.  Multiscale Methods for Composites: A Review , 2009 .

[38]  Julien Yvonnet,et al.  The reduced model multiscale method (R3M) for the non-linear homogenization of hyperelastic media at finite strains , 2007, J. Comput. Phys..

[39]  Jacob Fish,et al.  Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials , 2007 .

[40]  Kohei Yuge,et al.  Two-scale finite element analysis of heterogeneous solids with periodic microstructures , 2004 .

[41]  J. Michel,et al.  Nonuniform transformation field analysis , 2003 .

[42]  Kenjiro Terada,et al.  Two-scale kinematics and linearization for simultaneous two-scale analysis of periodic heterogeneous solids at finite strain , 2003 .

[43]  N. Kikuchi,et al.  A class of general algorithms for multi-scale analyses of heterogeneous media , 2001 .

[44]  A. Huerta,et al.  Numerical differentiation for local and global tangent operators in computational plasticity , 2000 .

[45]  N. Kikuchi,et al.  Simulation of the multi-scale convergence in computational homogenization approaches , 2000 .

[46]  J. Chaboche,et al.  FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials , 2000 .

[47]  Arthur E. Hoerl,et al.  Ridge Regression: Biased Estimation for Nonorthogonal Problems , 2000, Technometrics.

[48]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[49]  Frédéric Feyel,et al.  Multiscale FE2 elastoviscoplastic analysis of composite structures , 1999 .

[50]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[51]  Kenjiro Terada,et al.  Nonlinear homogenization method for practical applications , 1995 .

[52]  Ahmet S. Cakmak,et al.  A hardening orthotropic plasticity model for non‐frictional composites: Rate formulation and integration algorithm , 1994 .

[53]  G. Allaire.  Homogenization and two-scale convergence , 1992 .

[54]  N. Kikuchi,et al.  Preprocessing and postprocessing for materials based on the homogenization method with adaptive fini , 1990 .

[55]  M. Buhmann.  Multivariate cardinal interpolation with radial-basis functions , 1990 .

[56]  F. Devries,et al.  Homogenization and damage for composite structures , 1989 .

[57]  M. Stone.  Cross‐Validatory Choice and Assessment of Statistical Predictions , 1976 .

[58]  Rodney Hill,et al.  The essential structure of constitutive laws for metal composites and polycrystals , 1967 .

[59]  German Capuano,et al.  Smart constitutive laws: Inelastic homogenization through machine learning , 2021 .

[60]  F. Fritzen,et al.  Reduced order homogenization for viscoplastic composite materials including dissipative imperfect interfaces , 2017 .

[61]  P. Suquet,et al.  Elements of Homogenization Theory for Inelastic Solid Mechanics, in Homogenization Techniques for Composite Media , 1987 .

[62]  Dominique Leguillon,et al.  Homogenized constitutive law for a partially cohesive composite material , 1982 .