The formulation of the quadratic failure criterion for transversely isotropic materials: mathematical and logical considerations
The formulation of the quadratic failure criterion for transversely isotropic materials: mathematical and logical considerations
The quadratic function of the original Tsai–Wu failure criterion for transversely isotropic materials is re-examined in this paper. According to analytic geometry, two of the troublesome coefficients associated with the interactive terms—one between in-plane direct stresses and one between transverse direct stresses—can be determined based on mathematical and logical considerations. The analysis of the nature of the quadratic failure function in the context of analytic geometry enhances the consistency of the failure criterion based on it. It also reveals useful physical relationships as intrinsic properties of the quadratic failure function. Two clear statements can be drawn as the outcomes of the present investigation. Firstly, to maintain its basic consistency, a failure criterion based on a single quadratic failure function can only accommodate five independent strength properties, viz. the tensile and compressive strengths in the directions along fibres and transverse to fibres, and the in-plane shear strength. Secondly, amongst the three transverse strengths—tensile, compressive and shear—only two are independent.
failure envelope, quadratic failure function, strength, transverse shear strengths, transversely isotropic materials, Tsai–Wu criterion
Li, Shuguang
f99c53b3-e42e-456f-97df-4c4e06de4a40
Xu, Mingming
b1989557-3ad2-4fa9-8d94-a36c95524321
Sitnikova, Elena
e0c2f901-24fe-43d0-88e8-76f415675104
7 March 2022
Li, Shuguang
f99c53b3-e42e-456f-97df-4c4e06de4a40
Xu, Mingming
b1989557-3ad2-4fa9-8d94-a36c95524321
Sitnikova, Elena
e0c2f901-24fe-43d0-88e8-76f415675104
Li, Shuguang, Xu, Mingming and Sitnikova, Elena
(2022)
The formulation of the quadratic failure criterion for transversely isotropic materials: mathematical and logical considerations.
Journal of Composites Science, 6 (3), [82].
(doi:10.3390/jcs6030082).
Abstract
The quadratic function of the original Tsai–Wu failure criterion for transversely isotropic materials is re-examined in this paper. According to analytic geometry, two of the troublesome coefficients associated with the interactive terms—one between in-plane direct stresses and one between transverse direct stresses—can be determined based on mathematical and logical considerations. The analysis of the nature of the quadratic failure function in the context of analytic geometry enhances the consistency of the failure criterion based on it. It also reveals useful physical relationships as intrinsic properties of the quadratic failure function. Two clear statements can be drawn as the outcomes of the present investigation. Firstly, to maintain its basic consistency, a failure criterion based on a single quadratic failure function can only accommodate five independent strength properties, viz. the tensile and compressive strengths in the directions along fibres and transverse to fibres, and the in-plane shear strength. Secondly, amongst the three transverse strengths—tensile, compressive and shear—only two are independent.
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jcs-06-00082
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Accepted/In Press date: 1 March 2022
Published date: 7 March 2022
Keywords:
failure envelope, quadratic failure function, strength, transverse shear strengths, transversely isotropic materials, Tsai–Wu criterion
Identifiers
Local EPrints ID: 497763
URI: http://eprints.soton.ac.uk/id/eprint/497763
ISSN: 2504-477X
PURE UUID: e563e1d2-4082-4e90-95eb-526ea815238a
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Date deposited: 30 Jan 2025 17:59
Last modified: 22 Aug 2025 02:46
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Author:
Shuguang Li
Author:
Mingming Xu
Author:
Elena Sitnikova
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