### Abstract

We investigate the effect of the amount of disorder on the shrinkage-induced cracking of a thin brittle layer attached to a substrate. Based on a discrete element model we study how the dynamics of cracking and the size of fragments evolve when the amount of disorder is varied. In the model a thin layer is discretized on a random lattice of Voronoi polygons attached to a substrate. Two sources of disorder are considered: structural disorder captured by the local variation of the stiffness and strength disorder represented by the random strength of cohesive elements between polygons. Increasing the amount of strength disorder, our calculations reveal a transition from a cellular crack pattern, generated by the sequential branching and merging of cracks, to a disordered ensemble of cracks where the merging of randomly nucleated microcracks dominate. In the limit of low disorder, the statistics of fragment size is described by a log-normal distribution; however, in the limit of high disorder, a power-law distribution is obtained.

Original language | English |
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Article number | 033006 |

Journal | Physical Review E |

Volume | 96 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 25 2017 |

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### ASJC Scopus subject areas

- Statistics and Probability
- Condensed Matter Physics
- Statistical and Nonlinear Physics

### Cite this

*Physical Review E*,

*96*(3), [033006]. https://doi.org/10.1103/PhysRevE.96.033006

**Effect of disorder on shrinkage-induced fragmentation of a thin brittle layer.** / Halász, Zoltán; Nakahara, Akio; Kitsunezaki, So; Kun, F.

Research output: Contribution to journal › Article

*Physical Review E*, vol. 96, no. 3, 033006. https://doi.org/10.1103/PhysRevE.96.033006

}

TY - JOUR

T1 - Effect of disorder on shrinkage-induced fragmentation of a thin brittle layer

AU - Halász, Zoltán

AU - Nakahara, Akio

AU - Kitsunezaki, So

AU - Kun, F.

PY - 2017/9/25

Y1 - 2017/9/25

N2 - We investigate the effect of the amount of disorder on the shrinkage-induced cracking of a thin brittle layer attached to a substrate. Based on a discrete element model we study how the dynamics of cracking and the size of fragments evolve when the amount of disorder is varied. In the model a thin layer is discretized on a random lattice of Voronoi polygons attached to a substrate. Two sources of disorder are considered: structural disorder captured by the local variation of the stiffness and strength disorder represented by the random strength of cohesive elements between polygons. Increasing the amount of strength disorder, our calculations reveal a transition from a cellular crack pattern, generated by the sequential branching and merging of cracks, to a disordered ensemble of cracks where the merging of randomly nucleated microcracks dominate. In the limit of low disorder, the statistics of fragment size is described by a log-normal distribution; however, in the limit of high disorder, a power-law distribution is obtained.

AB - We investigate the effect of the amount of disorder on the shrinkage-induced cracking of a thin brittle layer attached to a substrate. Based on a discrete element model we study how the dynamics of cracking and the size of fragments evolve when the amount of disorder is varied. In the model a thin layer is discretized on a random lattice of Voronoi polygons attached to a substrate. Two sources of disorder are considered: structural disorder captured by the local variation of the stiffness and strength disorder represented by the random strength of cohesive elements between polygons. Increasing the amount of strength disorder, our calculations reveal a transition from a cellular crack pattern, generated by the sequential branching and merging of cracks, to a disordered ensemble of cracks where the merging of randomly nucleated microcracks dominate. In the limit of low disorder, the statistics of fragment size is described by a log-normal distribution; however, in the limit of high disorder, a power-law distribution is obtained.

UR - http://www.scopus.com/inward/record.url?scp=85029835214&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85029835214&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.96.033006

DO - 10.1103/PhysRevE.96.033006

M3 - Article

AN - SCOPUS:85029835214

VL - 96

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 3

M1 - 033006

ER -