Abonnement à la biblothèque: Guest
Portail numérique Bibliothèque numérique eBooks Revues Références et comptes rendus Collections
International Journal for Multiscale Computational Engineering
Facteur d'impact: 1.016 Facteur d'impact sur 5 ans: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Imprimer: 1543-1649
ISSN En ligne: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v8.i5.20
pages 447-461

Symmetric Mesomechanical Model for Failure Analysis of Heterogeneous Materials

Robert Crouch
Department of Civil and Environmental Engineering, Vanderbilt University, Nashville, TN 37235, USA; Altair Engineering 1820 E. Big Beaver Rd. Troy MI 48083, USA
Caglar Oskay
Department of Civil and Environmental Engineering, Vanderbilt University, Nashville, Tennessee 37235, USA


This paper provides a novel reduced-order multiscale modeling methodology for failure analysis of heterogeneous materials. The proposed methodology is based on the computational homogenization method for bridging multiple spatial scales and the eigendeformation-based model reduction method to incorporate failure in the microconstituents and interfaces. This computationally efficient modeling methodology leads to symmetric reduced-order algebraic systems for evaluation of the microscale boundary value problem. The order and coarse graining for the reduced-order system are systematically identified by a novel model development strategy. Verification studies reveal that the proposed methodology efficiently and accurately models the failure response. The proposed approach eliminates the spurious residual stress effect observed in reduced-order models, which pollutes the postfailure stress field at the macroscale.


  1. Aboudi, J., A continuum theory for fiber-reinforced elasticviscoplastic composites. DOI: 10.1016/0020-7225(82)90115-X

  2. Babuska, I., Homogenization and application: Mathematical and computational problems.

  3. Bahei-El-Din, Y. A., Rajendran, A. M., and Zikry, M. A., A micromechanical model for damage progression in woven composite systems. DOI: 10.1016/j.ijsolstr.2003.12.006

  4. Belytschko, T., Loehnert, S., and Song, J.-H., Multiscale aggregating discontinuities: A method for circumventing loss of material stability. DOI: 10.1002/nme.2156

  5. Benssousan, A., Lions, J. L., and Papanicolaou, G., Asymptotic Analysis for Periodic Structures.

  6. Berlyand, L. V. and Kolpakov, A. G., Network approximation in the limit of small interparticle distance of the effective properties of a high-contrast random dispersed composite. DOI: 10.1007/s002050100142

  7. Chaboche, J. L., Kruch, S., Maire, J. F., and Pottier, T., Towards a micromechanics based inelastic and damage modeling of composites. DOI: 10.1016/S0749-6419(00)00056-5

  8. Dvorak, G. J., Transformation field analysis of inelastic composite materials. DOI: 10.1098/rspa.1992.0063

  9. Feyel, F. and Chaboche, J.-L., Fe2 multiscale approach for modelling the elastoviscoplastic behavior of long fiber SiC/Ti composite materials. DOI: 10.1016/S0045-7825(99)00224-8

  10. Fish, J., Yu, Q., and Shek, K. L., Computational damage mechanics for composite materials based on mathematical homogenization. DOI: 10.1002/(SICI)1097-0207(19990820)45:11<1657::AID-NME648>3.0.CO;2-H

  11. Fish, J. and Fan, R., Mathematical homogenization of nonperiodic heterogeneous media subjected to large deformation transient loading. DOI: 10.1002/nme.2355

  12. Geers, M. G. D., Kouznetsova, V., and Brekelmans, W. A. M., Gradient-enhanced computational homogenization for the micro-macro scale transition. DOI: 10.1051/jp4:2001518

  13. Ghosh, S., Lee, K., and Raghavan, P., A multi-level computational model for multi-scale damage analysis in composite and porous materials. DOI: 10.1016/S0020-7683(00)00167-0

  14. Gosz, M., Moran, B., and Achenbach, J. D., Matrix cracking in transversely loaded fiber composites with compliant interphases.

  15. Guedes, J. M. and Kikuchi, N., Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods. DOI: 10.1016/0045-7825(90)90148-F

  16. Michel, J. C. and Suquet, P., Computational analysis of nonlinear composite structures using the nonuniform transformation field analysis. DOI: 10.1016/j.cma.2003.12.071

  17. Moulinec, H. and Suquet, P., A fast numerical method for computing the linear and nonlinear properties of composites.

  18. Nocedal, J. and Wright, S., Numerical Optimization.

  19. Oden, J. T. and Prudhomme, S., Goal-oriented error estimation and adaptivity for the finite element method. DOI: 10.1016/S0898-1221(00)00317-5

  20. Oskay, C. and Fish, J., Eigendeformation-based reduced order homogenization for failure analysis of heterogeneous materials. DOI: 10.1016/j.cma.2006.08.015

  21. Oskay, C. and Fish, J., On calibration and validation of eigendeformation-based multiscale models for failure analysis of heterogeneous systems. DOI: 10.1007/s00466-007-0197-3

  22. Sanchez-Palencia, E., Non-homogeneous Media and Vibration Theory. DOI: 10.1007/3-540-10000-8

  23. Suquet, P. M., Elements of homogenization for inelastic solid mechanics.

  24. Terada, K. and Kikuchi, N., Nonlinear homogenization method for practical applications.

  25. Van der Sluis, O., Schreurs, P. J. G., Brekelmans, W.A.M.A.M., and Meijer, H. E. H., Overall behaviour of heterogeneous elastoviscoplastic materials: Effect of microstructural modelling. DOI: 10.1016/S0167-6636(00)00019-3

  26. Yvonnet, J. and He, Q. C., The reduced model multiscale method (R3M) for the non-linear homogenization of hyperelastic media at finite strains. DOI: 10.1016/j.jcp.2006.09.019

Articles with similar content:

International Journal for Multiscale Computational Engineering, Vol.11, 2013, issue 3
Caglar Oskay, Paul Sparks
International Journal for Multiscale Computational Engineering, Vol.14, 2016, issue 5
Caglar Oskay, Paul Sparks
Anisotropic Micromechanical Creep Damage Model for Composite Materials: A Reduced-Order Approach
International Journal for Multiscale Computational Engineering, Vol.6, 2008, issue 2
Erez Gal, Jacob Fish
Three-Dimensional Finite Element Modeling for Concrete Materials Using Digital Image and Embedded Discontinuous Element
International Journal for Multiscale Computational Engineering, Vol.4, 2006, issue 4
Takahiro Yamada, Gakuji Nagai
Simulation of Biomolecular Systems at Multiple Length and Time Scales
International Journal for Multiscale Computational Engineering, Vol.2, 2004, issue 2
Gary S. Ayton, Gregory A. Voth