Premium
A variational multiscale method to model crack propagation at finite strains
Author(s) -
Mergheim J.
Publication year - 2009
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2602
Subject(s) - classification of discontinuities , finite element method , scale (ratio) , locality , extended finite element method , domain (mathematical analysis) , domain decomposition methods , computer science , mathematics , mechanics , mathematical analysis , structural engineering , physics , engineering , linguistics , philosophy , quantum mechanics
This contribution presents a hierarchical variational multiscale framework to model propagating discontinuities at finite strains. Thereby the deformation map is decomposed into coarse‐scale and fine‐scale displacements, which results in a decoupled system of coarse‐scale and fine‐scale equations. Both are solved numerically by means of the finite element method whereby crack propagation is taken into account at the fine scale. Growing cracks are numerically handled by the introduction of discontinuous elements. A locality assumption on the fine‐scale solution and an adaptive scheme to resize the fine‐scale domain are introduced and demonstrated to increase the efficiency of the method. Copyright © 2009 John Wiley & Sons, Ltd.