Laubie Hadrien, Radjai Farhang, Pellenq Roland, Ulm Franz-Josef
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
⟨MSE⟩2, UMI 3466 CNRS-MIT Energy Initiative, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.
Phys Rev Lett. 2017 Aug 18;119(7):075501. doi: 10.1103/PhysRevLett.119.075501. Epub 2017 Aug 14.
By means of extensive lattice-element simulations, we investigate stress transmission and its relation with failure properties in increasingly disordered porous systems. We observe a non-Gaussian broadening of stress probability density functions under tensile loading with increasing porosity and disorder, revealing a gradual transition from a state governed by single-pore stress concentration to a state controlled by multipore interactions and metric disorder. This effect is captured by the excess kurtosis of stress distributions and shown to be nicely correlated with the second moment of local porosity fluctuations, which appears thus as a (dis)order parameter for the system. By generating statistical ensembles of porous textures with varying porosity and disorder, we derive a general expression for the fracture stress as a decreasing function of porosity and disorder. Focusing on critical sites where the local stress is above the global fracture threshold, we also analyze the transition to failure in terms of a coarse-graining length. These findings provide a general framework which can also be more generally applied to multiphase and structural heterogeneous materials.
通过广泛的晶格元模拟，我们研究了在日益无序的多孔系统中的应力传递及其与破坏特性的关系。我们观察到在拉伸载荷下，随着孔隙率和无序度的增加，应力概率密度函数出现非高斯展宽，揭示了从单孔应力集中主导的状态到多孔隙相互作用和尺度无序控制的状态的逐渐转变。这种效应通过应力分布的过量峰度得以体现，并显示出与局部孔隙率波动的二阶矩有很好的相关性，因此局部孔隙率波动的二阶矩可作为系统的（无序）序参量。通过生成具有不同孔隙率和无序度的多孔纹理统计系综，我们推导出了断裂应力作为孔隙率和无序度递减函数的一般表达式。聚焦于局部应力高于全局断裂阈值的临界位置，我们还根据粗粒化长度分析了向破坏的转变。这些发现提供了一个通用框架，该框架也可更广泛地应用于多相和结构非均质材料。
