Доступ предоставлен для: Guest
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: 0.68 CiteScore™: 1.18

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

Том 17, 2019 Том 16, 2018 Том 15, 2017 Том 14, 2016 Том 13, 2015 Том 12, 2014 Том 11, 2013 Том 10, 2012 Том 9, 2011 Том 8, 2010 Том 7, 2009 Том 6, 2008 Том 5, 2007 Том 4, 2006 Том 3, 2005 Том 2, 2004 Том 1, 2003

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2012002975
pages 487-501


Franck J. Vernerey
Department of Civil, Environmental and Architectural Engineering, Program of Material Science and Engineering, University of Colorado, Boulder, Colorado, USA
Thibaud Chevalier
Departement de Genie Civil, ENS Cachan, 94230 Cachan, France

Краткое описание

This paper presents a plasticity/damage formulation in the context of the physically based micro-continuum theory for multiphase materials described in a companion paper (see Vernerey, A physically-based micro-continuum theory, Mech. Adv. Mater. Struct., 2012). Based on a micro-structurally motivated decomposition of the deformation, the presented inelastic formulation is capable of characterizing the independent plastic/damage processes occurring in different phases (such as fiber or inclusions) and predicting the overall material behavior. The inelastic constitutive relation can thus be cast in a simple, physically motivated form, compared to conventional models. Such a formulation is thus very attractive for establishing a link between materials structure and properties. To illustrate the presented framework, we apply the micro-continuum model to the tensile failure of fiber-reinforced composite and compare it to a "brute force" approach in which the microstructure is explicitly modeled. We show that the model captures accurately the evolution of various features that cannot be calculated with conventional methods such as the independent stress, strain, and damage in the matrix and fibers and the fiber/matrix interface. Moreover, the existence of a size effect during failure is accounted for correctly.

Ключевые слова: nonlocal theory, strain localization, damage, size effects


  1. Bazant, Z., Why continuum damage is nonlocal: Micromechanical arguments. DOI: 10.1061/(ASCE)0733-9399(1991)117:5(1070)

  2. Bazant, Z. and Jirasek, M., Nonlocal integral formulations of plasticity and damage: Survey of progress. DOI: 10.1061/(ASCE)0733-9399(2002)128:11(1119)

  3. Belytschko, T., Liu, W.K., and Moran, B., Nonlinear Finite Elements for Continua and Structures.

  4. Cosserat, E. and Cosserat, F., Theorie des Corps Deformables. DOI: 10.1038/081067a0

  5. Eringen, A.C., Microcontinuum Field Theories 1: Foundations and Solids.

  6. Fleck, N.A. and Hutchinson, J.W., Strain gradient plasticity. DOI: 10.1016/S0065-2156(08)70388-0

  7. Fleck, N.A. and Hutchinson, J.W., A reformulation of strain gradient plasticity. DOI: 10.1016/S0022-5096(01)00049-7

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

  9. Forest, S., Homogenization methods and the mechanics of generalized continua. Part 2. DOI: 10.2298/TAM0229113F

  10. Forest, S., Barbe, F., and Cailletaud, G., Cosserat modelling of size effects in the mechanical behaviour of polycrystals and multi-phase materials. DOI: 10.1016/S0020-7683(99)00330-3

  11. Forest, S., Pradel, F., and Sab, K., Asymptotic analysis of heterogeneous Cosserat media. DOI: 10.1016/S0020-7683(00)00295-X

  12. Germain, P., The method of virtual power in continuum mechanics. Part 2: Microstrucure. DOI: 10.1137/0125053

  13. Gonzalez, C. and Llorca, J., Multiscale modeling of fracture in fiber-reinforced composites. DOI: 10.1016/j.actamat.2006.05.007

  14. Hao, S., Liu, W.K., Moran, B., Vernerey, F., and Olson, G.B., Multi-scale constitutive model and computational framework for the design of ultra-high strength, high toughness steels. DOI: 10.1016/j.cma.2003.12.026

  15. Iatridis, J.C. and Gwynn, I., Mechanisms for mechanical damage in the intervertebral disc annulus fibrosus. DOI: 10.1016/j.jbiomech.2003.12.026

  16. Lemaitre, J. and Chaboche, J.L., Mecanique des Materiaux Solides.

  17. Olson, G.B., Beyond discovery: Design for a new material world. DOI: 10.1016/S0364-5916(01)00041-4

  18. Saje, M., Pan, J., and Needlman, A., Void nucleation effects on shear localization in porous plastic solids. DOI: 10.1007/BF00017128

  19. Vernerey, F.J., A physically-based micro-continuum theory.

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

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

Articles with similar content:

Multiscale Modeling of Composite Materials by a Multifield Finite Element Approach
International Journal for Multiscale Computational Engineering, Vol.3, 2005, issue 4
Patrizia Trovalusci, V. Sansalone, F. Cleri
Size of a Representative Volume Element in a Second-Order Computational Homogenization Framework
International Journal for Multiscale Computational Engineering, Vol.2, 2004, issue 4
Marc Geers, W. A. M. Brekelmans, Varvara G. Kouznetsova
International Journal for Multiscale Computational Engineering, Vol.11, 2013, issue 6
Mirmohammadreza Kabiri, Franck J. Vernerey
Modeling the Particle Size and Interfacial Hardening Effects in Metal Matrix Composites with Dispersed Particles at Decreasing Microstructural Length Scales
International Journal for Multiscale Computational Engineering, Vol.7, 2009, issue 4
Rashid K. Abu Al-Rub
International Journal for Multiscale Computational Engineering, Vol.9, 2011, issue 5
Valerio Varano, Patrizia Trovalusci