Abstract
We describe various spatial and temporal multiscale approaches for composite materials and structures. Spatial multiscale approaches are grouped into two categories: information-passing and concurrent. In the concurrent multiscale methods in space multiple scales are simultaneously resolved, whereas in the information-passing schemes, the fine scale is modeled and its gross response is infused into the continuum scale. The issue of appropriate scale selection is discussed. Among the temporal multiscale application we describe block cycle and temporal homogenization approaches with application to fatigue life prediction of composites.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Fish (Ed.), Bridging the Scales in Science and Engineering, Oxford University Press, 2009.
J. Fish, Multiscale computations: Boom or bust, IACM Expressions, 22, January 2008.
E. Sanchez-Palencia, Lecture Notes in Physics, Vol. 127. Springer-Verlag, Berlin, 1980.
J.M. Guedes and N. Kikuchi, Comput. Methods Appl. Mech. Engng., 83:143–198, 1990.
K. Terada and N. Kikuchi, In S. Ghosh and M. Ostoja-Starzewski (Eds.), Computational Methods in Micromechanics, Vol. AMD-212/MD-62, pp. 1–16, ASME, 1995.
Z. Yuan and J. Fish, Towards realization of computational homogenization in practice, J. Numer. Methods Engrg., 73(3):361–380, 2008.
M. Jardak and R. Ghanem, Comput. Methods Appl. Mech. Engng., 193(6/8):429–447, 2004.
C. Oskay and J. Fish, On calibration and validation of eigendeformation-based multiscale models for failure analysis of heterogeneous systems, Comput. Mech., 42(2):181–195, 2008.
J. Fish and A. Ghouli, Multiscale analytical sensitivity analysis for composite materials, Int. J. Numer. Methods Engrg., 50:1501–1520, 2001.
F. Feyel and J.-L. Chaboche, Comput. Methods Appl. Mech. Engrg., 183:309–330, 2000.
E. Giladi and H.B. Keller, Numer. Math., 93(2), 2002.
H. Waisman and J. Fish, Comput. Methods Appl. Mech. Engrg., 195(44/47):6542–6559, 2006.
S. Ghosh and S. Moorthy, Comput. Methods Appl. Mech. Engrg., 121(1/4):373–409, 1995.
J. Aboudi, J. Engrg. Sci., 20(55):605–621, 1982.
L.V. Berlyand and A.G. Kolpakov, Arch. for Rat. Mech. Anal., 159:179–227, 2001.
H. Moulinec and P. Suquet, C.R. Acad. Sci. Paris II, 318:1417–1423, 1994.
H. Moulinec and P. Suquet, Comput. Meth. Appl. Mech. Engrg., 157:69–94, 1998.
G.J. Dvorak, Proc. R. Soc. Lond. A, 437:311–327, 1992.
Y.A. Bahei-El-Din, A.M. Rajendran, and M.A. Zikry, Int. J. Sol. Structures, 41:2307–2330, 2004.
G.J. Dvorak and Y. Benveniste, Proc. R. Soc. Lond. A, 437:291–310, 1992.
N. Laws, On the thermostatics of composite materials, J. Mech. Phys. Solids, 21:9–17, 1973.
J.Willis. In C.S. Yih (Ed.), Advances in Applied Mechanics, Vol. 21, pp. 1–78, Academic Press, New York, 1981.
G.J. Dvorak, Proc. R. Soc. Lond. A, 431:89–110, 1990.
C. Oskay and J. Fish, Eigendeformation-based reduced order homogenization, Comp. Methods Appl. Mech. Engrg., 196:1216–1243, 2007.
Z. Yuan and J. Fish, Multiple scale eigendeformation-based reduced order homogenization, Comput. Methods Appl. Mech. Engrg., 198(21/26), 2016–2038, 2009.
C. Oskay and J. Fish, Comput. Mech., 42(2):181–195, 2008.
J. Fish and Z. Yuan, N-scale model reduction theory. In Bridging the Scales in Science and Engineering, J. Fish (Ed.), Oxford University Press, 2009.
T.I. Zohdi, J.T. Oden, and G.J. Rodin, Comput. Methods Appl. Mech. Engrg., 138:273–298, 1996.
S. Ghosh, K. Lee, and P. Raghavan, Int. J. Solids Struct., 38:2335–2385, 2001.
M.G.D. Geers, V. Kouznetsova, and W.A.M. Brekelmans, J. Phys. IV, 11:145–152, 2001.
E. Weinan and B. Engquist, Comm. Math. Sci., 1:87–132, 2003.
J. Fish and R. Fan, Mathematical homogenization of nonperiodic heterogeneous media subjected to large deformation transient loading, Int. J. Numer. Methods Engrg., 76(7):1044–1064, 2008.
J. Fish, P. Nayak and M.H. Holmes, Microscale reduction error indicators and estimators for a periodic heterogeneous medium, Comput. Mech., 14:1–16, 1994.
M. Ostoja-Starzewski, S.D. Boccara, and I. Jasiuk, Couple-stress moduli and characteristic length of a two-phase composite, Mech. Res. Comm., 26(4):387–396, 1999.
O. van der Sluis, P.H.J. Vosbeek, P.J.G. Schreurs, and H.E.H. Meijer, Homogenization of heterogeneous polymers, Int. J. Solids Struct., 36:3193–3214, 1999.
J. Fish and Z. Yuan, Multiscale enrichment based on the partition of Unity, Int. J. Numer. Methods Engrg., 62(10):1341–1359, 2005.
J. Fish and Z. Yuan, Multiscale enrichment based on partition of unity for nonperiodic fields and nonlinear problems, Comput. Mech., 40:249–259, 2007.
I. Babuska, G. Caloz, and J.E. Osborn, Special finite element methods for a class of second order elliptic problems with rough coefficients, SIAM. J. Numer. Anal., 4:945–981, 1994.
I. Babuska and J.M. Melenk, The partition of unity finite element method: Basic theory and applications, Comput. Methods Appl. Mech. Engrg., 139:289–314, 1996.
T. Belytschko and T. Black, Elastic crack growth in finite elements with minimal remeshing, Int. J. Numer. Methods Engrg., 45(5):601–620, 1999.
N. Moës, J. Dolbow and T. Belytschko, A finite element method for crack growth without remeshing, Int. J. Numer. Methods Engrg., 46(5):131–150, 1999.
M. Quaresimin and M. Ricotta, Life prediction of bonded joints in composite materials, Int. J. Fatigue, 28(10):1166–1176, October 2006.
J. Fish and Q. Yu, Computational mechanics of fatigue and life predictions for composite materials and structures, Comput. Methods Appl. Mech. Engrg., 191:4827–4849, 2002.
C. Oskay and J. Fish, Multiscale modeling of fatigue for ductile materials, Int. J. Multiscale Comput. Engrg., 2(3):1–25, 2004.
J. Fish and C. Oskay, Nonlocal multiscale fatigue model, Mech. Adv. Mater. Struct., 12(6):485–500, 2005.
E. Gal, Z. Yuan, W. Wu, and J. Fish, A multiscale design system for fatigue life prediction, Int. J. Multiscale Comput. Engrg., 5(6):435–446, 2007.
J. Fish and R. Fan, Mathematical homogenization of nonperiodic heterogeneous media subjected to large deformation transient loading, Int. J. Numer. Methods Engrg., 76:1044–1064, 2008.
C. Oskay and J. Fish, Eigendeformation-based reduced order homogenization, Comput. Methods Appl. Mech. Engrg., 196:1216–1243, 2007.
Simmetrix, Inc., SBIR Phase II Contract F33615-99-C-5021.
J. Fish and V. Belsky, Multi-grid method for periodic heterogeneous media, Part 2: Multiscale modeling and quality control in multidimensional case, Comput. Methods Appl. Mech. Engrg., 126:17–38, 1995.
J. Fish and V. Belsky, Multigrid method for periodic heterogeneous media, Part 1: Convergence studies for one-dimensional case, Comput. Methods Appl. Mech. Engrg., 126:1–16, 1995.
J. Fish, Bridging the scales in nano engineering and science, J. Nanoparticle Res., 8:577–594, 2006.
G. Wheatley, R. Niefanger, Y. Estrin, and X.Z. Hu, Fatigue crack growth in 316l stainless steel. Key Engrg. Mater., 145–149:631–636, 1998.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Fish, J. (2011). Multiscale Modeling and Simulation of Composite Materials and Structures. In: de Borst, R., Ramm, E. (eds) Multiscale Methods in Computational Mechanics. Lecture Notes in Applied and Computational Mechanics, vol 55. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9809-2_12
Download citation
DOI: https://doi.org/10.1007/978-90-481-9809-2_12
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-9808-5
Online ISBN: 978-90-481-9809-2
eBook Packages: EngineeringEngineering (R0)