分数阶塑性力学及其砂土本构模型

孙逸飞; 高玉峰; 鞠 雯

doi:10.11779/CJGE201808021

分数阶塑性力学及其砂土本构模型 English Version

1. 河海大学教育部岩土力学与堤坝工程教育部重点实验室，江苏南京 210098；
2. 中国核工业建设集团华兴建筑公司，江苏南京 210019

基金项目: 国家自然科学基金重点项目（41630638）; 国家重点基础研; 究发展计划（“973”计划）项目（2015CB057901）; 中央高校基本科; 研业务费项目（2017B05214）

详细信息

作者简介:
孙逸飞(1988- ),男,副教授,主要研究分数阶塑性力学与粗粒土本构模型。E-mail: sunny@hhu.edu.cn。

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出版历程
- 收稿日期: 2017-07-18
- 发布日期: 2018-08-24

Fractional plasticity and its application in constitutive model for sands

1. Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing 210098, China;
2. China Nuclear Industry Huaxing Construction Company Limited, Nanjing 210019, China

摘要

摘要: 砂土的剪胀以及应力-应变关系通常依赖于其物质状态; 其塑性流动方向不再与加载方向重合,而是随其状态改变而改变。为了描述这一非关联特性,传统的岩土塑性理论通常需要额外假定一个独立于屈服面的塑性势面,并人为地将塑性势面相关的参数与状态参数唯像地关联在一起。从而,使得模型参数增多、部分参数缺乏物理意义。不同于与传统塑性力学,分数阶塑性力学基于非局域性的微分算子和梯度,其在某一应力点的微分方向不仅与该点的应力状态有关,还与到达该应力点的加载历史、过程相关; 从而,无需额外假定塑性势面（或屈服面）,仅需要对已有屈服面（或塑性势面）进行分数阶微分求解,便可以建立砂土的状态依赖分数阶弹塑性力学模型。最后,通过模拟几种不同砂土的三轴排水与不排水试验结果,发现：所提出的模型可以较好地描述砂土在不同初始状态及加载条件下的应力应变行为。
- 分数阶微积分 /
- 分数阶塑性力学 /
- 本构模型 /
- 状态参数 /
- 砂土
Abstract: It has been recognized that the stress-dilatancy and stress-strain relationship of sand depend on the material state. The plastic flow direction does not usually coincide with the corresponding loading direction but evolves with the material state. To consider such non-associativity, an additional plastic potential surface that is independent of the yielding surface is usually assumed. A state parameter is then incorporated into the material constants of the plastic potential surface, which brings more model parameters where some of them even have no physical meanings. Unlike the traditional plasticity theory, the fractional plasticity is established on non-local fractional operators and gradients where the derivatives of a stress point are determined not only by the state of the stress point of interest but also by the loading history before reaching this point. Therefore, without the necessity of assuming an additional plastic potential (yielding) surface, a state-dependent non-associated fractional plasticity model for sands can be easily developed by conducting fractional order derivatives on the yielding (plastic potential) surface. To validate the proposed model, a series of drained and undrained triaxial compression test results of different sands are simulated and then compared. A good agreement between the model simulations and the corresponding test results can be observed.
- fractional calculus /
- fractional plasticity /
- constitutive model /
- state parameter /
- sand

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参考文献(24)

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