基于应力率正交分解的广义非共轴理论

王兴; 孔亮; 李学丰

doi:10.11779/CJGE202112004

基于应力率正交分解的广义非共轴理论

doi: 10.11779/CJGE202112004

王兴^{1, 2,},
孔亮^{1, 2,, ,},
李学丰³

1.
青岛理工大学理学院,山东　青岛　266033
2.
青岛理工大学土木工程学院,山东　青岛　266033
3.
宁夏大学固体力学研究所,宁夏　银川　750021

基金项目:

国家自然科学基金项目 51778311

宁夏重点研发项目 2018DWHZ0084

宁夏科技创新领军人才计划 KJT2019001

详细信息

作者简介:
王兴(1988— ),男,博士研究生,主要从事岩土本构关系方面的研究。E-mail：1306825892@qq.com。

通讯作者:
*通信作者（E-mail：qdkongliang@163.com）

中图分类号: TU43
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出版历程
- 收稿日期: 2021-02-26
- 网络出版日期: 2022-12-02
- 刊出日期: 2021-12-01

Generalized non-coaxial theory based on orthogonal decomposition of stress rate

WANG Xing^{1, 2
,},
KONG Liang^{1, 2,
, ,},
LI Xue-feng³

1.
School of Sciences, Qingdao University of Technology, Qingdao 266033, China
2.
School of Civil Engineering, Qingdao University of Technology, Qingdao 266033, China
3.
Solid Mechanics Institute, Ningxia University, Yinchuan 750021, China

摘要

摘要: 传统非共轴理论中非共轴塑性应变率与非共轴应力率之间通常采用线性假设并且二者始终同向,这与土体实际的非共轴变形特性不相符。为了弥补这一缺陷,首先基于数学推导证明了总应力率可以分解为6个正交方向上的分量应力率之和,由此揭示出传统非共轴理论中定义的非共轴应力率是由多项正交分量所构成。针对非共轴应力率中的每一正交分量,基于广义塑性力学,通过直接定义加载强度指标、塑性模量和塑性流动方向建立相应的非线性加载机制描述其所诱发的塑性变形。将总的非共轴塑性变形视为每一分量诱发的塑性变形之和,从而建立了一种广义形式的非共轴理论。推导了基于广义非共轴理论建立土体弹塑性模型时的应力应变关系式。针对模型评估的数值试验显示了广义非共轴理论的合理性,从而表明了新建理论能够为土体非共轴模型的建立提供更为广泛的理论基础。
- 传统非共轴理论 /
- 应力率正交分解 /
- 广义非共轴理论 /
- 数值试验
Abstract: In the traditional non-coaxial theories, linear assumption is usually made between non-coaxial plastic strain rate and non-coaxial stress rate, and they are always in the same direction, which is inconsistent with the real non-coaxial deformation characteristics of soils. In order to make up for this defect, firstly, it is proved by the mathematical derivation that the total stress rate can be decomposed into the sum of the component stress rates in six orthogonal directions, and then it is revealed that the non-coaxial stress rate defined in the traditional non-coaxial theories is composed of multiple orthogonal components. For each orthogonal component of the non-coaxial stress rate, based on the generalized plastic mechanics, the corresponding nonlinear loading mechanism is established by defining the loading strength index, plastic modulus and plastic flow direction explicitly, and the total non-coaxial plastic deformation is regarded as the sum of the plastic deformation induced by each component, thus a generalized non-coaxial theory is established. The stress-strain relationship of elastoplastic model for soils based on the generalized non-coaxial theory is derived. The numerical tests for model evaluation show the rationality of the generalized non-coaxial theory, which preliminarily indicates that the new theory can provide a broader theoretical basis for the establishment of non-coaxial model for soils.
- traditional non-coaxial theory /
- orthogonal decomposition of stress rate /
- generalized non-coaxial theory /
- numerical test

HTML全文

图 1 传统的非共轴理论^[14]

Figure 1. Traditional non-coaxial theory by Ref. [14]

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图 2 传统的非共轴理论^[15]

Figure 2. Traditional non-coaxial theory by Ref. [15]

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图 3 传统的非共轴理论^[16]

Figure 3. Traditional non-coaxial theory by Ref. [16]

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图 4 塑性流动方向^[22]

Figure 4. Plastic flow direction by Ref [22]

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图 5 几何映射方法示意图

Figure 5. Schematic diagram of geometric mapping method

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图 6 插值系数法示意图

Figure 6. Schematic diagram of interpolation coefficient method

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图 7 加载与反向加载

Figure 7. Loading and reverse loading

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图 8 第二类非共轴加载

Figure 8. Second kind of non-coaxial loading

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图 9 应力探测示意图

Figure 9. Schematic diagram of stress probe tests

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图 10 应变探测示意图

Figure 10. Schematic diagram of stress probe tests

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图 11 应力率响应包络线

Figure 11. Response envelopes of stress rate

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