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International Journal for Multiscale Computational Engineering

Impact factor: 1.103

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2012002926
pages 391-405


Xiaowei Zeng
Department of Civil and Environmental Engineering, University of California, Berkeley; Department of Mechanical Engineering, University of Texas, San Antonio, TX 78249, USA
Shaofan Li
Department of Civil and Environmental Engineering, University of California, Berkeley, California 94720, USA


One of the major problems in failure analysis of composite materials is how to accurately describe interfacial material properties and related interface constitutive modeling at the nanoscale, mesoscale, and macroscale. In this work, we have applied a recently developed multiscale cohesive zone method to model composite materials and, subsequently, we have simulated the failure process of laminar composites. We have shown that the multiscale cohesive zone method can adequately describe mesoscale interface material properties such as interface strength, microstructures, and possible defects or damage. Moreover, we have applied the multiscale cohesive zone model to simulate spall fracture in composite materials induced by high-speed impacts. Simulations of different fracture patterns for composite materials with defects are also presented.


  1. Alfaro, M. V., Suiker, A. S. J., deBorst, R., and Remmers, J. J. C., Analysis of fracture and delamination in laminates using 3D numerical modelling. DOI: 10.1016/j.engfracmech.2008.09.0

  2. Alfaro, M.V., Suiker, A.S.J., Verhoosel, C.V., and de Borst, R., Numerical homogenization of cracking processes in thin fibreepoxy layers. DOI: 10.1016/j.euromechsol.2009.09.00

  3. Barenblatt, G.I., The mathematical theory of equilibrium of cracks in brittle fracture. DOI: 10.1016/S0065-2156(08)70121-2

  4. Braides, A., Lew, A.J., and Ortiz, M., Effective cohesive behavior of layers of interatomic planes. DOI: 10.1007/s00205-005-0399-9

  5. Daw, M.S. and Baskes, M.I., Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals. DOI: 10.1103/PhysRevB.29.6443

  6. Dugdale, D.S., Yielding of steel sheets containing slits. DOI: 10.1016/0022-5096(60)90013-2

  7. Ericksen, J.L., The Cauchy and Born hypotheses for crystals.

  8. Geers, M.G.D., Kouznetsova, V.G., and Brekelmans, W.A.M., Multi-scale computational homogenization: Trends and challenges. DOI: 10.1016/

  9. Hayes, R.L., Ortiz, M., and Carter, E.A., Universal binding-energy relation for crystals that accounts for surface relaxation. DOI: 10.1103/PhysRevB.69.172104

  10. Hill, R., On constitutive macro-variables for heterogeneous solids at finite strain. DOI: 10.1098/rspa.1972.0001

  11. Hilleborg, A., Modeer, M., and Petersson, P.E., Analysis of crack formation and crack growth in concrete by fracture mechanics and finite elements. DOI: 10.1016/0008-8846(76)90007-7

  12. Hirschberger, C.B., Ricker, S., Steinmann, P., and Sukumar, N., Computational multiscale modelling of heterogeneous material layers. DOI: 10.1016/j.engfracmech.2008.10.01

  13. Hughes, T.J.R., Talor, R., Sackman, J., Curnier, A., and Kamoknukulchai, W., A finite element method for a class of contact-impact problem. DOI: 10.1016/0045-7825(76)90018-9

  14. Hughes, T.J.R., The finite element method: Linear static and dynamic finite element analysis. DOI: 10.1111/j.1467-8667.1989.tb00025

  15. Israelachvili, J., Intermolecular & surface forces. DOI: 10.1002/bbpc.19860901226

  16. Matous, K., Kulkarnib, M.G., and Geubelleb, P.H., Multiscale cohesive failure modeling of heterogeneous adhesives. DOI: 10.1016/j.jmps.2007.08.005

  17. McVeigh, C., Vernerey, F., Liu, W.K., and Brinson, L.C., Multiresolution analysis for material design. DOI: 10.1016/j.cma.2005.07.027

  18. McVeigh, C. and Liu, W.K., Multiresolution modeling of ductile reinforced brittle composites. DOI: 10.1016/j.jmps.2008.10.015

  19. Nguyen, O. and Ortiz, M., Coarse-graining and renormalization of atomistic binding relations and universal macroscopic cohesive be havior. DOI: 10.1016/S0022-5096(01)00133-8

  20. Park, K., Paulino, G.H., and Roesler, J.R., A unified potential-based cohesive model of mixed-mode fracture. DOI: 10.1016/j.jmps.2008.10.003

  21. Qian, J. and Li, S., Application of multiscale cohesive zone model to simulate fracture in polycrystalline solids. DOI: 10.1115/1.4002647

  22. Samimi, M., van Dommelen, J.A.W., and Geers, M.G.D., An enriched cohesive zone model for delamination in brittle interfaces. DOI: 10.1002/nme.2651

  23. Vernerey, F., Liu, W.K., and Moran, B., Multiscale micromorphic theory for hierarchical materials. DOI: 10.1016/j.jmps.2007.04.008

  24. Vernerey, F., Liu, W. K., Moran, B., and Olson, G.B., A micromorphic model for the multiple scale failure of heterogeneous materials. DOI: 10.1016/j.jmps.2007.09.008

  25. Xu, X.-P. and Needleman, A., Numerical simulations of fast crack growth in brittle solids. DOI: 10.1016/0022-5096(94)90003-5

  26. Zeng, X. and Li, S., A multiscale cohesive zone model and simulations of fractures. DOI: 10.1016/j.cma.2009.10.008