Abstract
To analyze complex, heterogeneous materials, a fast and accurate method is needed. This means going beyond the classical finite element method, in a search for the ability to compute, with modest computational resources, solutions previously infeasible even with large cluster computers. In particular, this advance is motivated by composites design. Here, we apply similar principle to another complex, heterogeneous system: additively manufactured metals.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
T. Belytschko, S. Loehnert, J.H. Song, Multiscale aggregating discontinuities: a method for circumventing loss of material stability. Int. J. Numer. Methods Eng. 73(6), 869–894 (2008)
M.A. Bessa et al., A framework for data-driven analysis of materials under uncertainty: countering the curse of dimensionality. Comput. Methods Appl. Mech. Eng. 320, 633–667 (2017)
I. Doghri, A. Ouaar, Homogenization of two-phase elasto-plastic composite materials and structures: study of tangent operators, cyclic plasticity and numerical algorithms. Int. J. Solid. Struct. 40(7), 1681–1712 (2003)
J.D. Eshelby, The determination of the elastic field of an ellipsoidal inclusion, and related problems, in Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 241 (The Royal Society, 1957) pp. 376–396
Z. Hashin, S. Shtrikman, A variational approach to the theory of the elastic behaviour of multiphase materials. J. Mech. Phys. Solid. 11(2), 127–140 (1963)
R. Hill, A self-consistent mechanics of composite materials. J. Mech. Phys. Solid. 13(4), 213–222 (1965)
International A, Standard Terminology for Additive Manufacturing Technologies, F2792-12a edn (2015)
P. Krysl, S. Lall, J. Marsden, Dimensional model reduction in non linear finite element dynamics of solids and structures. Int. J. Numer. Methods Eng. 51, 479–504 (2001)
B. Le, J. Yvonnet, Q.C. He, Computational homogenization of nonlinear elastic materials using neural networks. Int. J. Numer. Methods Eng. (2015)
R.A. Lebensohn, A.K. Kanjarla, P. Eisenlohr, An elasto-viscoplastic formulation based on fast fourier transforms for the prediction of micromechanical fields in polycrystalline materials. Int. J. Plast. 32, 59–69 (2012)
Z. Liu, J.A. Moore, S. M. Aldousari, H.S. Hedia, S.A. Asiri, W.K. Liu, A statistical descriptor based volume-integral micromechanics model of heterogeneous material with arbitrary inclusion shape. Comput. Mech. 1–19 (2015)
Z. Liu, M. Bessa, W. Liu, Self-consistent clustering analysis: an efficient multi-scale scheme for inelastic heterogeneous materials. Comput. Methods Appl. Mech. Eng. 306, 319–341 (2016a)
Z. Liu, J. Moore, W. Liu, An extended micromechanics method for probing interphase properties in polymer nanocomposites. J. Mech. Phys. Solid. (2016). doi:10.1016/j.jmps.2016.05.002
J. MacQueen et al., Some methods for classification and analysis of multivariate observations, in Proceedings Of The Fifth Berkeley Symposium On Mathematical Statistics And Probability, vol. 14, Oakland, CA, USA, pp. 281–297 (1967)
R.D. McGinty, Multiscale representation of polycrystalline inelasticity. PhD thesis, Geogia Tech, 2001
J.C. Michel, P. Suquet, Computational analysis of nonlinear composite structures using the nonuniform transformation field analysis. Comput. Methods Appl. Mech. Eng. 193, 5477–5502 (2004)
C. Oskay, J. Fish, Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials. Comput. Methods Appl. Mech. Eng. 196, 1216–1243 (2007)
D.R. Owen, E. Hinton, Finite Elements in Plasticity (Pineridge Press, 1980)
F. Roters, P. Eisenlohr, L. Hantcherli, D. Tjahjanto, T. Bieler, D. Raabe, Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: theory, experiments, applications. Acta Mater. 58, 1152–1211 (2010)
S. Roussette, J.C. Michel, P. Suquet, Nonuniform transformation field analysis of elastic viscoplastic composites. Compos. Sci. Technol. 69, 22–27 (2009)
C. Ventola, Medical applications for 3d printing: current and projected uses. Pharm. Ther. 39, 704–711 (2014)
I.H. Witten, E. Frank, Data Mining: Practical machine learning tools and techniques (Morgan Kaufmann, 2005)
J. Yvonnet, Q.C. He, The reduced model multiscale method (r3m) for the non-linear homogenization of hyperelastic media at finite strains. J. Comput. Phys. 223, 341–368 (2007)
J. Yvonnet, E. Monteiro, Q.C. He, Computational homogenization method and reduced database model for hyperelastic heterogeneous structures. Int. J. Multiscale Comput. Eng. 11 (2013)
Acknowledgements
Z.L., O.L.K., C.Y. and W.K.L. warmly thank the support from AFOSR grant No. FA9550-14-1-0032, National Institute of Standards and Technology and Center for Hierarchical Materials Design (CHiMaD) under grant No. 70NANB13Hl94 and 70NANB14H012, and DOE CF-ICME project under grant No. DE-EE0006867. O.L.K. thanks United States National Science Foundation (NSF) for their support through the NSF Graduate Research Fellowship Program (GRFP) under financial award number DGE-1324585.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Liu, Z., Kafka, O.L., Yu, C., Liu, W.K. (2018). Data-Driven Self-consistent Clustering Analysis of Heterogeneous Materials with Crystal Plasticity. In: Oñate, E., Peric, D., de Souza Neto, E., Chiumenti, M. (eds) Advances in Computational Plasticity. Computational Methods in Applied Sciences, vol 46. Springer, Cham. https://doi.org/10.1007/978-3-319-60885-3_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-60885-3_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-60884-6
Online ISBN: 978-3-319-60885-3
eBook Packages: EngineeringEngineering (R0)