On the objectivity of the nonlinear along-fibre shear stress–strain relationship for unidirectionally fibre-reinforced composites

Li, Shuguang; Xu, Mingming; Yan, Shibo; Sitnikova, Elena

Abstract

The nonlinear along-fibre shear stress–strain relationship for unidirectionally fibre-reinforced composites has been investigated in this paper aiming at its applications in general 3D stress conditions in a consistent manner. So far, such relationship has only been addressed in plane stress conditions. In this paper, it has been shown that its straightforward generalisation to 3D stress states lacks objectivity, which is a basic requirement for all theoretical studies of physical problems. A new formulation is proposed based on the stress invariants and the complementary strain energy guided by the rational theoretical framework of nonlinear elasticity. A consistent and objective stress–strain relationship has been obtained and verified through an example of application to a torsion problem.

• Journal Article Type: Article
• Acceptance Date: Apr 3, 2021
• Online Publication Date: Mar 14, 2021
• Publication Date: Apr 1, 2021
• Deposit Date: Aug 31, 2021
• Publicly Available Date: Sep 6, 2021
• Journal: Journal of Engineering Mathematics
• Print ISSN: 0022-0833
• Electronic ISSN: 1573-2703
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 127
• Issue: 1
• DOI: https://doi.org/10.1007/s10665-021-10098-3
• Keywords: General Engineering; General Mathematics
• Public URL: https://nottingham-repository.worktribe.com/output/5403095
• Publisher URL: https://link.springer.com/article/10.1007%2Fs10665-021-10098-3
• Additional Information: Received: 2 October 2020; Accepted: 23 January 2021; First Online: 14 March 2021