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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: 0.68 CiteScore™: 1.18

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

Выпуски:
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.v4.i1.40
pages 29-46

Multiscale Total Lagrangian Formulation for Modeling Dislocation-Induced Plastic Deformation in Polycrystalline Materials

Xinwei Zhang
Civil & Environmental Engineering Department, University of California, Los Angeles (UCLA), 5731G Boelter Hall, Los Angeles, CA 90095, USA
Shafigh Mehraeen
Civil & Environmental Engineering Department, University of California, Los Angeles (UCLA), 5731G Boelter Hall, Los Angeles, CA 90095, USA
Jiun-Shyan Chen
Civil & Environmental Engineering Department, University of California, Los Angeles (UCLA), 5731G Boelter Hall, Los Angeles, CA 90095, USA
Nasr M. Ghoniem
Mechanical and Aerospace Engineering, University of California, Los Angeles, Los Angeles, CA 90095, USA

Краткое описание

Multiscale mathematical and computational formulation for coupling mesoscale dislocation mechanics and macroscale continuum mechanics for prediction of plastic deformation in polycrystalline materials is presented. In this development a total Lagrangian multiscale variational formulation for materials subjected to geometric and material nonlinearities is first introduced. By performing scale decomposition of kinematic variables and the corresponding dislocation kinematic variables, several leading-order equations, including a scale-coupling equation, a mesoscale dislocation evolution equation, and a homogenized macroscale equilibrium equation, are obtained. By further employing the Orowan relation, a mesoscopic plastic strain is obtained from dislocation velocity and its distribution, and a homogenized elastoplastic stress-strain relation for macroscale is constructed. The macroscale, mesoscale, and scale-coupling equations are solved interactively at each macroscopic load increment, and information on the two scales is passed through the macroscale integration points. In this multiscale approach the phenomenological hardening rule and flow rule in the classical plasticity theory are avoided, and they are replaced by a homogenized mesoscale material response characterized by dislocation evolution and their interactions.


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