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International Journal for Multiscale Computational Engineering

Impact factor: 1.103

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2013005685
pages 581-596

EXTENSIONS OF THE TWO-SCALE GENERALIZED FINITE ELEMENT METHOD TO NONLINEAR FRACTURE PROBLEMS

Varun Gupta
Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Newmark Laboratory, 205 North Mathews Avenue, Urbana, Illinois 61801, USA
Dae-Jin Kim
Department of Architectural Engineering, Kyung Hee University, Engineering Building, 1 Sochon-Dong Kihung-Gu, Yongin, Kyunggi-Do, Korea 446-701
Armando Duarte
Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Newmark Laboratory, 205 North Mathews Avenue, Urbana, Illinois 61801, USA

ABSTRACT

This paper presents an extension of a two-scale generalized finite element method (GFEM) to three-dimensional fracture problems involving confined plasticity. This two-scale procedure, also known as the generalized finite element method with global-local enrichments (GFEMgl), involves the solution of a fine-scale boundary value problem defined around a region undergoing plastic deformations and the enrichment of the coarse-scale solution space with the resulting nonlinear fine-scale solution through the partition-of-unity framework. The approach provides accurate nonlinear solutions with reduced computational costs compared to standard finite element methods, since the nonlinear iterations are performed on much smaller problems. The efficacy of the method is demonstrated with the help of numerical examples, which are three-dimensional fracture problems with nonlinear material properties and considering small-strain, rate-independent J2 plasticity.

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