Lavrentyev Institute of Hydrodynamics, pr. Lavrentyeva 15, Novosibirsk, Russia, 630090.
Novosibirsk State University, ul. Pirogova 1, Novosibirsk, Russia, 630090.
Biomech Model Mechanobiol. 2021 Feb;20(1):323-337. doi: 10.1007/s10237-020-01388-3. Epub 2020 Oct 3.
Mechanical behaviour of pre-stressed fibre-reinforced composites is modelled in a geometrically exact setting. A general approach which includes two different reference configurations is employed: one configuration corresponds to the load-free state of the structure and another one to the stress-free state of each material particle. The applicability of the approach is demonstrated in terms of a viscoelastic material model; both the matrix and the fibre are modelled using a multiplicative split of the deformation gradient tensor; a transformation rule for initial conditions is elaborated and specified. Apart from its simplicity, an important advantage of the approach is that well-established numerical algorithms can be used for pre-stressed inelastic structures. The interrelation between the advocated approach and the widely used "opening angle" approach is clarified. A full-scale FEM simulation confirms the main predictions of the "opening angle" approach. A locking effect is discovered: in some cases the opening angle of the composite is essentially smaller than the opening angles of its individual layers. Thus, the standard cutting test typically used to analyse pre-stresses does not carry enough information and more refined experimental techniques are needed.
预应力纤维增强复合材料的力学行为在几何精确的环境中进行建模。采用了一种包括两种不同参考配置的通用方法：一种配置对应于结构的无负载状态，另一种对应于每个材料颗粒的无应力状态。该方法的适用性通过粘弹性材料模型来证明；基体和纤维都使用变形梯度张量的乘法分解进行建模；阐述并指定了初始条件的转换规则。除了简单性之外，该方法的一个重要优点是可以为预应力弹塑性结构使用成熟的数值算法。提倡的方法和广泛使用的“张开角”方法之间的关系得到了澄清。全尺寸有限元模拟证实了“张开角”方法的主要预测。发现了一种锁定效应：在某些情况下，复合材料的张开角实质上小于其各个层的张开角。因此，通常用于分析预应力的标准切割测试没有提供足够的信息，需要更精细的实验技术。
