软固体的深层渗透机制,应用于注射和皮肤损伤

Oliver A. Shergold, N. Fleck
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引用次数: 176

摘要

建立了平底和尖头圆柱冲床对软固体的深穿透微观力学模型。软固体被用来代表哺乳动物的皮肤和硅橡胶,并被视为不可压缩的、超弹性的、各向同性的固体,由一项奥格登应变能函数描述。通过平底冲床穿透软固体是通过在穿透器尖端前方传播的ii型环形裂纹的形成。尖头冲头通过在冲头处形成平面i型裂纹的方式穿透,随后推进冲头将裂纹楔开。对于两种冲床推进方式,稳态侵彻载荷的计算方法是将冲床推进过程中所做的功等同于断裂功和固体中储存的应变能之和。对于尖头穿孔器的情况,采用有限元方法考虑楔形物打开平面应变裂纹的情况。分析方法足以满足平底冲床。在这两种模型中,裂纹尺寸是这样的,在冲床上的载荷是最小的。对于两种形状的冲头,预测侵彻压力均随冲头半径的减小而增大,随固体韧性和应变硬化能力的增大而增大。平底冲头的侵彻压力是尖头冲头的两到三倍(假设i型和ii型韧性相等),这与一篇论文中报告的实验观察结果一致。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Mechanisms of deep penetration of soft solids, with application to the injection and wounding of skin
Micromechanical models are developed for the deep penetration of a soft solid by a flat–bottomed and by a sharp–tipped cylindrical punch. The soft solid is taken to represent mammalian skin and silicone rubbers, and is treated as an incompressible, hyperelastic, isotropic solid described by a one–term Ogden strain energy function. Penetration of the soft solid by a flat–bottomed punch is by the formation of a mode–II ring crack that propagates ahead of the penetrator tip. The sharp–tipped punch penetrates by the formation of a planar mode–I crack at the punch tip, followed by wedging open of the crack by the advancing punch. For both modes of punch advance the steady–state penetration load is calculated by equating the work done in advancing the punch to the sum of the fracture work and the strain energy stored in the solid. For the case of a sharp penetrator, this calculation is performed by considering the opening of a plane–strain crack by a wedge using a finite–element approach. Analytical methods suffice for the flat–bottomed punch. In both models the crack dimensions are such that the load on the punch is minimized. For both geometries of punch tip, the predicted penetration pressure increases with diminishing punch radius, and with increasing toughness and strain–hardening capacity of solid. The penetration pressure for a flat–bottomed punch is two to three times greater than that for a sharp–tipped punch (assuming that the mode–I and mode–II toughnesses are equal), in agreement with experimental observations reported in a companion paper.
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