Generalized Continuum: from Voigt to the Modeling of Quasi-Brittle Materials.

Jamile Salim Fuina, Roque Luiz da Silva Pitangueira, Samuel Silva Penna

Abstract


This article discusses the use of the generalized continuum theories to incorporate the effects of the microstructure in the nonlinear finite element analysis of quasi-brittle materials and, thus, to solve mesh dependency problems. A description of the problem called numerically induced strain localization, often found in Finite Element Method material non-linear analysis, is presented. A brief historic about the Generalized Continuum Mechanics based models is presented, since the initial work of Voigt (1887) until the more recent studies. By analyzing these models, it is observed that the Cosserat and microstretch approaches are particular cases of a general formulation that describes the micromorphic continuum. After reporting attempts to incorporate the material microstructure in Classical Continuum Mechanics based models, the article shows the recent tendency of doing it according to assumptions of the Generalized Continuum Mechanics. Finally, it presents numerical results which enable to characterize this tendency as a promising way to solve the problem.


Keywords


Generalized continuums; Quasi-brittle media; Numerically induced strain localization; Finite element method



DOI: http://dx.doi.org/10.5433/1679-0375.2010v31n2p119

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Semin., Ciênc. Exatas Tecnol.
Londrina - PR - Brazil
E-ISSN: 16790375
DOI: 10.5433/1679-0375
Email: seminaexatas@uel.br
 
This journal is licensed with a license Creative Commons Attribution-NonCommercial 4.0 International.