A Numerical Study on the Dynamic Tensile Behavior of Helical Auxetic Yarns
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摘要: 螺旋拉胀纱线是由高模量纱线螺旋式包缠低模量纱线所形成的复合纱线，在纵向拉伸下呈现沿横向膨胀的负泊松比现象。为揭示其抗冲击机理，基于有限元模拟，开展了螺旋拉胀纱线的动态拉伸行为研究，发现在螺旋拉胀纱线中存在着分别由包缠纱和芯纱所主导的一快和一慢两个应力波，且在两个波阵面之间横向变形和Mises应力均随时间和空间周期性变化。给出了双波波速随加载速度和摩擦系数的变化规律，并结合等效模量的概念进行了定性讨论。模拟结果还显示，螺旋拉胀纱线中内能与动能基本相等，且摩擦对能量吸收有重要贡献。Abstract: A helical auxetic yarn (HAY) is a composite yarn which is formed by helically wrapping a high modulus yarn on a low modulus yarn, and it exhibits the so-called negative Poisson’s ratio phenomenon of transverse expansion upon longitudinal stretching. To reveal the mechanisms of HAY’s shock resistance, a study on its dynamic tensile behavior was carried out based on finite element simulation. It was found that there are two stress waves in a shock loaded HAY, one is a fast wave and another is a slow wave which are dominated respectively by the wrap yarn and the core yarn, and between the two wavefronts, both the transverse deformation and the Mises stress change periodically with time and space. The relationships between the wave speeds and loading velocity and friction coefficient are presented and qualitatively discussed based on the concept of effective modulus. The simulation results also show that the internal energy is almost equal to the kinetic energy, and friction has a significant contribution to energy absorption.
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图 1 准静态模拟呈现的拉胀效应：模型在拉伸度为0、10.5%、35.0%时的构型
Figure 1. Auxetic effect revealed from the quasistatic simulation: configurations of the model at elongations of 0, 10.5% and 35.0%
图 2 0.1 ms时某典型算例的对数应变云图
Figure 2. Logarithmic strain contour of a typical simulation at 0.1 ms
图 4 不同加载速度下的快波（a）和慢波（b）波速
Figure 4. Speeds of fast wave (a) and slow wave (b) at different loading velocities
图 5 不同摩擦系数下的快波（a）和慢波（b）波速
Figure 5. Speeds of fast wave (a) and slow wave (b) at different friction coefficients
图 6 典型算例中的内能、动能及摩擦耗能的时间历史曲线
Figure 6. Time histories of internal energy, kinetic energy and friction dissipation for a typical simulation
表 1 计算模型的材料和几何参数
Table 1. Material and geometry parameters of the computational model
Yarns E/GPa $\;\mu $ Diameter/mm Density/(kg·m−3) Mesh size/mm Wrap angle/(°) Wrap yarn 143.0 0.3 0.18 1440 0.09 20 Core yarn 1.6 0.4 0.64 1500 0.10 
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