Based on a numerical model to simulate the static behaviour of a smooth fibre extracted from a cementitious matrix, a rate dependent friction law, widely used in earthquake engineering for steady-state slip phenomena, is proposed to capture the rate effect observed in dynamic pull-out tests for both smooth and hooked-end fibres. After calibrating the friction coefficients with the experimental results of smooth fibres, the model is subsequently applied to predict the pullout behaviour of both smooth and hooked-end fibres at different inclination angles ( $$0^{\circ }$$ 0 ∘ , $$30^{\circ }$$ 30 ∘ and $$60^{\circ }$$ 60 ∘ ) loaded at three different velocities (0.01, 0.1 and 1 mm/s). The global tendency of all the pull-out curves was captured, fibre’s cross sectional deformations were also reproduced remarkably well. Moreover, the developed model helps to cast light on the different mechanisms related to the pull-out process.

中文翻译：

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平滑纤维和钩状纤维的倾斜纤维拉拔速率效应：数值研究

基于模拟从水泥基体中提取的光滑纤维的静态行为的数值模型，提出了一种在地震工程中广泛用于稳态滑动现象的速率相关摩擦定律，以捕捉在动态拉动中观察到的速率效应。对光滑和钩端纤维进行测试。在用光滑纤维的实验结果校准摩擦系数后，该模型随后被应用于预测光滑纤维和钩端纤维在不同倾角 ($$0^{\circ}$$ 0 ∘ , $$30 ^{\circ }$$ 30 ∘ 和 $$60^{\circ }$$ 60 ∘ ) 以三种不同的速度（0.01、0.1 和 1 mm/s）加载。捕获了所有拉出曲线的整体趋势，纤维的横截面变形也得到了很好的再现。而且，