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.

本文针对单向纤维增强复合材料的非线性沿纤维剪切应力-应变关系进行了研究，旨在以一致的方式将其应用于一般3D应力条件。到目前为止，仅在平面应力条件下解决了这种关系。在本文中，已证明其对3D应力状态的直接概括缺乏客观性，这是所有物理问题理论研究的基本要求。在非线性弹性的合理理论框架的指导下，基于应力不变性和互补应变能，提出了一种新的公式。通过应用到扭转问题的实例，已经获得了一致且客观的应力-应变关系。