刺穿软固体：针插入的力学理论
Piercing soft solids: A mechanical theory for needle insertion
AI总结：
该研究提出针插入软固体的力学理论，将其视为压痕到穿透的能量驱动构型突变，模型预测与实验高度吻合，可扩展至不同压头与材料场景。
摘要：
本文研究了用针穿刺软固体的力学问题，该现象由针插入的临界条件主导。针插入过程涉及物理与几何非线性以及复杂的失效机制。为克服问题的复杂性，我们将针插入描述为“压痕”与“穿透”两种针-试样构型之间的突变，这种构型突变源于力学不稳定性且遵循能量最小原理。我们以施加在针尾部的力以及针尖朝向材料的轴向位移来描述针-试样系统。当针位移较小时，能量上更有利的构型是压痕；反之，当针位移超过临界阈值时，针会通过 rupturing 试样表面实现穿透，形成新的能量有利构型：穿透。我们的分析针对带球形针尖的圆柱形针，忽略针与材料间的摩擦与粘附，并假设为准静态条件。尽管分析的数学形式较为简单，但我们关于针插入力的理论预测与实验吻合，精度出人意料。本方法提供了一种有效的预测工具，可扩展应用于不同压头几何形状与材料行为的研究。
英文摘要：
In this paper we investigate the mechanical problem of piercing a soft solid body with a needle. This phenomenon is controlled by the critical condition of needle insertion. Needle insertion involves physical and geometrical nonlinearities and a complex failure mechanism. To overcome the complexity of the problem, we describe needle insertion as a sharp transition between two needle-specimen configurations, namely "indentation" and "penetration". The sharp configurational change emerges from a mechanical instability and follows the principle of energy minimum. We describe the needle-specimen system in terms of the force applied to the back of the needle and the axial displacement of the needle tip toward the material. At small needle displacements, the energetically favoured configuration is indentation. Conversely, when the needle displaces beyond a critical threshold, it penetrates the specimen by rupturing its surface. This creates a new energetically favoured configuration: penetration. Our analysis considers a cylindrical needle with a spherical tip, neglects friction and adhesion between the needle and the material, and assumes quasi-static conditions. Despite the mathematical simplicity of our analysis, our theoretical predictions on the needle insertion force have been validated against experiments with surprising accuracy. Our method provides an effective predictive tool, which can be extended to account for different indenter geometry and material behaviour.
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