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

WANG Xing; KONG Liang; LI Xue-feng

doi:10.11779/CJGE202112004

Volume 43 Issue 12

Dec 2022

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JOURNAL OF MECHANICAL ENGINEERING > 2021 > 43(12): 2180-2189.

WANG Xing, KONG Liang, LI Xue-feng. Generalized non-coaxial theory based on orthogonal decomposition of stress rate[J]. JOURNAL OF MECHANICAL ENGINEERING, 2021, 43(12): 2180-2189. doi: 10.11779/CJGE202112004

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WANG Xing, KONG Liang, LI Xue-feng. Generalized non-coaxial theory based on orthogonal decomposition of stress rate[J]. JOURNAL OF MECHANICAL ENGINEERING, 2021, 43(12): 2180-2189. doi: 10.11779/CJGE202112004

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

doi: 10.11779/CJGE202112004

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

Received Date: 26 Feb 2021
Available Online: 02 Dec 2022
Issue Publish Date: 01 Dec 2021

Abstract

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

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References

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

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