### Abstract

This paper presents the recent finding by Muhlhaus et al [1] that bifurcation of crack growth patterns exists for arrays of two-dimensional cracks. This bifurcation is a result of the nonlinear effect due to crack interaction, which is, in the present analysis, approximated by the "dipole asymptotic" or "pseudo-traction" method. The nonlinear parameter for the problem is the crack length/ spacing ratio λ = a/h. For parallel and edge crack arrays under far field tension, uniform crack growth patterns (all cracks having same size) yield to nonuniform crack growth patterns (i.e. bifurcation) if λ is larger than a critical value λ_{cr} (note that such bifurcation is not found for collinear crack arrays). For parallel and edge crack arrays respectively, the value of λ_{cr} decreases monotonically from (2/9)^{1/2} and (2/15.096)^{1/2} for arrays of 2 cracks, to (2/3)^{1/2}/π and (2/5.032)^{1/2}/π for infinite arrays of cracks. The critical parameter λ_{cr} is calculated numerically for arrays of up to 100 cracks, whilst discrete Fourier transform is used to obtain the exact solution of λ_{cr} for infinite crack arrays. For geomaterials, bifurcation can also occurs when array of sliding cracks are under compression.

Original language | English |
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Pages (from-to) | 71-76 |

Number of pages | 6 |

Journal | Key Engineering Materials |

Volume | 145-149 |

Publication status | Published - 1 Dec 1998 |

Externally published | Yes |

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## Cite this

*Key Engineering Materials*,

*145-149*, 71-76.