Higher order numerical homogenization in modeling of asphalt concrete
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Cracow University of Technology, Cracow, Poland
These authors had equal contribution to this work
Submission date: 2023-10-29
Final revision date: 2024-01-08
Acceptance date: 2024-01-22
Online publication date: 2024-04-14
Publication date: 2024-04-30
Corresponding author
Marek Klimczak   

Faculty of Civil Engineering, Cracow University of Technology, Warszawska 24, 31-155, Cracow, Poland
Journal of Theoretical and Applied Mechanics 2024;62(2):351-364
In this paper, we present an enhanced version of the two-scale numerical homogenization with application to asphalt concrete modeling in the elastic range. We modified the method of effective material parameters tensor assessment for analysis based on the representative volume element (RVE). As the method was tested on asphalt concrete, we also present two possible approaches to geometrical modeling of its internal microstructure. Selected numerical tests were performed to verify the proposed approach. The main novelties of this study, i.e. higher order approximation at the macroscale and modification of boundary conditions at the level of RVE analysis, improved the efficiency of our methodology by error reduction. Practically, we obtained a reduction of NDOF up to 3 orders of magnitude (comparing to full-scale and homogenized analysis) that was accompanied with the introduced error of order of several percent (measured in L2 norm).
Aigner E., Lackner R., Pichler Ch., 2009, Multiscale prediction of viscoelastic properties of asphalt concrete, Journal of Materials in Civil Engineering, 21, 12, 771-780.
Belytschko T., de Borst R., 2010, Multiscale methods in computational mechanics, International Journal for Numerical Methods in Engineering, 83, 8-9, 939-939.
Collop A.C., Scarpas A.T., Kasbergen C., de Bondt A., 2003, Development and finite element implementation of a stress dependent elasto-visco-plastic constitutive model with damage for asphalt, Transportation Research Record: Journal of the Transportation Research Board, 1832, 96-104.
Fakhari Tehrani F., Absi J., Allou F., Petit Ch., 2013, Heterogeneous numerical modeling of asphalt concrete through use of a biphasic approach: Porous matrix/inclusions, Computational Materials Science, 69, 186-196.
Feyel F., Chaboche L., 2000, FE2 multiscale approach for modelling the elasto-visco-plastic behaviour of long fibre SiC/Ti composite materials, Computer Methods in Applied Mechanics and Engineering, 183, 309-330.
Fish J., 2014, Practical Multiscaling, John Wiley & Sons, Ltd, Chichester.
GDDKiA, 2014, Asphalt pavement structures on national roads WT-2, Part I (in Polish), Warsaw.
Guedes J.M., Kikuchi N., 1990, Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods, Computer Methods in Applied Mechanics and Engineering, 83, 143-198.
Kim Y.R., Souza F.V., Teixeira J.E.S.L., 2013, A two-way coupled multiscale model for predicting damage-associated performance of asphaltic roadways, Computational Mechanics, 51, 2, 187-201.
Klimczak M., Cecot W., 2020a, Synthetic microstructure generation and multiscale analysis of asphalt concrete, Applied Sciences, 10, 765.
Klimczak M., Cecot W., 2020b, Towards asphalt concrete modeling by the multiscale finite element method, Finite Elements in Analysis and Design, 171, 103367.
Kouznetsova V., Geers M., Brekelmans W., 2002, Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme, International Journal for Numerical Methods in Engineering, 54, 8, 1235-1260.
Mitra K., Das A., Basu S., 2012, Mechanical behavior of asphalt mix: An experimental and numerical study, Construction and Building Materials, 27, 1, 545-552.
Mo L.T., Huurman M., Wu S.P., Molenaar A.A.A., 2008, 2D and 3D meso-scale finite element models for ravelling analysis of porous asphalt concrete, Finite Elements in Analysis and Design, 44, 4, 186-196.
Mori T., Tanaka K., 1973, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metallurgica, 21, 571-574.
Oleksy M., Cecot W., 2015, Application of the fully automatic hp-adaptive FEM to elastic-plastic problems, Computer Methods in Materials Science, 15, 204-212.
Schüller T., Jänicke R., Steeb H., 2016, Nonlinear modeling and computational homogenization of asphalt concrete on the basis of XRCT scans, Construction and Building Materials, 109, 96-108.
Wimmer J., Stier B., Simon J.-W., Reese S., 2016, Computational homogenisation from a 3D finite element model of asphalt concrete – linear elastic computations, Finite Elements in Analysis and Design, 110, 43-57.
Woldekidan M., Huurman M., Pronk A., 2013, Linear and nonlinear viscoelastic analysis of bituminous mortar, Transportation Research Record: Journal of the Transportation Research Board, 2370, 1, 53-62.
Ziaei-Rad V., Nouri N., Ziaei-Rad S., Abtahi M., 2012, A numerical study on mechanical performance of asphalt mixture using a meso-scale finite element model, Finite Elements in Analysis and Design, 57, 81-91.
Zohdi T.I., Wriggers P., 2005, An Introduction to Computational Mechanics, Springer Berlin, Heidelberg.
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