Under external perturbations, inter-particle forces in disordered granular media are well known to form a heterogeneous distribution with filamentary patterns. Better understanding these forces and the distribution is important for predicting the collective behavior of granular media, the media second only to water as the most manipulated material in global industry. However, studies in this regard so far have been largely confined to granular media exhibiting only geometric heterogeneity, leaving the dimension of mechanical heterogeneity a rather uncharted area. Here, through a FEM contact mechanics model, we show that a heterogeneous inter-particle force distribution can also emerge from the dimension of mechanical heterogeneity alone. Specifically, we numerically study inter-particle forces in packing of mechanically heterogeneous disks arranged over either a square or a hexagonal lattice and under quasi-static isotropic compression. Our results show that, at the system scale, a hexagonal packing exhibit a more heterogeneous inter-particle force distribution than a square packing does; At the particle scale, for both packing lattices, preliminary analysis shows the consistent coexistence of outliers (i.e., softer disks sustaining larger forces while stiffer disks sustaining smaller forces) in comparison to their homogeneous counterparts, which implies the existence of nonlocal effect. Further analysis on the portion of outliers and on spatial contact force correlations suggest that the hexagonal packing shows more pronounced nonlocal effect over the square packing under small mechanical heterogeneity. However, such trend is reversed when assemblies becomes more mechanically heterogeneous. Lastly, we confirm that, in the absence of particle reorganization events, contact friction merely plays the role of packing stabilization while its variation has little effect on inter-particle forces and their distribution.

在外部扰动下，众所周知，无序颗粒介质中的颗粒间力会形成具有丝状图案的异质分布。更好地了解这些力和分布对于预测颗粒介质的集体行为很重要，颗粒介质是仅次于水的介质，是全球工业中被操纵最多的材料。然而，到目前为止，这方面的研究主要局限于仅表现出几何异质性的颗粒介质，从而使机械异质性的维度成为一个相当未知的领域。在这里，通过有限元接触力学模型，我们表明异质粒子间力分布也可以单独从机械异质性维度出现。具体来说，我们数值研究了排列在正方形或六边形晶格上并在准静态各向同性压缩下排列的机械异质盘的堆积中的粒子间力。我们的结果表明，在系统尺度上，六边形填料表现出比方形填料更不均匀的粒子间力分布；在粒子尺度上，对于两种堆积晶格，初步分析表明，与其同质对应物相比，异常值（即较软的磁盘承受较大的力而较硬的磁盘承受较小的力）一致共存，这意味着存在非局部效应。对异常值部分和空间接触力相关性的进一步分析表明，在小的机械异质性下，六边形堆积比方形堆积表现出更明显的非局部效应。然而，当组件在机械上变得更加异构时，这种趋势就会逆转。最后，我们确认，在没有粒子重组事件的情况下，接触摩擦仅起到填充稳定的作用，而其变化对粒子间力及其分布几乎没有影响。