Technical Papers
Jun 13, 2018

Metamodeling-Assisted Numerical Homogenization for Masonry and Cracked Structures

Publication: Journal of Engineering Mechanics
Volume 144, Issue 8

Abstract

In this article a numerical approach is proposed for the investigation of composite materials, like masonry. A number of simulations of a nonlinear, heterogeneous microstructure with gradually increasing loading, are considered. Average stress and stiffness are also derived. Then, this information is incorporated in databases, and a metamodel is created based on the data and used in an overall macroscopic analysis. On the micro scale, a classical plasticity model for masonry or a unilateral contact law representing a potential crack are considered. A satisfactory comparison between the proposed models and direct macroscopic models arises, indicating that the method can be used for an initial, quick assessment of the failure of heterogeneous materials on the structural scale. Due to its simplicity, it can be applied even by using commercial software for the creation of the databases. Thus, the creation of complex, sophisticated, nonlinear finite element codes may be avoided within the framework of this approach.

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References

Chatzigeorgiou, G., N. Charalambakis, Y. Chemiski, and F. Meraghni. 2016. “Periodic homogenization for fully coupled thermomechanical modeling of dissipative generalized standard materials.” Int. J. Plast. 81: 18–39. https://doi.org/10.1016/j.ijplas.2016.01.013.
Clément, A., C. Soize, and J. Yvonnet. 2012. “Computational nonlinear stochastic homogenization using a nonconcurrent multiscale approach for hyperelastic heterogeneous microstructures analysis.” Int. J. Numer. Methods Eng. 91 (8): 799–824. https://doi.org/10.1002/nme.4293.
Coenen, E. W. C., V. G. Kouznetsova, E. Bosco, and M. G. D. Geers. 2012. “A multi-scale approach to bridge microscale damage and macroscale failure: A nested computational homogenization-localization framework.” Int. J. Fract. 178 (1–2): 157–178. https://doi.org/10.1007/s10704-012-9765-4.
COMSOL Multiphysics. 2007. User’s guide. Stockholm Sweden: COMSOL AB.
Dascalu, C., G. Bilbie, and E. K. Agiasofitou. 2008. “Damage and size effects in elastic solids: A homogenization approach.” Int. J. Solids Struct. 45 (2): 409–430. https://doi.org/10.1016/j.ijsolstr.2007.08.025.
Drosopoulos, G. A., M. E. Stavroulaki, K. Giannis, L. Plymakis, G. E. Stavroulakis, and P. Wriggers. 2014a. “Nonlinear homogenization in masonry structures.” In Proc., WCCM XI-ECCM V-ECFD VI., edited by E. Oñate, X. Oliver, and A. E. Huerta, 6795–6806. Barcelona, Spain: International Center for Numerical Methods in Engineering.
Drosopoulos, G. A., P. Wriggers, and G. E. Stavroulakis. 2014b. “A multi-scale computational method including contact for the analysis of damage in composite materials.” Comput. Mater. Sci. 95: 522–535. https://doi.org/10.1016/j.commatsci.2014.08.004.
Drucker, D. C. 1954. “Coulomb friction, plasticity and limit loads.” J. Appl. Mech. 21: 71–74.
Feyel, F. 1999. “Multiscale FE2 elastoviscoplastic analysis of composite structures.” Comput. Mater. Sci. 16 (1–4): 344–354. https://doi.org/10.1016/S0927-0256(99)00077-4.
Hill, R. 1963. “Elastic properties of reinforced solids: Some theoretical principles.” J. Mech. Phys. Solids 11 (5): 357–372. https://doi.org/10.1016/0022-5096(63)90036-X.
Katz, A., C. Trinh, J. Wright, W. Tu, and M.-J. Pindera. 2015. “Plastic-strain localization in periodic materials with wavy brick-and-mortar architectures and its effect on the homogenized response.” Compos. Part B Eng. 68: 270–280. https://doi.org/10.1016/j.compositesb.2014.08.037.
Kouznetsova, V. 2002. “Computational homogenization for the multi-scale analysis of multi-phase materials.” Ph.D. thesis, Technical Univ. Eindhoven.
Lefik, M. 2004. “Hybrid, finite element-artificial neural network model for composite materials.” J. Theor. Appl. Mech. 42 (3): 539–563.
Lourenço, P. B., and J. Pina-Henriques. 2006. “Validation of analytical and continuum numerical methods for estimating the compressive strength of masonry.” Comput. Struct. 84 (29–30): 1977–1989. https://doi.org/10.1016/j.compstruc.2006.08.009.
Luciano, R., and E. Sacco. 1998. “A damage model for masonry structures.” Eur. J. Mech. A/Solids 17 (2): 285–303. https://doi.org/10.1016/S0997-7538(98)80087-9.
Massart, T. J., R. H. J. Peerlings, and M. G. D. Geers. 2007a. “An enhanced multi-scale approach for masonry wall computations with localization of damage.” Int. J. Numer Methods Eng. 69 (5): 1022–1059. https://doi.org/10.1002/nme.1799.
Massart, T. J., R. H. J. Peerlings, and M. G. D. Geers. 2007b. “Structural damage analysis of masonry walls using computational homogenization.” Int. J. Damage Mech. 16 (2): 199–226. https://doi.org/10.1177/1056789506064943.
MATLAB R2010a. 2010. User’s guide. Natick, Massachusetts: MathWorks.
Mercatoris, B. C. N., P. Bouillard, and T. J. Massart. 2009. “Multi-scale detection of failure in planar masonry thin shells using computational homogenisation.” Eng. Fract. Mech. 76 (4): 479–499. https://doi.org/10.1016/j.engfracmech.2008.10.003.
Miehe, C., and A. Koch. 2002. “Computational micro-to-macro transitions of discretized microstructures undergoing small strains.” Archit. Appl. Mech. 72 (4–5): 300–317. https://doi.org/10.1007/s00419-002-0212-2.
Miehe, C., J. Schröder, and J. Schotte. 1999. “Computational homogenization analysis in finite plasticity simulation of texture development in polycrystalline materials.” Comput. Methods Appl. Mech. Eng. 171 (3–4): 387–418. https://doi.org/10.1016/S0045-7825(98)00218-7.
Milani, G. 2011. “Simple lower bound limit analysis homogenization model for in- and out-of-plane loaded masonry walls.” Constr. Build. Mater. 25 (12): 4426–4443. https://doi.org/10.1016/j.conbuildmat.2011.01.012.
Milani, G., Y. W. Esquivel, P. B. Lourenço, B. Riveiro, and D. V. Oliveira. 2013a. “Characterization of the response of quasi-periodic masonry: Geometrical investigation, homogenization and application to the Guimarães castle Portugal.” Eng. Struct. 56: 621–641. https://doi.org/10.1016/j.engstruct.2013.05.040.
Milani, G., M. Pizzolato, and A. Tralli. 2013b. “Simple numerical model with second order effects for out-of-plane loaded masonry walls.” Eng. Struct. 48: 98–120. https://doi.org/10.1016/j.engstruct.2012.08.029.
Nguyen, V. P., M. Stroeven, and L. J. Sluys. 2011. “Multiscale continuous and discontinuous modeling of heterogeneous materials: A review on recent developments.” J. Multiscale Model 3 (4): 1–42. https://doi.org/10.1142/S1756973711000509.
Reccia, E., G. Milani, A. Cecchi, and A. Tralli. 2014. “Full 3D homogenization approach to investigate the behavior of masonry arch bridges: The Venice trans-lagoon railway bridge.” Constr. Build. Mater. 66: 567–586. https://doi.org/10.1016/j.conbuildmat.2014.05.096.
Sacco, E. 2009. “A nonlinear homogenization procedure for periodic masonry.” Eur. J. Mech. A/Solids 28 (2): 209–222. https://doi.org/10.1016/j.euromechsol.2008.06.005.
Smit, R., W. Brekelmans, and H. Meijer. 1998. “Prediction of the mechanical behavior of non-linear heterogeneous systems by multi-level finite element modeling.” Comput. Methods Appl. Mech. Eng. 155 (1–2): 181–192. https://doi.org/10.1016/S0045-7825(97)00139-4.
Suquet, P. M. 1985. Local and global aspects in the mathematical theory of plasticity. Plasticity today: Modelling, methods and applications. London: Elsevier.
Theodossopoulos, D., and B. Sinha. 2013. “A review of analytical methods in the current design processes and assessment of performance of masonry structures.” Constr. Build. Mater. 41: 990–1001. https://doi.org/10.1016/j.conbuildmat.2012.07.095.
Tsalis, D., T. Baxevanis, G. Chatzigeorgiou, and N. Charalambakis. 2013. “Homogenization of elastoplastic composites with generalized periodicity in the microstructure.” Int. J. Plast. 51: 161–187. https://doi.org/10.1016/j.ijplas.2013.05.006.
Unger, J. F., and C. Könke. 2008. “Coupling of scales in a multiscale simulation using neural networks.” Comput. Struct. 86 (21–22): 1994–2003. https://doi.org/10.1016/j.compstruc.2008.05.004.
Verhoosel, C. V., J. J. C. Remmers, M. A. Gutiérrez, and R. de Borst. 2010. “Computational homogenization for adhesive and cohesive failure in quasi-brittle solids.” Int. J. Numer. Methods Eng. 83 (8–9): 1155–1179. https://doi.org/10.1002/nme.2854.
Yvonnet, J., D. Gonzalez, and Q.-C. He. 2009. “Numerically explicit potentials for the homogenization of nonlinear elastic heterogeneous materials.” Comput. Methods Appl. Mech. Eng. 198 (33–36): 2723–2737. https://doi.org/10.1016/j.cma.2009.03.017.
Zohdi, T. I., and P. Wriggers. 2008. An introduction to computational micromechanics. Dordrecht, Netherlands: Springer.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 144Issue 8August 2018

History

Received: Jan 17, 2017
Accepted: Mar 7, 2018
Published online: Jun 13, 2018
Published in print: Aug 1, 2018
Discussion open until: Nov 13, 2018

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Authors

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Georgios A. Drosopoulos [email protected]
Discipline of Civil Engineering, School of Engineering, Univ. of KwaZulu-Natal, 4041 Durban, South Africa (corresponding author). Email: [email protected]
Konstantinos Giannis
Institute for Particle Technology, Technical Univ. of Braunschweig, Volkmaroder Str. 5, 38104 Braunschweig, Germany.
Maria E. Stavroulaki
Faculty of Architecture, Applied Mechanics Laboratory, Technical Univ. of Crete, GR-73100 Chania, Crete, Greece.
Georgios E. Stavroulakis
School of Production Engineering and Management, Institute of Computational Mechanics and Optimization, Technical Univ. of Crete, GR-73100 Chania, Crete, Greece.

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