This paper presents a micro and macromechanical model to estimate the grading evolution and plastic strain caused by particle crushing in the isotropic compression of granular materials. A joint‐probability particle crushing criterion of the maximum contact force and the particle strength is proposed to calculate the incremental particle crushing probability. The dependence of the contact force and particle strength during a multistage loading process is recognized. The distribution of the maximum contact force and the magnitude of the mean contact force are strictly derived from the stress‐force relationship and maximizing the statistical entropy. The coordination number of polydisperse particles is derived from the geometric relationship and applies to any grading curve, which enables the consideration of the coupling effects of particle crushing and grading evolution during a multistage loading process. A multipoint load particle crushing criterion involving the particle strength size effect is adapted. To simulate the grading evolution, the fractal distribution assumption and Markov chain model are applied to describe the fragmentation mess after crushing. Finally, following the work equation by Mcdowell and Bolton, the energy consumption of particle crushing and the corresponding plastic strain are correlated with the increase in the particle surface area. The model is verified by published experimental data of silica sand with different initial grading curves and carbonate sand with different grain sizes.

中文翻译：

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基于概率方法和能量方面的颗粒材料破碎的微宏力学压缩模型

本文提出了一种微观和宏观力学模型，用于估计颗粒材料在各向同性压缩过程中由于颗粒破碎而引起的梯度演化和塑性应变。提出了最大接触力和颗粒强度的联合概率颗粒破碎准则，以计算增加的​​颗粒破碎概率。认识到在多级加载过程中接触力和颗粒强度的相关性。最大接触力的分布和平均接触力的大小严格根据应力与力的关系得出，并最大程度地提高了统计熵。多分散颗粒的配位数是根据几何关系得出的，适用于任何渐变曲线，这样就可以考虑在多阶段加载过程中颗粒粉碎和分级演化的耦合效应。适应了涉及颗粒强度尺寸效应的多点负载颗粒破碎准则。为了模拟分级的演变过程，采用分形分布假设和马尔可夫链模型来描述破碎后的破碎碎片。最后，按照Mcdowell和Bolton的工作方程，颗粒破碎的能耗和相应的塑性应变与颗粒表面积的增加相关。通过公开的具有不同初始分级曲线的硅砂和具有不同粒度的碳酸盐砂的实验数据验证了该模型。适应了涉及颗粒强度尺寸效应的多点负载颗粒破碎准则。为了模拟分级的演变过程，采用分形分布假设和马尔可夫链模型来描述破碎后的破碎碎片。最后，按照Mcdowell和Bolton的工作方程，颗粒破碎的能耗和相应的塑性应变与颗粒表面积的增加相关。通过公开的具有不同初始分级曲线的硅砂和具有不同晶粒尺寸的碳酸盐砂的实验数据验证了该模型。适应了涉及颗粒强度尺寸效应的多点负载颗粒破碎准则。为了模拟分级的演变过程，采用分形分布假设和马尔可夫链模型来描述破碎后的破碎碎片。最后，按照Mcdowell和Bolton的工作方程，颗粒破碎的能耗和相应的塑性应变与颗粒表面积的增加相关。通过公开的具有不同初始分级曲线的硅砂和具有不同粒度的碳酸盐砂的实验数据验证了该模型。根据Mcdowell和Bolton的工作方程，颗粒破碎的能耗和相应的塑性应变与颗粒表面积的增加相关。通过公开的具有不同初始分级曲线的硅砂和具有不同粒度的碳酸盐砂的实验数据验证了该模型。根据Mcdowell和Bolton的工作方程，颗粒破碎的能耗和相应的塑性应变与颗粒表面积的增加相关。通过公开的具有不同初始分级曲线的硅砂和具有不同粒度的碳酸盐砂的实验数据验证了该模型。