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A higher order scheme for two-dimensional quasi-static crack growth simulations

Englund, Jonas LU (2007) In Computer Methods in Applied Mechanics and Engineering 196(21-24). p.2527-2538
Abstract
An efficient scheme for the simulation of quasi-static crack growth in two-dimensional linearly elastic isotropic specimens is presented. The crack growth is simulated in a stepwise manner where an extension to the already existing crack is added in each step. In a local coordinate system each such extension is represented as a polynomial of some, user specified, degree, n. The coefficients of the polynomial describing an extension are found by requiring that the mode II stress intensity factor is equal to zero at certain points of the extension. If a crack grows from a, pre-existing crack so that a kink develops, the leading term describing the crack shape close to the kink will, in a local coordinate system, be proportional to x(3/2). We... (More)
An efficient scheme for the simulation of quasi-static crack growth in two-dimensional linearly elastic isotropic specimens is presented. The crack growth is simulated in a stepwise manner where an extension to the already existing crack is added in each step. In a local coordinate system each such extension is represented as a polynomial of some, user specified, degree, n. The coefficients of the polynomial describing an extension are found by requiring that the mode II stress intensity factor is equal to zero at certain points of the extension. If a crack grows from a, pre-existing crack so that a kink develops, the leading term describing the crack shape close to the kink will, in a local coordinate system, be proportional to x(3/2). We therefore allow the crack extensions to contain such a term in addition to the monomial terms. The discontinuity in the crack growth direction at a kink, the kink angle, is determined by requiring that the mode II stress intensity factor should be equal to zero for an infinitesimal extension of the existing crack. To implement the scheme, accurate values of the stress intensity factors and T-stress are needed in each step of the simulation. These fracture parameters are computed using a previously developed integral equation of the second kind. (c) 2007 Elsevier B.V. All rights reserved. (Less)
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author
organization
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type
Contribution to journal
publication status
published
subject
keywords
fast, integral equation, multipole method, stress intensity factor, crack growth
in
Computer Methods in Applied Mechanics and Engineering
volume
196
issue
21-24
pages
2527 - 2538
publisher
Elsevier
external identifiers
  • wos:000246126700017
  • scopus:33947634583
ISSN
0045-7825
DOI
10.1016/j.cma.2007.01.007
language
English
LU publication?
yes
id
2244dc65-4b98-44fe-ac07-4ab127de9da9 (old id 629682)
alternative location
http://www.maths.lth.se/na/staff/helsing/paperA.pdf
date added to LUP
2007-12-10 11:09:55
date last changed
2017-01-01 07:10:24
@article{2244dc65-4b98-44fe-ac07-4ab127de9da9,
  abstract     = {An efficient scheme for the simulation of quasi-static crack growth in two-dimensional linearly elastic isotropic specimens is presented. The crack growth is simulated in a stepwise manner where an extension to the already existing crack is added in each step. In a local coordinate system each such extension is represented as a polynomial of some, user specified, degree, n. The coefficients of the polynomial describing an extension are found by requiring that the mode II stress intensity factor is equal to zero at certain points of the extension. If a crack grows from a, pre-existing crack so that a kink develops, the leading term describing the crack shape close to the kink will, in a local coordinate system, be proportional to x(3/2). We therefore allow the crack extensions to contain such a term in addition to the monomial terms. The discontinuity in the crack growth direction at a kink, the kink angle, is determined by requiring that the mode II stress intensity factor should be equal to zero for an infinitesimal extension of the existing crack. To implement the scheme, accurate values of the stress intensity factors and T-stress are needed in each step of the simulation. These fracture parameters are computed using a previously developed integral equation of the second kind. (c) 2007 Elsevier B.V. All rights reserved.},
  author       = {Englund, Jonas},
  issn         = {0045-7825},
  keyword      = {fast,integral equation,multipole method,stress intensity factor,crack growth},
  language     = {eng},
  number       = {21-24},
  pages        = {2527--2538},
  publisher    = {Elsevier},
  series       = {Computer Methods in Applied Mechanics and Engineering},
  title        = {A higher order scheme for two-dimensional quasi-static crack growth simulations},
  url          = {http://dx.doi.org/10.1016/j.cma.2007.01.007},
  volume       = {196},
  year         = {2007},
}