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We use machine learning (ML) to infer stress and plastic flow rules using data from repre- sentative polycrystalline simulations.
G. I. Taylor, The mechanism of plastic deformation of crystals. part i. theoretical, Proceedings of the Royal Society of London. Series A 145 (855) (1934) 362–387
1934
Earlier work this paper cites.
J. Bishop, R. Hill, Xlvi. a theory of the plastic distortion of a polycrystalline aggregate under combined stresses., The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 42 (327) (1951) 414–427
1951
Earlier work this paper cites.
J. Bishop, R. Hill, Cxxviii. a theoretical derivation of the plastic properties of a polycrystalline face-centred metal, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 42 (334) (1951) 1298–1307
1951
Earlier work this paper cites.
R. S. Rivlin, Further remarks on the stress-deformation relations for isotropic materials, Journal of Rational Mechanics and Analysis 4 (1955) 681–702
1955
Earlier work this paper cites.
R. S. Rivlin, J. L. Ericksen, Stress-deformation relations for isotropic materials, Journal of Rational Mechanics and Analysis 4 (1955) 323–425
1955
Earlier work this paper cites.
T. Doyle, J. L. Ericksen, Nonlinear elasticity, in: Advances in applied mechanics, Vol. 4, Elsevier, 1956, pp. 53–115
1956
Earlier work this paper cites.
G. Smith, R. S. Rivlin, Stress-deformation relations for anisotropic solids, Archive for Rational Mechanics and Analysis 1 (1) (1957) 107–112
1957
Earlier work this paper cites.
G. Smith, R. S. Rivlin, The anisotropic tensors, Quarterly of Applied Mathematics 15 (3) (1957) 308–314
1957
Earlier work this paper cites.
A. J. M. Spencer, R. Rivlin, Finite integrity bases for five or fewer symmetric 3 × \times 3 matrices, Archive for rational mechanics and analysis 2 (1) (1958) 435–446
1958
Earlier work this paper cites.
A. J. M. Spencer, R. S. Rivlin, The theory of matrix polynomials and its application to the mechanics of isotropic continua, Archive for rational mechanics and analysis 2 (1) (1958) 309–336
1958
Earlier work this paper cites.
B. Seth, Generalized strain measure with applications to physical problems, Tech. rep., Wisconsin University-Madison, Mathematics Research Center (1961)
1961
Earlier work this paper cites.
E. Kroner, On the plastic deformation of polycrystals, Acta Metallurgica 9 (2) (1961) 155–161
1961
Earlier work this paper cites.
A. Spencer, R. Rivlin, Isotropic integrity bases for vectors and second-order tensors, Archive for rational mechanics and analysis 9 (1) (1962) 45–63
1962
Earlier work this paper cites.
A. Pipkin, A. Wineman, Material symmetry restrictions on non-polynomial constitutive equations, Archive for Rational Mechanics and Analysis 12 (1) (1963) 420–426
1963
Earlier work this paper cites.
B. D. Coleman, W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Archive for Rational Mechanics and Analysis 13 (1) (1963) 167–178
1963
Earlier work this paper cites.
A. S. Wineman, A. Pipkin, Material symmetry restrictions on constitutive equations, Archive for Rational Mechanics and Analysis 17 (3) (1964) 184–214
1964
Earlier work this paper cites.
G. Smith, R. Rivlin, Integrity bases for vectors–the crystal classes, Archive for Rational Mechanics and Analysis 15 (3) (1964) 169–221
1964
Earlier work this paper cites.
G. Smith, On isotropic integrity bases, Archive for rational mechanics and analysis 18 (4) (1965) 282–292
1965
Earlier work this paper cites.
J. Mandel, Généralisation de la théorie de plasticité de WT Koiter, International Journal of Solids and structures 1 (3) (1965) 273–295
1965
Earlier work this paper cites.
R. Hill, On constitutive inequalities for simple materials—i, Journal of the Mechanics and Physics of Solids 16 (4) (1968) 229–242
1968
Earlier work this paper cites.
R. Rivlin, G. Smith, Orthogonal integrity basis for N symmetric matrices, Contributions to mechanics: Markus Reiner eightieth anniversary volume (1969) 121
1969
Earlier work this paper cites.
C.-C. Wang, On a general representation theorem for constitutive relations, Archive for Rational Mechanics and Analysis 33 (1) (1969) 1–25
1969
Earlier work this paper cites.
E. H. Lee, Elastic-plastic deformation at finite strains, Journal of applied mechanics 36 (1) (1969) 1–6
1969
Earlier work this paper cites.
C.-C. Wang, A new representation theorem for isotropic functions: An answer to professor gf smith’s criticism of my papers on representations for isotropic functions, Archive for rational mechanics and analysis 36 (3) (1970) 166–197
1970
Earlier work this paper cites.
A. Spencer, Part III. Theory of invariants, Continuum physics 1 (1971) 239–353
1971
Earlier work this paper cites.
M. E. Gurtin, An introduction to continuum mechanics, Vol. 158, Academic press, 1982
1982
Earlier work this paper cites.
A. Spencer, The formulation of constitutive equation for anisotropic solids, in: Mechanical Behavior of Anisotropic Solids/Comportment Méchanique des Solides Anisotropes, Springer, 1982, pp. 3–26
1982
Earlier work this paper cites.
J. E. Marsden, T. J. Hughes, Mathematical foundations of elasticity, Prentice-Hall, 1983
1983
Earlier work this paper cites.
G. C. Johnson, D. J. Bammann, A discussion of stress rates in finite deformation problems, International Journal of Solids and Structures 20 (8) (1984) 725–737
1984
Earlier work this paper cites.
D. E. Rumelhart, G. E. Hinton, R. J. Williams, Learning representations by back-propagating errors, Nature 323 (6088) (1986) 533–538
1986
Cited alongside, same era.
A. Spencer, Isotropic polynomial invariants and tensor functions, in: Applications of tensor functions in solid mechanics, Springer, 1987, pp. 141–169
1987
Cited alongside, same era.
J.-P. Boehler, Representations for isotropic and anisotropic non-polynomial tensor functions, in: Applications of tensor functions in solid mechanics, Springer, 1987, pp. 31–53
1987
Cited alongside, same era.
H. Adeli, C. Yeh, Perceptron learning in engineering design, Computer-Aided Civil and Infrastructure Engineering 4 (4) (1989) 247–256
1989
Cited alongside, same era.
L. SzABo, M. Balla, Comparison of some stress rates, International journal of solids and structures 25 (3) (1989) 279–297
1989
J. Lubliner, Plasticity theory, Dover, 2008
2008
Later among the works it cites.
R. Goodman, N. R. Wallach, Symmetry, representations, and invariants, Vol. 255, Springer, 2009
2009
Later among the works it cites.
M. E. Gurtin, E. Fried, L. Anand, The mechanics and thermodynamics of continua, Cambridge University Press, 2010
2010
Later among the works it cites.
F. Roters, P. Eisenlohr, L. Hantcherli, D. D. Tjahjanto, T. R. Bieler, D. Raabe, Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Materialia 58 (4) (2010) 1152–1211
2010
Later among the works it cites.
H.-Y. Li, X.-F. Wang, D.-D. Wei, J.-D. Hu, Y.-H. Li, A comparative study on modified zerilli–armstrong, arrhenius-type and artificial neural network models to predict high-temperature deformation behavior in t24 steel, Materials Science and Engineering: A 536 (2012) 216–222
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Cited alongside, same era.
P. Haupt, C. Tsakmakis, On the application of dual variables in continuum mechanics, Continuum Mechanics and Thermodynamics 1 (3) (1989) 165–196
1989
Cited alongside, same era.
A. Khotanzad, Y. H. Hong, Invariant image recognition by zernike moments, IEEE Transactions on pattern analysis and machine intelligence 12 (5) (1990) 489–497
1990
Cited alongside, same era.
J. Zhang, J. Rychlewski, Structural tensors for anisotropic solids, Archives of Mechanics 42 (3) (1990) 267–277
1990
Cited alongside, same era.
P. Hajela, L. Berke, Neurobiological computational models in structural analysis and design, Computers & Structures 41 (4) (1991) 657–667
1991
Cited alongside, same era.
P. Theocaris, P. Panagiotopoulos, Neural networks for computing in fracture mechanics. methods and prospects of applications, Computer Methods in Applied Mechanics and Engineering 106 (1-2) (1993) 213–228
1993
Cited alongside, same era.
Q.-S. Zheng, Theory of representations for tensor functions–a unified invariant approach to constitutive equations, Applied Mechanics Reviews 47 (11) (1994) 545–587
1994
Cited alongside, same era.
B. Svendsen, On the representation of constitutive relations using structure tensors, International journal of engineering science 32 (12) (1994) 1889–1892
1994
Cited alongside, same era.
2012
Later among the works it cites.
A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, et al., Commentary: The materials project: A materials genome approach to accelerating materials innovation, APL Materials 1 (1) (2013) 011002
2013
Later among the works it cites.
J. E. Saal, S. Kirklin, M. Aykol, B. Meredig, C. Wolverton, Materials design and discovery with high-throughput density functional theory: the open quantum materials database (oqmd), Jom 65 (11) (2013) 1501–1509
2013
Later among the works it cites.
D. H. Sattinger, O. L. Weaver, Lie groups and algebras with applications to physics, geometry, and mechanics, Vol. 61, Springer Science & Business Media, 2013
2013
Later among the works it cites.
R. K. Desu, S. C. Guntuku, B. Aditya, A. K. Gupta, Support vector regression based flow stress prediction in austenitic stainless steel 304, Procedia Materials Science 6 (2014) 368–375
2014
Later among the works it cites.
R. Bobbili, B. Ramakrishna, V. Madhu, A. Gogia, Prediction of flow stress of 7017 aluminium alloy under high strain rate compression at elevated temperatures, Defence Technology 11 (1) (2015) 93–98
2015
Later among the works it cites.
J. Ling, J. Templeton, Evaluation of machine learning algorithms for prediction of regions of high reynolds averaged navier stokes uncertainty, Physics of Fluids 27 (8) (2015) 085103
2015
Later among the works it cites.
B. D. Tracey, K. Duraisamy, J. J. Alonso, A machine learning strategy to assist turbulence model development, in: 53rd AIAA Aerospace Sciences Meeting, 2015, p. 1287
2015
Later among the works it cites.
K. Duraisamy, Z. J. Zhang, A. P. Singh, New approaches in turbulence and transition modeling using data-driven techniques, in: 53rd AIAA Aerospace Sciences Meeting, 2015, p. 1284
2015
Later among the works it cites.
H. F. Alharbi, S. R. Kalidindi, Crystal plasticity finite element simulations using a database of discrete fourier transforms, International Journal of Plasticity 66 (2015) 71–84
2015
Later among the works it cites.
A. P. Bartók, G. Csányi, Gaussian approximation potentials: A brief tutorial introduction, International Journal of Quantum Chemistry 115 (16) (2015) 1051–1057
2015
Later among the works it cites.
M. A. Nielsen, Neural networks and deep learning, Determination Press, 2015
2015
Later among the works it cites.
A. Asgharzadeh, H. J. Aval, S. Serajzadeh, A study on flow behavior of aa5086 over a wide range of temperatures, Journal of Materials Engineering and Performance 25 (3) (2016) 1076–1084
2016
Later among the works it cites.
J. Ling, A. Kurzawski, J. Templeton, Reynolds averaged turbulence modelling using deep neural networks with embedded invariance, Journal of Fluid Mechanics 807 (2016) 155–166
2016
Later among the works it cites.
T. Kirchdoerfer, M. Ortiz, Data-driven computational mechanics, Computer Methods in Applied Mechanics and Engineering 304 (2016) 81–101
2016
Later among the works it cites.
J. Smith, W. Xiong, W. Yan, S. Lin, P. Cheng, O. L. Kafka, G. J. Wagner, J. Cao, W. K. Liu, Linking process, structure, property, and performance for metal-based additive manufacturing: computational approaches with experimental support, Computational Mechanics 57 (4) (2016) 583–610
2016
Later among the works it cites.
M. Shaughnessy, R. Jones, Efficient use of an adapting database of ab initio calculations to generate accurate newtonian dynamics, Journal of chemical theory and computation 12 (2) (2016) 664–675
2016
Later among the works it cites.
P. Raccuglia, K. C. Elbert, P. D. Adler, C. Falk, M. B. Wenny, A. Mollo, M. Zeller, S. A. Friedler, J. Schrier, A. J. Norquist, Machine-learning-assisted materials discovery using failed experiments, Nature 533 (7601) (2016) 73
2016
Later among the works it cites.
J. Ling, R. Jones, J. Templeton, Machine learning strategies for systems with invariance properties, Journal of Computational Physics 318 (2016) 22–35
2016
Later among the works it cites.
D. Versino, A. Tonda, C. A. Bronkhorst, Data driven modeling of plastic deformation, Computer Methods in Applied Mechanics and Engineering 318 (2017) 981–1004
2017
Later among the works it cites.
M. Bessa, R. Bostanabad, Z. Liu, A. Hu, D. W. Apley, C. Brinson, W. Chen, W. K. Liu, A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality, Computer Methods in Applied Mechanics and Engineering 320 (2017) 633–667
2017
Later among the works it cites.
Albany: a Trilinos-based PDE code, https://github.com/gahansen/Albany
2017
Later among the works it cites.
Dream3d: Open, extensible software environment to allow integrated processing, characterization and manipulation of microstructure digitally., http://dream3d.bluequartz.net
2017
Later among the works it cites.
Lasagne: a lightweight library to build and train neural networks in theano, https://lasagne.readthedocs.io/en/latest/
2017
Later among the works it cites.