Porous brittle solids evidence complex mechanical behavior, where localized failure patterns originate from mechanical processes on the microstructural level. In order to investigate the failure mechanics of porous brittle solids, we outline a general stochastic and numerical microstructure-based approach. To this end, we generate random porous microstructures by level-cutting Gaussian random fields, and conduct numerical simulations using the material point method. This allows investigating both small and large deformation characteristics of irregular porous media where a segmentation into grains and bonds is ambiguous. We demonstrate the versatility of our approach by examining elasticity and failure as a function of a wide range of porosities, from 20% to 80%. Observing that onset of failure can be well described through the second order work, we show that the stress at failure follows a power law similar to that of the elastic modulus. Moreover, we propose that the failure envelope can be approximated by a simple quadratic fitting curve, and that plastic deformation appears to be governed by an associative plastic flow rule. Finally, large deformation simulations reveal a transition in the mode of localization of the deformation, from compaction bands for highly porous samples to shear bands for denser ones.

多孔脆性固体证明了复杂的机械行为，其中局部失效模式源自微观结构水平上的机械过程。为了研究多孔脆性固体的破坏力学，我们概述了一种基于随机和数值微观结构的一般方法。为此，我们通过水平切割高斯随机场生成随机多孔微结构，并使用材料点方法进行数值模拟。这允许研究不规则多孔介质的小变形和大变形特征，其中颗粒和键的分割不明确。我们通过检查弹性和失效作为各种孔隙率（从 20% 到 80%）的函数来证明我们方法的多功能性。观察到可以通过二阶工作很好地描述失败的开始，我们表明，破坏时的应力遵循类似于弹性模量的幂律。此外，我们建议可以通过简单的二次拟合曲线来近似破坏包络线，并且塑性变形似乎受关联塑性流动规则控制。最后，大变形模拟揭示了变形局部化模式的转变，从高度多孔样品的压实带到致密样品的剪切带。