基于二维最简颗粒排列的线性与赫兹模型参数研究

Research on the relationship of the parameters between the linear model and the Hertz model based on the two-dimensional simple particle arrangement

为了研究PFC2D数值分析中线性接触模型与赫兹接触模型细观参数的关系,以规则颗粒排列为基础,推导了在总应力-应变等效的情况下,赫兹模型剪切模量、泊松比和线性接触模型法向刚度的关系。在此基础上,通过数值模拟的方法,验证了两个模型细观参数的关系表达式。结果表明:相同条件下,赫兹接触模型的剪切模量随着其泊松比的增大而线性减小,随着线性接触模型法向刚度的增大而指数增大。研究成果表明,在总应力-应变等效的情况下,可以用线性接触模型代替赫兹接触模型进行数值模拟研究。

In order to study the relationship between the linear model and the mesoscopic parameters of the Hertz model in the numerical analysis of PFC2D,based on the regular particle arrangement,the study has derived the shear modulus and Poisson’s ratio in Hertz contact model,and the normal stiffness in linear contact model under the circumstances of equivalent stress-strain in total.On this basis,the relational expressions of the mesoscopic parameters of the two models are verified by numerical simulation.The results show that under the same conditions,the shear modulus of the Hertz contact model decreases linearly with the increase of Poisson’s ratio,and increases exponentially with the increase of the normal stiffness of the linear contact model.The study shows that in the case of total stress-strain equivalent,a linear model can be used instead of the Hertz contact model for numerical simulation.