School of Civil Engineering, Tianjin Chengjian University, Tianjin, China.
State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, China.
PLoS One. 2021 Nov 18;16(11):e0259655. doi: 10.1371/journal.pone.0259655. eCollection 2021.
The strain state in 3D space is usually expressed by the conventional method of combining three linear and shear strains. Due to the obvious differences between the first two strains, it is necessary to uncover their properties when describing deformation, studying yield and failure, and developing test apparatus or equipment. The difficulties encountered in the above work would be greatly simplified if strain states could be expressed in a single strain form, namely including only linear or shear strains. As a start, this paper explores the meaning and nature of strain states. Then, based on the hypothesis of small deformations, two strain state expressions, the linear strain expression method (LSEM) and shear strain expression method (SSEM), were established for incompressible materials with only linear strain and shear strain as parameters respectively. Furthermore, conditions, implementation steps and specific forms for the application of SSEM in 1D, 2D and 3D strain states are obtained. As an example, two representations based on tetragonal pyramid and rotating tetrahedron are especially given. Therefore, conventional strain representation methods can be expressed as a combination of line strains in a certain direction or a combination of characteristic shear strains. The results of this paper provide a new way for understanding deformation characteristics, revealing yielding process, establishing constitutive models, and developing testing apparatus or equipment.
三维空间中的应变状态通常通过结合三个线应变和剪应变的常规方法来表示。由于前两个应变之间存在明显差异，因此在描述变形、研究屈服和失效以及开发测试仪器或设备时，有必要揭示它们的特性。如果应变状态可以用单一应变形式表示，即仅包括线应变或剪应变，那么在上述工作中遇到的困难将大大简化。本文首先探讨了应变状态的含义和性质。然后，基于小变形假设，为仅具有线应变和剪应变的不可压缩材料分别建立了线性应变表示方法（LSEM）和剪应变表示方法（SSEM）。此外，还获得了 SSEM 在 1D、2D 和 3D 应变状态中的应用条件、实施步骤和具体形式。作为一个例子，特别给出了基于四棱锥和旋转四面体的两种表示方法。因此，传统的应变表示方法可以表示为沿特定方向的线应变的组合或特征剪应变的组合。本文的研究结果为理解变形特性、揭示屈服过程、建立本构模型以及开发测试仪器或设备提供了一种新的途径。
