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 behavior.

在本文中，我们研究了用针刺穿软固体的机械问题。这种现象是由针插入的临界条件控制的。针插入涉及物理和几何非线性以及复杂的故障机制。为了克服问题的复杂性，我们将针插入描述为两种针-标本配置之间的急剧过渡，即“压痕”和“穿透”. 急剧的构型变化源于机械不稳定性，并遵循能量最小原则。我们根据施加到针后部的力和针尖朝向材料的轴向位移来描述针-标本系统。在小针位移时，能量上有利的配置是压痕。相反，当针头位移超过临界阈值时，它会通过破坏样品表面来穿透样品。这创造了一种新的大力支持的配置：渗透. 我们的分析考虑了具有球形尖端的圆柱形针，忽略了针和材料之间的摩擦和粘附，并假设了准静态条件。尽管我们的分析在数学上很简单，但我们对针插入力的理论预测已通过实验以惊人的准确性得到验证。我们的方法提供了一种有效的预测工具，可以扩展到解释不同的压头几何形状和材料行为。