Numerical modelling of 3D-printed Fused Filament Fabrication (FFF) specimens with thermoplastic matrices reinforced with continuous fibres is still in its infancy. The existing numerical work is mostly related to the adhesion between printed filaments and not to the mechanical properties. However, the latter are one of the most important parameters that define the structural behaviour of the material.

A numerical three-step multi-scale model is introduced in the present study, concentrating on the fundamental aspect of the elastic properties. The most encountered reinforced Nylon FFF structures with continuous fibres of glass, carbon and, Kevlar, are examined. The concept of Representative Volume Element (RVE) is utilized for the combination of matrix and fibres at the micro-scale and the addition of voids at the meso-scale. Finally, at the macro-scale, tension simulations are performed for specimens with various lay-ups.

The results of the numerical model are validated using analytical models and experimental data. A new analytical micro-mechanical model is developed as an alternative to the more cumbersome Mori–Tanaka model. A series of experimental testing is performed for Kevlar-reinforced Nylon specimens to accompany the limited existing data and aid the validation process. The comparison reveals a good correlation with the analytical models for the micro- and meso-scale and to the experimental data for the macro-scale, leading to a robust conclusion for its validity and efficiency.

带有连续纤维增强的热塑性基体的3D打印熔融长丝加工（FFF）标本的数值模型仍处于起步阶段。现有的数值工作主要与印花长丝之间的粘附力有关，而与机械性能无关。但是，后者是定义材料结构行为的最重要参数之一。

在本研究中引入了一个数值三步多尺度模型，重点是弹性特性的基本方面。研究了使用玻璃，碳和凯夫拉尔纤维连续纤维的最常见的增强尼龙FFF结构。代表性体积元素（RVE）的概念用于微观尺度的基体和纤维的结合以及中观尺度的空隙的增加。最后，在宏观尺度上，对具有各种叠层的样本进行张力模拟。

使用分析模型和实验数据验证了数值模型的结果。开发了一种新的分析微机械模型，以替代较繁琐的Mori-Tanaka模型。对凯夫拉尔增强尼龙标本进行了一系列实验测试，以伴随有限的现有数据并协助验证过程。比较结果表明，该模型与微观和中观规模的分析模型以及宏观规模的实验数据具有良好的相关性，从而得出了有效性和有效性的可靠结论。