This paper presents a fabric tensor-based bounding surface model accounting for anisotropic behaviour (e.g. the dependency of peak strength on loading direction and non-coaxial deformation) of granular materials. This model is developed based on a well-calibrated isotropic bounding surface model. The yield surface is modified by incorporating the back stress which is proportional to a contact normal-based fabric tensor for characterising fabric anisotropy. The evolution law of the fabric tensor, which is dependent on both rates of the stress ratio and the plastic strain, rules that the material fabric tends to align with the loading direction and evolves towards a unique critical state fabric tensor under monotonic shearing. The incorporation of the evolution law leads to a rotational hardening of the yield surface. The anisotropic critical state is assumed to be independent of the initial values of void ratio and fabric tensor. The critical state fabric tensor has the same intermediate stress ratio (i.e. b value) and principal directions as the critical state stress tensor. A non-associated flow rule in the deviatoric plane is adopted, which is able to predict the non-coaxial flow naturally. The stress–strain relation and fabric evolution of model predictions show a satisfactory agreement with DEM simulation results under monotonic shearing with different loading directions. The model is also validated by comparing with laboratory test results of Leighton Buzzard sand and Toyoura sand under various loading paths. The comparison results demonstrate encouraging applicability of the model for predicting the anisotropic behaviour of granular materials.

中文翻译：

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使用基于接触法线的织物张量对颗粒材料进行本构模型

本文提出了一种基于织物张量的边界表面模型，该模型考虑了颗粒材料的各向异性行为（例如，峰值强度对载荷方向的依赖性和非同轴变形）。该模型是基于经过良好校准的各向同性边界表面模型开发的。通过并入与基于接触法线的织物张量成比例的背应力来修正屈服面，以表征织物的各向异性。织物张量的演变规律取决于应力比率和塑性应变，它决定了材料织物趋于与加载方向对齐并在单调剪切下向唯一的临界状态织物张量发展。演化定律的引入导致屈服面的旋转硬化。假定各向异性临界状态与空隙率和织物张量的初始值无关。临界状态织物张量具有相同的中间应力比（即b值）和主要方向作为临界状态应力张量。采用了偏平面内的非关联流规则，能够自然地预测非同轴流。模型预测的应力-应变关系和织物演化表明，在不同载荷方向下单调剪切下，DEM模拟结果令人满意。该模型还通过与Leighton Buzzard沙和Toyoura沙在各种载荷路径下的实验室测试结果进行比较来验证。比较结果证明了该模型在预测粒状材料各向异性行为方面的令人鼓舞的适用性。