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 transvers...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-03-01
|
| Series: | Journal of Composites Science |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-477X/6/3/82 |
| _version_ | 1797470469047189504 |
|---|---|
| author | Shuguang Li Mingming Xu Elena Sitnikova |
| author_facet | Shuguang Li Mingming Xu Elena Sitnikova |
| author_sort | Shuguang Li |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T19:36:40Z |
| format | Article |
| id | doaj.art-85f5101c7baa488499388101a30fadc5 |
| institution | Directory Open Access Journal |
| issn | 2504-477X |
| language | English |
| last_indexed | 2024-03-09T19:36:40Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Journal of Composites Science |
| spelling | doaj.art-85f5101c7baa488499388101a30fadc52023-11-24T01:52:38ZengMDPI AGJournal of Composites Science2504-477X2022-03-01638210.3390/jcs6030082The Formulation of the Quadratic Failure Criterion for Transversely Isotropic Materials: Mathematical and Logical ConsiderationsShuguang Li0Mingming Xu1Elena Sitnikova2Faculty of Engineering, University of Nottingham, Nottingham NG8 1BB, UKFaculty of Engineering, University of Nottingham, Nottingham NG8 1BB, UKFaculty of Engineering, University of Nottingham, Nottingham NG8 1BB, UKThe 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.https://www.mdpi.com/2504-477X/6/3/82quadratic failure functionTsai–Wu criterionfailure envelopestrengthtransverse shear strengthstransversely isotropic materials |
| spellingShingle | Shuguang Li Mingming Xu Elena Sitnikova The Formulation of the Quadratic Failure Criterion for Transversely Isotropic Materials: Mathematical and Logical Considerations Journal of Composites Science quadratic failure function Tsai–Wu criterion failure envelope strength transverse shear strengths transversely isotropic materials |
| title | The Formulation of the Quadratic Failure Criterion for Transversely Isotropic Materials: Mathematical and Logical Considerations |
| title_full | The Formulation of the Quadratic Failure Criterion for Transversely Isotropic Materials: Mathematical and Logical Considerations |
| title_fullStr | The Formulation of the Quadratic Failure Criterion for Transversely Isotropic Materials: Mathematical and Logical Considerations |
| title_full_unstemmed | The Formulation of the Quadratic Failure Criterion for Transversely Isotropic Materials: Mathematical and Logical Considerations |
| title_short | The Formulation of the Quadratic Failure Criterion for Transversely Isotropic Materials: Mathematical and Logical Considerations |
| title_sort | formulation of the quadratic failure criterion for transversely isotropic materials mathematical and logical considerations |
| topic | quadratic failure function Tsai–Wu criterion failure envelope strength transverse shear strengths transversely isotropic materials |
| url | https://www.mdpi.com/2504-477X/6/3/82 |
| work_keys_str_mv | AT shuguangli theformulationofthequadraticfailurecriterionfortransverselyisotropicmaterialsmathematicalandlogicalconsiderations AT mingmingxu theformulationofthequadraticfailurecriterionfortransverselyisotropicmaterialsmathematicalandlogicalconsiderations AT elenasitnikova theformulationofthequadraticfailurecriterionfortransverselyisotropicmaterialsmathematicalandlogicalconsiderations AT shuguangli formulationofthequadraticfailurecriterionfortransverselyisotropicmaterialsmathematicalandlogicalconsiderations AT mingmingxu formulationofthequadraticfailurecriterionfortransverselyisotropicmaterialsmathematicalandlogicalconsiderations AT elenasitnikova formulationofthequadraticfailurecriterionfortransverselyisotropicmaterialsmathematicalandlogicalconsiderations |