Danku Zsuzsa, Kun Ferenc, Herrmann Hans J
Department of Theoretical Physics, University of Debrecen, P.O. Box 5, H-4010 Debrecen, Hungary.
Computational Physics IfB, HIF, ETH, Hönggerberg, 8093 Zürich, Switzerland and Departamento de Fisica, Universidade Federal do Ceara, 60451-970 Fortaleza, Ceara, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062402. doi: 10.1103/PhysRevE.92.062402. Epub 2015 Dec 2.
We investigate the geometrical structure of breaking bursts generated during the creep rupture of heterogeneous materials. Using a fiber bundle model with localized load sharing we show that bursts are compact geometrical objects; however, their external frontiers have a fractal structure which reflects their growth dynamics. The perimeter fractal dimension of bursts proved to have the universal value 1.25 independent of the external load and of the amount of disorder in the system. We conjecture that according to their geometrical features, breaking bursts fall in the universality class of loop-erased self-avoiding random walks with perimeter fractal dimension 5/4 similar to the avalanches of Abelian sand pile models. The fractal dimension of the growing crack front along which bursts occur proved to increase from 1 to 1.25 as bursts gradually cover the entire front.
我们研究了非均质材料蠕变断裂过程中产生的破裂爆发的几何结构。使用具有局部载荷分担的纤维束模型，我们表明爆发是紧凑的几何对象；然而，它们的外部边界具有分形结构，这反映了它们的生长动力学。爆发的周长分形维数被证明具有通用值1.25，与外部载荷和系统中的无序量无关。我们推测，根据它们的几何特征，破裂爆发属于周长分形维数为5/4的环擦除自回避随机游走的普适类，类似于阿贝尔沙堆模型的雪崩。事实证明，随着爆发逐渐覆盖整个前沿，发生爆发的生长裂纹前沿的分形维数从1增加到1.25。
