软可压缩固体的切割力学：力-半径标度与体积模量
Cutting Mechanics of Soft Compressible Solids: Force-radius scaling versus bulk modulus
AI总结：
本文研究软固体切割中材料可压缩性对切割力与线半径关系的影响，发现不可压缩材料在大半径状态下需更大切割力，而可压缩材料因弹性-内聚长度更大更易处于摩擦主导状态并需更大切割力。
摘要：
软固体中的切割力学由于软韧性材料在裂纹成核和扩展过程中的复杂行为而构成一个复杂的力学挑战。近期研究探索了连续切割软材料所需的切割力与切割线（刀片）半径之间的关系。一个典型的简化假设是材料不可压缩，尽管自然界中没有任何材料真正不可压缩。在本研究中，我们放宽这一假设，考察材料的（不可）压缩性如何影响切割力与材料性质（如韧性和模量）之间的相关性。比值 μ/κ（其中 μ 和 κ 分别为剪切模量和体积模量）表征材料的可压缩程度，不可压缩材料对应 μ/κ=0，而较大的 μ/κ 表示更高的体积可压缩性。基于先前的观察，我们得到两种切割状态：（i）高韧性或小线半径，以及（ii）低韧性或大线半径。状态（i）由摩擦耗散主导，而状态（ii）由粘附脱粘和/或材料的耐磨性主导。这些状态由线半径与材料弹性-内聚长度的比值控制：即单轴拉伸下快速断裂时的临界裂纹张开位移。在大半径状态（ii）下，我们的理论发现表明不可压缩材料需要更大的力。然而值得注意的是，材料的弹性-内聚长度（它定义了状态（i）和（ii）之间的转变线半径）对于可压缩材料更大，因此可压缩材料更可能在状态（i）下被切割，从而需要更大的切割力。
英文摘要：
Cutting mechanics in soft solids present a complex mechanical challenge due to the intricate behavior of soft ductile materials as they undergo crack nucleation and propagation. Recent research has explored the relationship between the cutting force needed to continuously cut a soft material and the radius of the wire (blade). A typical simplifying assumption is that of material incompressibility, albeit no material in nature is really incompressible. In this study, we relax this assumption and examine how material (in)compressibility influences the correlation between cutting forces and material properties like toughness and modulus. The ratio μ/\k{appa}, where μ and \k{appa} are the shear and bulk moduli, indicates the material's degree of compressibility, where incompressible materials have μ/\k{appa}=0, and larger μ/\k{appa} provide higher volumetric compressibility. Following previous observations, we obtain two cutting regimes: (i) high toughness or small wire radius, and (ii) low toughness or large wire radius. Regime (i) is dominated by frictional dissipation, while regime (ii) is dominated by adhesive debonding and/or the wear resistance of the material. These regimes are controlled by the ratio between the wire radius and the elasto-cohesive length of the material: the critical crack opening displacement at fast fracture under uniaxial tension. In the large radius, regime (ii), our theoretical findings reveal that incompressible materials require larger forces. Notably, however, the elasto-cohesive length of the material, defining the transition wire radius between regimes (i) and (ii), is larger for compressible materials, which are therefore more likely to be cut in regime (i), and thus requiring larger cutting forces.
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