×

zbMATH — the first resource for mathematics

Microstructural material database for self-consistent clustering analysis of elastoplastic strain softening materials. (English) Zbl 1439.74063
Summary: Multiscale modeling of heterogeneous material undergoing strain softening poses computational challenges for localization of the microstructure, material instability in the macrostructure, and the computational requirement for accurate and efficient concurrent calculation. In the paper, a stable micro-damage homogenization algorithm is presented which removes the material instability issues in the microstructure with representative volume elements (RVE) that are not sensitive to size when computing the homogenized stress-strain response.
The proposed concurrent simulation framework allows the computation of the macroscopic response to explicitly consider the behavior of the separate constituents (material phases), as well as the complex microstructural morphology. A non-local material length parameter is introduced in the macroscale model, which will control the width of the damage bands and prevent material instability.
The self-consistent clustering analysis (SCA) recently proposed by the first author et al. [ibid. 306, 319–341 (2016; Zbl 1436.74070)] provides an effective way of developing a microstructural database based on a clustering algorithm and the Lippmann-Schwinger integral equation, which enables an efficient and accurate prediction of nonlinear material response. The self-consistent clustering analysis is further generalized to consider complex loading paths through the projection of the effective stiffness tensor. In the concurrent simulation, the predicted macroscale strain localization is observed to be sensitive to the combination of microscale constituents, showing the unique capability of the SCA microstructural database for complex material simulations.

MSC:
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)
74M25 Micromechanics of solids
74A45 Theories of fracture and damage
74Q15 Effective constitutive equations in solid mechanics
Software:
HYPLAS
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Liu, Z.; Bessa, M. A.; Liu, W. K., Self-consistent clustering analysis: An efficient multi-scale scheme for inelastic heterogeneous materials, Comput. Methods Appl. Mech. Engrg., 306, 319-341 (2016)
[2] McVeigh, C.; Liu, W. K., Linking microstructure and properties through a predictive multiresolution continuum, Comput. Methods Appl. Mech. Engrg., 197, 41, 3268-3290 (2008)
[3] McVeigh, C.; Vernerey, F.; Liu, W. K.; Brinson, L. C., Multiresolution analysis for material design, Comput. Methods Appl. Mech. Engrg., 195, 37, 5053-5076 (2006)
[4] Geers, M. G.; Kouznetsova, V. G.; Brekelmans, W., Multi-scale computational homogenization: Trends and challenges, J. Comput. Appl. Math., 234, 7, 2175-2182 (2010)
[5] Bažant, Z. P., Can multiscale-multiphysics methods predict softening damage and structural failure?, Int. J. Multiscale Comput. Eng., 8, 1 (2010)
[6] Gurson, A. L., Continuum theory of ductile rupture by void nucleation and growth: Part I—Yield criteria and flow rules for porous ductile media, J. Eng. Mater. Technol., 99, 1, 2-15 (1977)
[7] Bažant, Z. P.; Jirásek, M., Nonlocal integral formulations of plasticity and damage: survey of progress, J. Eng. Mech., 128, 11, 1119-1149 (2002)
[8] Vernerey, F.; Liu, W. K.; Moran, B., Multi-scale micromorphic theory for hierarchical materials, J. Mech. Phys. Solids, 55, 12, 2603-2651 (2007)
[9] Vernerey, F.; Liu, W. K.; Moran, B.; Olson, G., A micromorphic model for the multiple scale failure of heterogeneous materials, J. Mech. Phys. Solids, 56, 4, 1320-1347 (2008) · Zbl 1171.74312
[10] Forest, S., Micromorphic approach for gradient elasticity, viscoplasticity, and damage, J. Eng. Mech., 135, 3, 117-131 (2009)
[11] Miehe, C.; Welschinger, F.; Hofacker, M., Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations, Internat. J. Numer. Methods Engrg., 83, 10, 1273-1311 (2010)
[12] Miehe, C.; Hofacker, M.; Schaenzel, L.-M.; Aldakheel, F., Phase field modeling of fracture in multi-physics problems. Part II. Coupled brittle-to-ductile failure criteria and crack propagation in thermo-elastic-plastic solids, Comput. Methods Appl. Mech. Engrg., 294, 486-522 (2015)
[13] Bažant, Z. P.; Oh, B. H., Crack band theory for fracture of concrete, Mat. Constr., 16, 3, 155-177 (1983)
[14] Pandolfi, A.; Ortiz, M., An eigenerosion approach to brittle fracture, Internat. J. Numer. Methods Engrg., 92, 8, 694-714 (2012)
[15] Holdren, J. P., Materials Genome Initiative: Strategic Plan, Vol. 6 (2014), Office of Science and Technology Policy: Office of Science and Technology Policy Washington DC
[16] Liu, W. K.; Siad, L.; Tian, R.; Lee, S.; Lee, D.; Yin, X.; Chen, W.; Chan, S.; Olson, G. B.; Lindgen, L.-E., Complexity science of multiscale materials via stochastic computations, Internat. J. Numer. Methods Engrg., 80, 6-7, 932-978 (2009)
[17] de Souza Neto, E. A.; Peric, D.; Owen, D., Computational Methods for Plasticity: Theory and Applications (2008), Wiley
[18] Xue, L.; Wierzbicki, T., Ductile fracture initiation and propagation modeling using damage plasticity theory, Eng. Fract. Mech., 75, 11, 3276-3293 (2008)
[19] Xue, L., Constitutive modeling of void shearing effect in ductile fracture of porous materials, Eng. Fract. Mech., 75, 11, 3343-3366 (2008)
[20] Camanho, P.; Bessa, M.; Catalanotti, G.; Vogler, M.; Rolfes, R., Modeling the inelastic deformation and fracture of polymer composites -Part II: Smeared crack model, Mech. Mater., 59, 0, 36-49 (2013)
[21] Feyel, F.; Chaboche, J.-L., \( FE {}^2\) multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials, Comput. Methods Appl. Mech. Engrg., 183, 3, 309-330 (2000)
[22] Kouznetsova, V.; Geers, M. G.D.; Brekelmans, W. A.M., Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme, Internat. J. Numer. Methods Engrg., 54, 8, 1235-1260 (2002)
[23] Feyel, F., A multilevel finite element method \(( FE {}^2)\) to describe the response of highly non-linear structures using generalized continua, Comput. Methods Appl. Mech. Engrg., 192, 28-30, 3233-3244 (2003)
[24] Wagner, G. J.; Liu, W. K., Coupling of atomistic and continuum simulations using a bridging scale decomposition, J. Comput. Phys., 190, 1, 249-274 (2003)
[25] Kadowaki, H.; Liu, W. K., Bridging multi-scale method for localization problems, Comput. Methods Appl. Mech. Engrg., 193, 30-32, 3267-3302 (2004)
[26] Kadowaki, H.; Liu, W. K., A multiscale approach for the micropolar continuum model, Comput. Model. Eng. Sci., 7, 3, 269-282 (2005)
[27] Park, H. S.; Karpov, E. G.; Klein, P. A.; Liu, W. K., Three-dimensional bridging scale analysis of dynamic fracture, J. Comput. Phys., 207, 2, 588-609 (2005)
[28] Tang, S.; Hou, T. Y.; Liu, W. K., A pseudo-spectral multiscale method: Interfacial conditions and coarse grid equations, J. Comput. Phys., 213, 1, 57-85 (2006)
[29] Bessa, M.; Bostanabad, R.; Liu, Z.; Hu, A.; Apley, D.; Brinson, C.; Chen, W.; Liu, W. K., A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality, Comput. Methods Appl. Mech. Engrg., 320, 633-667 (2017)
[30] Eshelby, J. D., The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. Roy. Soc. Lond. A, 241, 1226, 376-396 (1957), The Royal Society
[31] Hashin, Z.; Shtrikman, S., A variational approach to the theory of the elastic behaviour of multiphase materials, J. Mech. Phys. Solids, 11, 2, 127-140 (1963)
[32] Hill, R., A self-consistent mechanics of composite materials, J. Mech. Phys. Solids, 13, 4, 213-222 (1965)
[33] Liu, Z.; Moore, J. A.; Aldousari, S. M.; Hedia, H. S.; Asiri, S. A.; Liu, W. K., A statistical descriptor based volume-integral micromechanics model of heterogeneous material with arbitrary inclusion shape, Comput. Mech., 1-19 (2015)
[34] Liu, Z.; Moore, J. A.; Liu, W. K., An extended micromechanics method for probing interphase properties in polymer nanocomposites, J. Mech. Phys. Solids, 95, 663-680 (2016)
[35] Belytschko, T.; Loehnert, S.; Song, J.-H., Multiscale aggregating discontinuities: A method for circumventing loss of material stability, Internat. J. Numer. Methods Engrg., 73, 6, 869-894 (2008)
[36] Moulinec, H.; Suquet, P., A numerical method for computing the overall response of nonlinear composites with complex microstructure, Comput. Methods Appl. Mech. Engrg., 157, 1-2, 69-94 (1998)
[37] Le, B.; Yvonnet, J.; He, Q.-C., Computational homogenization of nonlinear elastic materials using neural networks, Internat. J. Numer. Methods Engrg., 104, 12, 1061-1084 (2015)
[38] Yvonnet, J.; Monteiro, E.; He, Q.-C., Computational homogenization method and reduced database model for hyperelastic heterogeneous structures, Int. J. Multiscale Comput. Eng., 11, 3 (2013)
[39] Ibañez, R.; Borzacchiello, D.; Aguado, J. V.; Abisset-Chavanne, E.; Cueto, E.; Ladeveze, P.; Chinesta, F., Data-driven non-linear elasticity: constitutive manifold construction and problem discretization, Comput. Mech., 1-14 (2017)
[40] Michel, J.; Suquet, P., Nonuniform transformation field analysis, Int. J. Solids Struct., 40, 25, 6937-6955 (2003) · Zbl 1057.74031
[41] Chaboche, J.; Kanouté, P.; Roos, A., On the capabilities of mean-field approaches for the description of plasticity in metal matrix composites, Int. J. Plast., 21, 7, 1409-1434 (2005)
[42] Michel, J.-C.; Suquet, P., A model-reduction approach in micromechanics of materials preserving the variational structure of constitutive relations, J. Mech. Phys. Solids, 90, 254-285 (2016)
[44] Loève, M., Probability Theory; Foundations, Random Sequences (1955), D. Van Nostrand Company: D. Van Nostrand Company New York
[45] Jolliffe, I., Principal component analysis (2002), Wiley Online Library
[46] Yvonnet, J.; He, Q.-C., The reduced model multiscale method (r3m) for the non-linear homogenization of hyperelastic media at finite strains, J. Comput. Phys., 223, 1, 341-368 (2007)
[47] Kerfriden, P.; Goury, O.; Rabczuk, T.; Bordas, S. P.-A., A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics, Comput. Methods Appl. Mech. Engrg., 256, 169-188 (2013)
[48] Oliver, J.; Caicedo, M.; Huespe, A.; Hernández, J.; Roubin, E., Reduced order modeling strategies for computational multiscale fracture, Comput. Methods Appl. Mech. Engrg., 313, 560-595 (2017)
[49] Tasan, C.; Hoefnagels, J.; Geers, M., Identification of the continuum damage parameter: An experimental challenge in modeling damage evolution, Acta Mater., 60, 8, 3581-3589 (2012)
[50] Liu, W. K.; Chen, Y., Wavelet and multiple scale reproducing kernel methods, Internat. J. Numer. Methods Fluids, 21, 10, 901-931 (1995)
[51] Li, S.; Liu, W. K., Moving Least Square Reproducing Kernel Method (III): Wavelet Packet & its Applications, Methods, 7825, 96, 1-52 (1996)
[53] Witten, I. H.; Frank, E., Data Mining: Practical Machine Learning Tools and Techniques (2005), Morgan Kaufmann
[54] Mediavilla Varas, J., Continuous and discontinuous modelling of ductile fracture (2005), Eindhoven University of Technology, (Ph.D. Thesis)
[55] Lloyd, S. P., Least squares quantization in PCM, IEEE Trans. Inf. Theory, 28, 2, 129-137 (1982)
[56] Forgy, E. W., Cluster analysis of multivariate data: efficiency versus interpretability of classifications, Biometrics, 21, 768-769 (1965)
[57] Ester, M.; Kriegel, H.-P.; Sander, J.; Xu, X., A density-based algorithm for discovering clusters in large spatial databases with noise, Kdd, 96, 34, 226-231 (1996)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.