In this study, we use micromechanics-based modeling to investigate the effect of a non-uniform void size distribution on the plastic flow and fracture behavior of porous ductile solids. We perform 2D plane strain finite element simulations of statistical volume elements containing between 3 × 3 and 22 × 22 uniformly-spaced voids of varying sizes, using two different modeling approaches: (i) resolving the voids spatially and (ii) using a porous plasticity model and spatially varying the initial porosity. For each sample size, thirty statistical volume elements are generated through random sampling from a log-normal void size distribution to quantify the variation for a given number of voids. The macroscopic behavior and microstructural evolution are analyzed under different imposed stress states. Our findings indicate that non-uniform void sizes have negligible effects on initial yielding and behavior before peak stress, but the strain at which maximum stress is attained varies. Beyond peak stress, there is a significant variation in the macroscopic stress–strain response and void growth between the statistical volume elements. Mean failure strain decreases and scatter diminishes as sample size increases, but even large samples retain scatter in failure strain. We achieve tremendous speed-up using models with porous plasticity while producing results comparable to models with spatially resolved voids. This suggests that a cost-effective modeling approach, where the voided subregions of the model are described using a porous plasticity model and spatially varying initial porosity, facilitates simulations of 3D volume elements with a statistically representative number of voids.

中文翻译：

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具有不均匀空隙尺寸分布的多孔延性固体的有限元建模

在本研究中，我们使用基于微观力学的建模来研究不均匀的空隙尺寸分布对多孔韧性固体的塑性流动和断裂行为的影响。我们使用两种不同的建模方法对包含 3 × 3 到 22 × 22 个不同大小的均匀间距空隙的统计体积单元进行 2D 平面应变有限元模拟：（i） 在空间上解析空隙和 （ii） 使用多孔塑性模型并在空间上改变初始孔隙率。对于每个样本量，通过从对数正态空隙大小分布中随机抽样生成 30 个统计体积元素，以量化给定空隙数的变化。分析了不同施加应力状态下的宏观行为和微观结构演变。我们的研究结果表明，不均匀的空隙大小对峰值应力之前的初始屈服和行为的影响可以忽略不计，但达到最大应力的应变会有所不同。在峰值应力之外，统计体积元素之间的宏观应力-应变响应和空隙增长存在显着变化。平均失效应变随着样本量的增加而减小，散射减少，但即使是大样本在失效应变中也保持散射。我们使用具有多孔塑性的模型实现了巨大的加速，同时产生的结果与具有空间分辨空隙的模型相当。这表明，一种经济高效的建模方法，其中使用多孔塑性模型和空间变化的初始孔隙率来描述模型的空隙子区域，有助于模拟具有统计代表性空隙数的 3D 体积单元。