Abstract Orb webs are strong biological structures that are crucial for orb-weaving spiders’ survival in nature. These light weight and reusable structures not only serve for prey capture but also provide vibration signal transmission to spider. In this paper, we present a model for the spider dragline silk constitutive equation, by considering its biological micro-structure. The model is validated using experimental data. A full model of spider web with two lumped masses (spider at its web center and a prey impacting a radial line) is then developed and its dynamic response due to prey impact is investigated. The results show that the dynamic response of the web is related to the amount of silk materials used in the web construction and may be little affected by the number of radial lines. The effects of pre-stretch on the dynamic response of the web is also investigated. The results show frequency of the vibration is smaller with larger pre-stretch. This is in contrast to the frequency of linear elastic string where the frequency increases with larger pre-stretch. Considering material microstructure and developed constitutive equation, this discrepancy is attributed to the reduction of shear modulus and damage to the dragline silk when pre-stretch is applied. Furthermore, the effects of damage (missing radial line) on the dynamic response of our model web are investigated. The results show that while the prey-impacted radial line transmits the largest force to the spider for undamaged web, for damaged web, other fibers could transmit larger force. The frequency of peak force that is inserted to the spider also shifts to the lower frequencies for damaged web compared to intact web. This may provide a signaling mechanism to spider that its web is damaged and should be repaired. This paper suggests possible sensing mechanisms to spider when the web is subjected to impact or its web is damaged. These suggestions should provide an avenue of research to biologist. The results obtained in this research could lead to development of artificial webs for capturing and repulsing projectile impacting the web or development of sensors.

中文翻译：

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蜘蛛球网在猎物撞击下的动态响应

摘要 圆网是一种强大的生物结构，对织网蜘蛛在自然界中的生存至关重要。这些重量轻且可重复使用的结构不仅用于捕获猎物，还为蜘蛛提供振动信号传输。在本文中，我们通过考虑其生物微结构，提出了蜘蛛拉索丝本构方程的模型。该模型使用实验数据进行验证。然后开发了具有两个集中质量的蜘蛛网的完整模型（蜘蛛在其网中心，猎物撞击径向线），并研究了由于猎物撞击引起的动态响应。结果表明，幅材的动态响应与幅材构造中使用的丝材数量有关，受径向线数的影响可能很小。还研究了预拉伸对幅材动态响应的影响。结果表明，预拉伸越大，振动频率越小。这与线性弹性弦的频率形成对比，其中频率随着更大的预拉伸而增加。考虑到材料微观结构和发展的本构方程，这种差异归因于应用预拉伸时剪切模量的降低和拉铲丝的损坏。此外，还研究了损坏（缺少径向线）对我们模型网动态响应的影响。结果表明，对于未损坏的网，被猎物撞击的径向线向蜘蛛传递的力最大，对于损坏的网，其他纤维可以传递更大的力。与完整的网相比，插入到蜘蛛网的峰值力的频率也转移到受损网的较低频率。这可能会向蜘蛛提供一种信号机制，表明其网已损坏并且应该修复。本文提出了当网受到冲击或网被损坏时蜘蛛可能的感知机制。这些建议应该为生物学家提供研究的途径。在这项研究中获得的结果可能会导致人造网的开发，用于捕获和排斥撞击网的弹丸或传感器的开发。这些建议应该为生物学家提供研究的途径。在这项研究中获得的结果可能会导致人造网的开发，用于捕获和排斥撞击网的弹丸或传感器的开发。这些建议应该为生物学家提供研究的途径。在这项研究中获得的结果可能会导致人造网的开发，用于捕获和排斥撞击网的弹丸或传感器的开发。