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Портал Begell Электронная Бибилиотека e-Книги Журналы Справочники и Сборники статей Коллекции
International Journal for Multiscale Computational Engineering
Импакт фактор: 1.016 5-летний Импакт фактор: 1.194 SJR: 0.554 SNIP: 0.82 CiteScore™: 2

ISSN Печать: 1543-1649
ISSN Онлайн: 1940-4352

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International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2013005569
pages 565-580


Mirmohammadreza Kabiri
Department of Civil, Environmental and Architectural Engineering, Program of Material Science and Engineering, University of Colorado, Boulder, Colorado, USA
Franck J. Vernerey
Department of Civil, Environmental and Architectural Engineering, Program of Material Science and Engineering, University of Colorado, Boulder, Colorado, USA

Краткое описание

This paper introduces a concurrent adaptive multiscale methodology in which both macroscopic and microscopic deformation fields strongly interact. The method is based on the balance between numerical and homogenization error; while the first type of error states that the element's should be refined in regions of high deformation gradients, the second implies that elements size may not be smaller than a threshold determined by the size of the representative volume element (RVE). In this context, we introduce a multiscale method in which RVEs can be embedded in the continuum region through appropriate macro-micro boundary coupling conditions. By combining the idea of adaptive refinement with the embedded RVE method, the methodology ensures that appropriate descriptions of the material are used adequately, regardless of the severity of deformations. We show that this method, in conjunction with the extended finite element method, is ideal to study the strong interactions between a crack and the microstructure of heterogeneous media. In particular, the method enables an explicit description of microstructural features near the crack tip, while a computationally inexpensive coarse scale continuum description is used in the rest of the domain. We illustrate the method with several examples showing its accuracy and relatively low computational cost and discuss its potential in relating microstructure to the fracture toughness of a diversity of heterogeneous media.


  1. Belytschko, T. and Xiao, S., Coupling methods for continuum model with molecular model.

  2. Cosserat, E. and Cosserat, F., Theorie des Corps Deformables.

  3. D‘Azevedo, E. F., Optimal triangular mesh generation by coordinate transformation. DOI: 10.1137/0912040

  4. de Borst, R., Simulation of strain localization: A reappraisal of the cosserat continuum. DOI: 10.1108/eb023842

  5. de Borst, R., On gradient-enhanced coupled plastic damage theories.

  6. Farsad, M., Vernerey, F. J., and Park, H. S., An extended finite element/level set method to study surface effects on the mechanical behavior and properties of nanomaterials. DOI: 10.1002/nme.2946

  7. Fleck, N. and Hutchinson, J., A phenomenological theory for strain gradient effects in plasticity. DOI: 10.1016/0022-5096(93)90072-N

  8. Fleck, N., Muller, G., Ashby, M., and Hutchinson, J., Strain gradient plasticity: Theory and experiment. DOI: 10.1016/0956-7151(94)90502-9

  9. Forest, S. and Sab, K., Cosserat overall modeling of heterogeneous materials. DOI: 10.1016/S0093-6413(98)00059-7

  10. Fries, T., Byfut, A., Alizada1, A., Cheng, K., and Schröer, A., Hanging nodes and XFEM. DOI: 10.1002/nme.3024

  11. Ghosh, S., Lee, K., and Moorthy, S., Multiple scale analysis of heterogeneous elastic structures using homogenisation theory and voronoi cell finite element method. DOI: 10.1016/0020-7683(94)00097-G

  12. Ghosh, S., Lee, K., and Moorthy, S., Two scale analysis of heterogeneous elasticplastic materials with asymptotic homogenisation and voronoi cell finite element model. DOI: 10.1016/0045-7825(95)00974-4

  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. Ghosh, S., Bai, J., and Raghavan, P., Concurrent multi-level model for damage evolution in microstructurally debonding composites. DOI: 10.1016/j.mechmat.2006.05.004

  15. Guedes, J. 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. Gurson, A. L., Continuum theory of ductile rupture by void nucleation and growth: Part I — yield criteria and flow rules for porous ductile media. DOI: 10.1115/1.3443401

  17. Hill, R., Elastic properties of reinforced solids: Some theoretical principles. DOI: 10.1016/0022-5096(63)90036-X

  18. Hiriyur, B., Waisman, H., and Deodatis, G., Uncertainty quantification in homogenization of heterogeneous microstructures modeled by XFEM. DOI: 10.1002/nme.3174

  19. Kadowaki, H. and Liu, W., Bridging multi-scale method for localization problems. DOI: 10.1016/j.cma.2003.11.014

  20. Kouznetsova, V., Brekelmans, W. A. M., and Baaijens, F. P. T., An approach to micromacro modelling of heterogeneous materials. DOI: 10.1007/s004660000212

  21. Liu, W., Karpov, E., Zhang, S., and Park, H., An introduction to computational nanomechanics and materials. DOI: 10.1016/j.cma.2003.12.008

  22. Mo&#246;s, N., Dolbow, J., and Belytschko, T., A finite element method for crack growth without remeshing. DOI: 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J

  23. Stolarska, M., Chopp, D. L., Mo&#246;s, N., and Belytschko, T., Modelling crack growth by level sets in the extended finite element method. DOI: 10.1002/nme.201

  24. Moorthy, S. and Ghosh, S., A model for analysis of arbitrary composite and porous microstructures with Voronoi cell finite elements. DOI: 10.1002/(SICI)1097-0207(19960730)39:14<2363::AID-NME958>3.0.CO;2-D

  25. Needleman, A. and Tvergaard, V., An analysis of ductile rupture in notched bars. DOI: 10.1016/0022-5096(84)90031-0

  26. Nemat-Nasser, S. and Hori, M., Micromechanics: Overall Properties of Heterogeneous Materials.

  27. Park, H., Karpov, E., Liu, W., and Klein, P., The bridging scale for two dimensional atomistic/continuum coupling. DOI: 10.1080/14786430412331300163

  28. Park, H. and Liu, W., An introduction and tutorial on multiple-scale analysis in solids. DOI: 10.1016/j.cma.2003.12.054

  29. Raghavan, P. and Ghosh, S., Adaptive multi-scale computational modeling of composite materials.

  30. Raghavan, P. and Ghosh, S., Concurrent multi-scale analysis of elastic composites by a multi-level computational model. DOI: 10.1016/j.cma.2003.10.007

  31. Rice, J. and Tracey, D. M., On the ductile enlargement of voids in triaxial stress fields. DOI: 10.1016/0022-5096(69)90033-7

  32. Suquet, P., Local and Global Aspects in the Mathematical Theory of Plasticity.

  33. Vernerey, F., The effective permeability of cracks and interfaces in porous media. DOI: 10.1007/s11242-012-9985-0

  34. Vernerey, F., A theoretical treatment on the mechanics of interfaces in deformable porous media. DOI: 10.1016/j.ijsolstr.2011.07.005

  35. Vernerey, F. J. and Chevalier, T., A multiscale micro-continuum model to capture strain localization in composite materials.

  36. Vernerey, F. J. and Kabiri, M., An adaptive concurrent multiscale method for microstructured elastic solids. DOI: 10.1016/j.cma.2012.04.021

  37. Vernerey, F. J., Liu, W. K., and Moran, B., Multi-scale micromorphic theory for hierarchical materials. DOI: 10.1016/j.jmps.2007.04.008

  38. Vernerey, F. J., 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

  39. Vernerey, F. J., Liu, W. K., Moran, B., and Olson, G. B., Multi-length scale micromorphic process zone model. DOI: 10.1007/s00466-009-0382-7

  40. Wagner, G. and Liu, W., Coupling of atomistic and continuum simulations using a bridging scale decomposition. DOI: 10.1016/S0021-9991(03)00273-0

  41. Yazdani, A., Gakwaya, A., and Dhatt, G., A posteriori error estimator based on the second derivative of the displacement field for two-dimensional elastic problems. DOI: 10.1016/S0045-7949(96)00047-8

  42. Zohdi, T., Oden, J., and Rodin, G., Hieratchical modeling of heterogeneous bodies. DOI: 10.1016/S0045-7825(96)01106-1

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