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经典连续介质理论的粘塑性本构关系缺乏材料尺度的相关性,难以表征颗粒材料流变的尺寸效应,而Cosserat连续体中的内禀特征长度为刻画材料的尺寸效应提供了一种可能途径。该文旨在Cosserat连续体的理论框架下发展Perzyna粘塑性模型,以探讨颗粒材料流变的尺寸效应与影响机制。首先基于Drucker-Prager屈服准则导出了Cosserat连续体粘塑性模型的一致性算法,获得了过应力本构方程积分算法与一致切向模量的封闭形式,并在ABAQUS二次平台上采用用户自定义单元(UEL)予以程序实现。有限元数值算例模拟了软岩试样的三轴压缩蠕变和两种堆石料试样在常规三轴条件下的蠕变和应力松弛,数值预测结果与相应试验结果具有较好的一致性,表明该流变模型的适应性。同时,将颗粒的球型指数、圆度和平均粒径作为表征颗粒材料内禀特征长度的一种度量,以反映颗粒材料的试样尺寸及其颗粒粒径与形状对流变过程中的轴向应变、偏应变和偏应力的影响关系,表明所发展的流变模型可以捕捉颗粒材料流变行为的压力相关性和尺寸效应。
The visco-plastic constitutive relationship of classical continuum theory lacks the correlation between material scales and it is difficult to characterize the size effect of the rheological behavior of the granular material. The intrinsic feature length of the Cosserat continuum provides a possible way to characterize the size effect of the material. This paper aims to develop the Perzyna viscoplastic model under the framework of Cosserat continuum in order to investigate the size effect and mechanism of rheological behavior of granular materials. First, based on the Drucker-Prager yield criterion, the consistency algorithm of the Cosserat continuum viscoplastic model is derived. The integral algorithm of the over stress constitutive equation and the closed form of the consistent tangential modulus are obtained. The user-defined ABAQUS secondary platform Unit (UEL) to be programmed. The finite element numerical examples simulate the triaxial compression creep of soft rock samples and the creep and stress relaxation of two kinds of rockfill samples under the normal triaxial conditions. The numerical prediction results are in good agreement with the corresponding experimental results , Indicating the adaptability of the rheological model. At the same time, the spherical index, roundness and average particle size of the particles were taken as a measure of the intrinsic characteristic length of the particulate material to reflect the sample size of the particulate material and the particle size and shape of the particles in the axial The relationship between strain, partial strain and deviatoric stress shows that the developed rheological model can capture the pressure dependence and size effect of the rheological behavior of granular materials.