一种考虑尺寸效应的颗粒材料流变模型及其验证

A RHEOLOGY MODEL INCORPORATING SCALE EFFECT FOR GRANULAR MATERIALS AND ITS VALIDATIONS

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。

Viscoplastic models in classical continua theory were unable to incorporate scale effect for granular materials due to the independence on scale. Cosserat continua theory with the internal length scale provides a possible approach to incorporate scale effect. A Perzyna＇s viscoplastic model is developed based on Cosserat continua theory to investigate the scale effect on rheology for granular materials. The consistent operator in the framework of Cosserat continua theory is derived. The constitutive integration algorithm and its closed form of the consistent tangent modulus are also derived. The code is implemented by User-defined elements （UEL） in ABAQUS platform. Triaxial compression creep tests of soft rock, creep and stress relaxation tests of rockfill, are simulated by finite element method. The results using finite element analysis show good agreement with the experimental data in literatures, which verified the model. Meanwhile, sphericity index, roundness index, and mean diameter of the particle are adopted as measures of the internal length scale to incorporate the influence of particle size and shape on axial strain, deviator strain and deviator stress, showing that the pressure-sensitive and the scale effect on rheology for granular materials can be captured.