On the micromechanics of deep material networks
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Matti Schneider | Thomas Böhlke | Sebastian Gajek | M. Schneider | S. Gajek | T. Böhlke | Sebastian Gajek
[1] M. Schneider. The sequential addition and migration method to generate representative volume elements for the homogenization of short fiber reinforced plastics , 2017 .
[2] George Cybenko,et al. Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..
[3] Javier Segurado,et al. On the accuracy of spectral solvers for micromechanics based fatigue modeling , 2018, Computational Mechanics.
[4] G. Srinivasu,et al. Artificial Neural Network Approach for Prediction of Titanium Alloy Stress-Strain Curve , 2012 .
[5] Pierre Suquet,et al. Extension of the Nonuniform Transformation Field Analysis to linear viscoelastic composites in the presence of aging and swelling , 2014 .
[6] Frank Hutter,et al. SGDR: Stochastic Gradient Descent with Warm Restarts , 2016, ICLR.
[7] Felix Fritzen,et al. GPU accelerated computational homogenization based on a variational approach in a reduced basis framework , 2014 .
[8] Fredrik Larsson,et al. On-the-Fly Adaptivity for Nonlinear Twoscale Simulations Using Artificial Neural Networks and Reduced Order Modeling , 2019, Front. Mater..
[9] J. Mandel. Generalisation de la theorie de plasticite de W. T. Koiter , 1965 .
[10] M. Schneider. On the mathematical foundations of the self-consistent clustering analysis for non-linear materials at small strains , 2019, Computer Methods in Applied Mechanics and Engineering.
[11] J. Michel,et al. A model-reduction approach to the micromechanical analysis of polycrystalline materials , 2016 .
[12] Orion L. Kafka,et al. Data-Driven Self-consistent Clustering Analysis of Heterogeneous Materials with Crystal Plasticity , 2018 .
[13] M. Schneider. On the Barzilai‐Borwein basic scheme in FFT‐based computational homogenization , 2019, International Journal for Numerical Methods in Engineering.
[14] Matti Schneider,et al. Fiber orientation interpolation for the multiscale analysis of short fiber reinforced composite parts , 2018 .
[15] J. Chaboche,et al. Multiscale analysis of SiC/Ti composites , 2004 .
[16] R. E. Miles. On random rotations in R3 , 1965 .
[17] S. Marfia. Micro–macro analysis of shape memory alloy composites , 2005 .
[18] Timon Rabczuk,et al. A surrogate model for computational homogenization of elastostatics at finite strain using the HDMR-based neural network approximator , 2019, ArXiv.
[19] Mark A Fleming,et al. Microstructural material database for self-consistent clustering analysis of elastoplastic strain softening materials , 2018 .
[20] Thomas Böhlke,et al. Reduced basis homogenization of viscoelastic composites , 2013 .
[21] J. Michel,et al. Effective potentials in nonlinear polycrystals and quadrature formulae , 2017, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[22] M. Diehl,et al. A spectral method solution to crystal elasto-viscoplasticity at finite strains , 2013 .
[23] K. Chandrashekhara,et al. Neural Network Based Constitutive Model for Rubber Material , 2004 .
[24] Jan Novák,et al. Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients , 2010, J. Comput. Phys..
[25] A. Philipse,et al. Random packings of spheres and spherocylinders simulated by mechanical contraction. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.
[26] Graeme W. Milton,et al. A fast numerical scheme for computing the response of composites using grid refinement , 1999 .
[27] Zeliang Liu,et al. Exploring the 3D architectures of deep material network in data-driven multiscale mechanics , 2019, Journal of the Mechanics and Physics of Solids.
[28] I. Sandberg. Series expansions for nonlinear systems , 1983 .
[29] Luca Antiga,et al. Automatic differentiation in PyTorch , 2017 .
[30] I. W. Sandberg,et al. Expansions for nonlinear systems , 1982, The Bell System Technical Journal.
[31] Kurt Hornik,et al. Approximation capabilities of multilayer feedforward networks , 1991, Neural Networks.
[32] Pierre Suquet,et al. Computational analysis of nonlinear composite structures using the Nonuniform Transformation Field Analysis , 2004 .
[33] R. Rogers,et al. An introduction to partial differential equations , 1993 .
[34] Laurent Adam,et al. A second-moment incremental formulation for the mean-field homogenization of elasto-plastic composites , 2011 .
[35] M. Schneider,et al. On Quasi‐Newton methods in fast Fourier transform‐based micromechanics , 2019, International Journal for Numerical Methods in Engineering.
[36] S. Torquato,et al. Random Heterogeneous Materials: Microstructure and Macroscopic Properties , 2005 .
[37] Miguel A. Bessa,et al. Self-consistent clustering analysis: An efficient multi-scale scheme for inelastic heterogeneous materials , 2016 .
[38] G. Milton. The Theory of Composites , 2002 .
[39] S. Shtrikman,et al. A variational approach to the theory of the elastic behaviour of polycrystals , 1962 .
[40] Xuejun Zhou,et al. Least Squares Support Vector Machine for Constitutive Modeling of Clay , 2015 .
[41] R. Hill. A self-consistent mechanics of composite materials , 1965 .
[42] H. Moulinec,et al. A fast numerical method for computing the linear and nonlinear mechanical properties of composites , 1994 .
[43] R. Müller,et al. A multiscale approach for modeling progressive damage of composite materials using fast Fourier transforms , 2014 .
[44] G. J. Dvorak,et al. Implementation of the transformation field analysis for inelastic composite materials , 1994 .
[45] M. D. McKay,et al. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code , 2000 .
[46] George J. Dvorak,et al. The modeling of inelastic composite materials with the transformation field analysis , 1994 .
[47] Marc G. D. Geers,et al. A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials , 2017, J. Comput. Phys..
[48] Hervé Moulinec,et al. A numerical method for computing the overall response of nonlinear composites with complex microstructure , 1998, ArXiv.
[49] K. Tanaka,et al. Average stress in matrix and average elastic energy of materials with misfitting inclusions , 1973 .
[50] Jean-Louis Chaboche,et al. Towards a micromechanics based inelastic and damage modeling of composites , 2001 .
[51] Sanjiv Kumar,et al. On the Convergence of Adam and Beyond , 2018 .
[52] M. Stone. The Generalized Weierstrass Approximation Theorem , 1948 .
[53] R. Hill. Elastic properties of reinforced solids: some theoretical principles , 1963 .
[54] M. Schneider,et al. The composite voxel technique for inelastic problems , 2017 .
[55] W. Rugh. Nonlinear System Theory: The Volterra / Wiener Approach , 1981 .
[56] Zeliang Liu,et al. A Deep Material Network for Multiscale Topology Learning and Accelerated Nonlinear Modeling of Heterogeneous Materials , 2018, Computer Methods in Applied Mechanics and Engineering.
[57] Leon O. Chua,et al. Fading memory and the problem of approximating nonlinear operators with volterra series , 1985 .
[58] Matti Schneider,et al. An efficient solution scheme for small-strain crystal-elasto-viscoplasticity in a dual framework , 2020 .
[59] B. A. Le,et al. Computational homogenization of nonlinear elastic materials using neural networks , 2015 .
[60] T. Carleman. Application de la théorie des équations intégrales linéaires aux systèmes d'équations différentielles non linéaires , 1932 .
[61] Javier Segurado,et al. On the accuracy of mean-field approaches to simulate the plastic deformation of composites , 2002 .
[62] Joos Vandewalle,et al. Multi-Valued and Universal Binary Neurons: Theory, Learning and Applications , 2012 .
[63] Pierre Suquet,et al. On the effective behavior of nonlinear inelastic composites: I. Incremental variational principles , 2007 .
[64] I. Sandberg. Volterra expansions for time-varying nonlinear systems , 1982, The Bell System Technical Journal.
[65] Zvi Hashin,et al. Complex moduli of viscoelastic composites—I. General theory and application to particulate composites , 1970 .
[66] S. Reese,et al. Model order reduction of nonlinear homogenization problems using a Hashin–Shtrikman type finite element method , 2018 .
[67] Sonia Marfia,et al. Analysis of SMA composite laminates using a multiscale modelling technique , 2007 .
[68] Jean-Louis Chaboche,et al. On the capabilities of mean-field approaches for the description of plasticity in metal matrix composites , 2005 .
[69] A. Isidori. Nonlinear Control Systems , 1985 .
[70] Hongbo Zhao,et al. Simulating the Stress-Strain Relationship of Geomaterials by Support Vector Machine , 2014 .
[71] Y. Benveniste,et al. On transformation strains and uniform fields in multiphase elastic media , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.
[72] Alexander Mielke,et al. A Mathematical Framework for Generalized Standard Materials in the Rate-Independent Case , 2006 .
[73] Matti Schneider,et al. Use of composite voxels in FFT-based homogenization , 2015 .
[74] S. Shtrikman,et al. Note on a variational approach to the theory of composite elastic materials , 1961 .
[75] Felix Fritzen,et al. Reduced basis hybrid computational homogenization based on a mixed incremental formulation , 2013 .
[76] E. Sacco,et al. Micromechanics and Homogenization of SMA-Wire-Reinforced Materials , 2005 .
[77] Pierre Suquet,et al. Continuum Micromechanics , 1997, Encyclopedia of Continuum Mechanics.
[78] M. N. Jadid,et al. Prediction of Stress-strain Relationships for Reinforced Concrete Sections by Implementing Neural Network Techniques , 1997 .
[79] T. Böhlke,et al. Nonlinear homogenization using the nonuniform transformation field analysis , 2011 .
[80] Pierre Suquet,et al. A model-reduction approach in micromechanics of materials preserving the variational structure of constitutive relations , 2016 .
[81] J. Michel,et al. Nonuniform transformation field analysis , 2003 .