摘要
变形和应变是材料在受力或外界环境改变时的客观力学反应,而对该属性的描述是主观的。常规的应变状态表示方法由3个正应变和3个剪应变组成,这种表示方法在测试和表述方面存在诸多不便。为寻求新的应变状态表示方法,在常规剪应变定义基础上提出了一种更具普遍意义的剪应变-广义角应变。提出的广义角应变定义为任意角度的弧度改变量而不再局限于直角。在此基础上,基于应变理论中任意角度改变量的表达式,建立了广义角应变与常规应变状态表示方法之间的关系,并给出了由广义角应变返算常规应变状态的条件和具体方法。在考虑方向均匀分布基础上,着重研究了基于正四面体的广义角应变表示方法和基于等直角四面体的广义角应变表示方法。依据给出的方法,常规应变状态可以表示为这两种广义角应变;由这两种广义角应变也可以得到对应的常规应变状态。从而实现了应变状态的单一表示,即仅用6个广义角应变就可以表示三维应变状态而不必用3个正应变和3个剪应变的联合形式。研究成果为应变状态测试手段的研制开发和本构模型研究提供了新的思路。
Deformation and strain are the objective mechanical responses of materials when the stress or external environment changes, and the description of this property is subjective. The conventional representation of strain state consists of three normal strains and three shear strains, which is inconvenient in testing and expression. In order to find a new method to express the strain state——a more universal shear strain generalized angular strain is proposed based on the shear strain. In this paper, the generalized angular strain is defined as the change of radian at any angle and is no longer limited to the right angle. On this basis, the relationship between the generalized angular strain and the expression of the conventional strain state is established based on the expression of the change of any angle in the strain theory, and the conditions and specific methods for the calculation of the conventional strain state from the generalized angular strain are given. By considering the uniform distribution of directions, the generalized angular strain representation based on tetrahedron and equal right angle tetrahedron are studied. According to the given method, the conventional strain state can be expressed as these two generalized angular strains, and the corresponding conventional strain state can also be obtained from these two generalized angular strains. Thus, a single representation of strain state is realized, that is, only six generalized angular strains can be used to represent three-dimensional strain state without the joint form of three positive strains and three shear strains. The research results of this paper provide a new idea for the development of strain state testing methods and the research of constitutive model.
作者
李顺群
周亚东
李琳
肖成志
LI Shun-qun;ZHOU Ya-dong;LI Lin;XIAO Cheng-zhi(School of Civil Engineering,Tianjin Chengjian University,Tianjin 300384,China;Tianjin Key Laboratory of Soft Soil Characteristics and Engineering Environment,Tianjin 300384,China;School of Civil and Transportation,Hebei University of Technology,Tianjin 300401,China)
出处
《岩土力学》
EI
CAS
CSCD
北大核心
2021年第11期2961-2966,共6页
Rock and Soil Mechanics
基金
国家自然科学基金(No.41877251)
天津市重点研发计划科技支撑重点项目(No.19YFZCSF00820)。
关键词
应变状态
剪应变
广义角应变
四面体
二面角
strain state
shear strain
generalized angular strain
tetrahedron
dihedral angle
