1. Line strain representation and shear strain representation of 3D strain states
- Author
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Jianbao Fu, Shunqun Li, Xuelei Cheng, Pan Lin, and Ran Hai
- Subjects
Yield (engineering) ,Science ,Vector Spaces ,Materials Science ,Material Properties ,Equipment ,Solid Mechanics ,Stereochemistry ,Shear stress ,Representation (mathematics) ,Shear Stresses ,Mathematics ,Damage Mechanics ,Multidisciplinary ,Strain (chemistry) ,Physics ,Mathematical analysis ,Classical Mechanics ,Molecular Strains ,State (functional analysis) ,Models, Theoretical ,Deformation ,Elasticity ,Shear (sheet metal) ,Chemistry ,Algebra ,Linear Algebra ,Physical Sciences ,Tetrahedron ,Medicine ,Engineering and Technology ,Mechanical Stress ,Deformation (engineering) ,Shear Strength ,Research Article - Abstract
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.
- Published
- 2021