Finite element analysis and algorithms for single-crystal strain-gradient plasticity

被引：20

作者：

Reddy, B. D. ^{[2
]}

Wieners, C. ^{[1
]}

Wohlmuth, B. ^{[3
]}

机构：

[1] KIT, Inst Angew & Numer Math, Karlsruhe, Germany

[2] Univ Cape Town, Ctr Res Computat & Appl Mech, ZA-7700 Rondebosch, South Africa

[3] Tech Univ Munich, Fak Math M2, D-8046 Garching, Germany

来源：

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING | 2012年 / 90卷 / 06期

基金：

奥地利科学基金会; 新加坡国家研究基金会;

关键词：

strain-gradient plasticity; single crystal; rate-independent; a priori finite element estimates; variational inequality; closest-point projection; FREE-ENERGY; DEFORMATION; FORMULATIONS; CONTINUUM; MODEL;

D O I：

10.1002/nme.3347

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We provide optimal a priori estimates for finite element approximations of a model of rate-independent single-crystal strain-gradient plasticity. The weak formulation of the problem takes the form of a variational inequality in which the primary unknowns are the displacement and slips on the prescribed slip systems, as well as the back-stress associated with the vectorial microstress. It is shown that the return mapping algorithm for local plasticity can be applied element-wise to this non-local setting. Some numerical examples illustrate characteristic features of the non-local model. Copyright (C) 2012 John Wiley & Sons, Ltd.

引用

页码：784 / 804

页数：21

共 38 条

[1]

Alber HD, LECT NOTES MATH, V1682

[2] A computational procedure for rate-independent crystal plasticity [J].

Anand, L ;

Kothari, M .

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 1996, 44 (04) :525-558

[3] Modeling of polycrystals with gradient crystal plasticity: A comparison of strategies [J].

Bargmann, Swantje ;

Ekh, Magnus ;

Runesson, Kenneth ;

Svendsen, Bob .

PHILOSOPHICAL MAGAZINE, 2010, 90 (10) :1263-1288

[4] A three-dimensional dislocation field crystal plasticity approach applied to miniaturized structures [J].

Bayley, C. J. ;

Brekelmans, W. A. M. ;

Geers, M. G. D. .

PHILOSOPHICAL MAGAZINE, 2007, 87 (8-9) :1361-1378

[5] A comparison of dislocation induced back stress formulations in strain gradient crystal plasticity [J].

Bayley, C. J. ;

Brekelmans, W. A. M. ;

Geers, M. G. D. .

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2006, 43 (24) :7268-7286

[6] A comparison of nonlocal continuum and discrete dislocation plasticity predictions [J].

Bittencourt, E ;

Needleman, A ;

Gurtin, ME ;

Van der Giessen, E .

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 2003, 51 (02) :281-310

[7] DISCRETE MICROMECHANICS OF ELASTOPLASTIC CRYSTALS [J].

BORJA, RI ;

WREN, JR .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1993, 36 (22) :3815-3840

[8] Concurrent multiscale computing of deformation microstructure by relaxation and local enrichment with application to single-crystal plasticity [J].

Conti, Sergio ;

Hauret, Patrice ;

Ortiz, Michael .

MULTISCALE MODELING & SIMULATION, 2007, 6 (01) :135-157

[9] COMPUTATIONAL MODELING OF SINGLE-CRYSTALS [J].

CUITINO, AM ;

ORTIZ, M .

MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING, 1993, 1 (03) :225-263

[10] Non-local crystal plasticity model with intrinsic SSD and GND effects [J].

Evers, LP ;

Brekelmans, WAM ;

Geers, MGD .

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 2004, 52 (10) :2379-2401

← 1 2 3 4 →