Phase field model for mode III crack growth in two dimensional elasticity

Takeshi Takaishi; Masato Kimura

Kybernetika (2009)

  • Volume: 45, Issue: 4, page 605-614
  • ISSN: 0023-5954

Abstract

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A phase field model for anti-plane shear crack growth in two dimensional isotropic elastic material is proposed. We introduce a phase field to represent the shape of the crack with a regularization parameter ϵ > 0 and we approximate the Francfort–Marigo type energy using the idea of Ambrosio and Tortorelli. The phase field model is derived as a gradient flow of this regularized energy. We show several numerical examples of the crack growth computed with an adaptive mesh finite element method.

How to cite

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Takaishi, Takeshi, and Kimura, Masato. "Phase field model for mode III crack growth in two dimensional elasticity." Kybernetika 45.4 (2009): 605-614. <http://eudml.org/doc/37724>.

@article{Takaishi2009,
abstract = {A phase field model for anti-plane shear crack growth in two dimensional isotropic elastic material is proposed. We introduce a phase field to represent the shape of the crack with a regularization parameter $\epsilon >0$ and we approximate the Francfort–Marigo type energy using the idea of Ambrosio and Tortorelli. The phase field model is derived as a gradient flow of this regularized energy. We show several numerical examples of the crack growth computed with an adaptive mesh finite element method.},
author = {Takaishi, Takeshi, Kimura, Masato},
journal = {Kybernetika},
keywords = {crack growth; phase field model; numerical simulation; crack growth; phase field model; numerical simulation; anti-plane shear crack regularization parameter; Francfort-Marigo type energy; gradient flow; adaptive mesh finite element method},
language = {eng},
number = {4},
pages = {605-614},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Phase field model for mode III crack growth in two dimensional elasticity},
url = {http://eudml.org/doc/37724},
volume = {45},
year = {2009},
}

TY - JOUR
AU - Takaishi, Takeshi
AU - Kimura, Masato
TI - Phase field model for mode III crack growth in two dimensional elasticity
JO - Kybernetika
PY - 2009
PB - Institute of Information Theory and Automation AS CR
VL - 45
IS - 4
SP - 605
EP - 614
AB - A phase field model for anti-plane shear crack growth in two dimensional isotropic elastic material is proposed. We introduce a phase field to represent the shape of the crack with a regularization parameter $\epsilon >0$ and we approximate the Francfort–Marigo type energy using the idea of Ambrosio and Tortorelli. The phase field model is derived as a gradient flow of this regularized energy. We show several numerical examples of the crack growth computed with an adaptive mesh finite element method.
LA - eng
KW - crack growth; phase field model; numerical simulation; crack growth; phase field model; numerical simulation; anti-plane shear crack regularization parameter; Francfort-Marigo type energy; gradient flow; adaptive mesh finite element method
UR - http://eudml.org/doc/37724
ER -

References

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  10. Quantitative study of adaptive mesh FEM with localization index of pattern, In: Proc. of the Czech–Japanese Seminar in Applied Mathematics 2006 (M. Beneš, M. Kimura, and T. Nakaki, eds.), COE Lecture Note Vol. 6, Faculty of Mathematics, Kyushu University 2007, pp. 114–136. MR2277123
  11. Modeling and numerical simulations of dendritic crystal growth, Physica D 63 (1993), 410–423. Zbl0797.35175
  12. Design of Adaptive Finite Element Software, The Finite Element Toolbox ALBERTA (Lecture Notes in Comput. Sci. Engrg. 42.) Springer–Verlag, Berlin 2005. MR2127659
  13. Models of Phase Transitions, Birkhäuser–Verlag, Basel 1996. Zbl0903.35097MR1423808

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