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International Journal for Multiscale Computational Engineering
Factor de Impacto: 1.016 Factor de Impacto de 5 años: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Imprimir: 1543-1649
ISSN En Línea: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v8.i1.20
pages 1-15

Eigendeformation-Based Homogenization of Concrete

Wei Wu
Rensselaer Polytechnic Institute
Zheng Yuan
Multiscale Design Systems, LLC 280 Park Avenue South New York, NY 10010, USA
Jacob Fish
Civil Engineering and Engineering Mechanics, Columbia University, New York, New York 10027, USA


A two-scale approach based on eigendeformation-based homogenization is explored to predict the behavior of concrete targets subjected to impact loading by high-speed projectiles. The method allows us to account for micromechanical features of concrete at a computational cost comparable to single-scale phenomenological models of concrete. The inelastic behavior of concrete is modeled using three types of eigenstrains. The eigenstrains in the mortar phase include pore compaction (or lock-in), rate-dependent damage, and plasticity eigenstrains, whereas the inelastic behavior of aggregates is assumed to be governed by plasticity only. Material parameters were identified using inverse methods against unconfined compression and uniaxial compression tests. A unit cell was constructed from a 3D digital image of concrete. The eigendeformation-based homogenization approach was validated for projectile penetration into a concrete target. The simulation results were found to be in reasonable agreement with the experimental data. Attention is restricted to nonreinforced concrete.


  1. Bazant, Z. P., Caner, F. C., Carol, I., Adley, M. D., and Akers, S. A., Microplane model M4 for concrete: I. Formulation with work-conjugate deviatoric stress. DOI: 10.1061/(ASCE)0733-9399(2000)126:9(944)

  2. Cusatis, G., Pelessone, D., Mencarelli, A., and Baylot, J. T., Simulation of reinforced concrete structures under blast and penetration through lattice discrete particle modeling. DOI: 10.1115/IMECE2007-43744

  3. Fish, J. and Yuan, Z., N-scale model reduction theory. In Bridging the Scales in Science and Engineering.

  4. Forrestal, M. J., A spherical cavity-expansion penetration model for concrete targets. DOI: 10.1016/S0020-7683(97)00017-6

  5. Forrestal, M. J., Frew, D. J., Hanchak, S. J., and Brar, N. S., Penetration of grout and concrete targets with ogive-nose steel projectiles. DOI: 10.1016/0734-743X(95)00048-F

  6. Forrestal, M. J., Frew, D. J., Hickerson, J. P., and Rohwer, T. A., Penetration of concrete targets with deceleration-time measurements. DOI: 10.1016/S0734-743X(02)00108-2

  7. Foster, C. D., Regueiro, R. A., Fossum, A. F., and Borja, R. I., Implicit numerical integration of a three-invariant, isotropic/kinematic hardening cap plasticity model for geomaterials. DOI: 10.1016/j.cma.2005.01.001

  8. Frew, D. J., Hanchak, S. J., Green, M. L., and Forrestal, M. J., Penetration of concrete targets with ogive-nose steel rods. DOI: 10.1016/S0734-743X(98)00008-6

  9. Frew, D. J., Conventional strength portland cement (cspc) concrete instrumented penetration results.

  10. Gal, E. and Fish, J., Anisotropic Micromechanical creep damage model for composite materials: A reduced-order approach. DOI: 10.1615/IntJMultCompEng.v6.i2.10

  11. Gal, E., Yuan, Z., Wu, W., and Fish, J., A multiscale design system for fatigue life prediction. DOI: 10.1615/IntJMultCompEng.v5.i6.10

  12. Hain, H. and Wriggers, P., Computational homogenization of micro-structural damage due to frost in hardened cement paste. DOI: 10.1016/j.finel.2007.11.020

  13. Ju, J. W., Monteiro, P. J. M., and Rashed, A. I., On continuum damage of cement paste and mortar as affected by porosity and sand concentration. DOI: 10.1061/(ASCE)0733-9399(1989)115:1(105)

  14. Lackner, R., Mang, H. A., and Pichler, C., Computational concrete mechanics. In Encyclopedia of Computational Mechanics.

  15. Lubliner, J., Oliver, J., Oller, S., and Onate, E., A plastic-damage model for concrete.

  16. Mounajed, G., Grondin, F., Dumontet, H., and Ben Hamid, A., Digital concrete: A multi-scale approach for the concrete behavior. DOI: 10.1142/9789812704658_0046

  17. Nagai, G. and Yamada, T., Three-dimensional finite element modeling for concrete materials using digital image and embedded discontinuous element. DOI: 10.1615/IntJMultCompEng.v4.i4.40

  18. Ortiz, M. and Popov, E. P., Plain concrete as a composite material. DOI: 10.1016/0167-6636(82)90042-4

  19. Ortiz, M., A constitutive theory for the inelastic behavior of concrete. DOI: 10.1016/0167-6636(85)90007-9

  20. Ortiz, M., An analytical study of the localized failure modes of concrete. DOI: 10.1016/0167-6636(87)90006-8

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

  22. Polanco-Loria, M., Hopperstad, O. S., Borvik, T., and Berstad, T., Numerical predictions of ballistic limits for concrete slabs using a modified version of the HJC concrete model. DOI: 10.1016/j.ijimpeng.2007.03.001

  23. Salari, M. R., Saeb, S., Willam, K. J., Patchet, S. J., and Carrasco, R. C., A coupled elastoplastic damage model for geomaterials. DOI: 10.1016/j.cma.2003.11.013

  24. Schlangen, E., Experimental and numerical analysis of fracture processes in concrete.

  25. Simo, J. C. and Hughes, T. J. R., Computational Inelasticity.

  26. Tham, C. Y., Numerical and empirical approach in predicting the penetration of a concrete target by an ogive-nosed projectile. DOI: 10.1016/j.finel.2006.06.011

  27. Tikhomirov, D. and Stein, E., Finite element computations of anisotropic continuum damage in reinforced concrete. DOI: 10.1016/S0045-7949(01)00081-5

  28. Warren, T. L., Fossum, A. F., and Frew, D. J., Penetration into low-strength (23MPa) concrete: Target characterization and simulations. DOI: 10.1016/S0734-743X(03)00092-7

  29. Wu, J. Y., Li, J., and Faria, R., An energy release rate-based plastic-damage model for concrete. DOI: 10.1016/j.ijsolstr.2005.05.038

  30. Yuan, Z. and Fish, J., Hierarchical model reduction at multiple scales. DOI: 10.1002/nme.2554

  31. Yuan, Z. and Fish, J., Multiple scale eigendeformation-based reduced order homogenization. DOI: 10.1016/j.cma.2008.12.038

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