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基于Feng Y T提出的精确缩尺方法,即根据几何相似、静力相似、动力相似3个相似原理建立一套缩尺准则,使得缩尺前后模型的力学响应保持一致。首次将该理论应用于颗粒材料的流变分析当中,采用Burgers黏塑性蠕变模型,引入流变参数,在原缩尺准则上进行理论推导,得到在二维和三维条件下的缩尺准则;其次在理论推导的基础上进行数值仿真验证。研究结果表明:严格按照拟定的缩尺准则选取参数后,缩尺后模型的力学响应能够保证和原尺寸模型完全一致,计算误差在3%以内,同时简要探讨了时间步长、黏性系数、颗粒数目、比尺数对数值试验的影响,为数值试验中相关参数的选取以及如何让数值模型反映材料真实的力学行为提供了有效参考。另外,由于缩尺模型采用与原模型相同的颗粒数目、颗粒形状、颗粒压实状态和比尺数,揭示了等比例缩尺对材料流变行为的影响。
Based on the precise scale method proposed by Feng Y T, a set of scale rule is established based on three similar principles: geometric similarity, static similarity, and dynamic similarity, so that the mechanical responses of the scale model are consistent. The theory was applied to the rheological analysis of granular materials for the first time. The Burgers visco-plastic creep model was used to introduce the rheological parameters. Theoretical deductions were made on the original scale rule, and the scale rule under two-dimensional and three-dimensional conditions was obtained; Based on the theoretical derivation, numerical simulation verification is performed. The research results show that the mechanical response of the scaled model can be guaranteed to be exactly the same as the original size model, the calculation error is within 3%, and the time step, the viscosity coefficient, are briefly discussed. The influence of the number of particles and the number of scales on the numerical test provides an effective reference for the selection of relevant parameters in the numerical test and how to allow the numerical model to reflect the true mechanical behavior of the material. In addition, because the scale model uses the same particle number, particle shape, particle compaction state, and scale number as the original model, it reveals the influence of equal-scale scale on the rheological behavior of the material.