标题： 软可压缩固体的切割力学：力-半径标度与体积模量 显示英文标题

标题： Cutting Mechanics of Soft Compressible Solids: Force-radius scaling versus bulk modulus

摘要： 软固体中的切割力学由于软延性材料在裂纹形核和扩展过程中的复杂行为，呈现出复杂的机械挑战。 最近的研究探讨了连续切割软材料所需的切割力与线（刀）半径之间的关系。 一种典型的简化假设是材料不可压缩性，尽管自然界中没有材料是真正不可压缩的。 在本研究中，我们放松这一假设，并研究材料（不）可压缩性如何影响切割力与材料特性（如韧性及模量）之间的关联。 比值{\mu }/\k{appa}，其中{\mu }和\k{appa}是剪切模量和体积模量，表示材料的压缩性程度，其中不可压缩材料有{\mu }/\k{appa}=0，而较大的{\mu }/\k{appa}提供更高的体积压缩性。 根据之前的观察，我们得到两种切割模式：(i) 高韧性或小线径，以及 (ii) 低韧性或大线径。 模式 (i) 由摩擦耗散主导，而模式 (ii) 由粘附脱粘和/或材料的耐磨性主导。 这些模式由线径与材料的弹性粘附长度之间的比值控制：单轴拉伸下快速断裂时的临界裂纹张开位移。 在大线径模式 (ii) 中，我们的理论结果表明，不可压缩材料需要更大的力。 值得注意的是，定义模式 (i) 和 (ii) 之间过渡线径的材料的弹性粘附长度对于可压缩材料更大，因此这些材料更可能在模式 (i) 中被切割，从而需要更大的切割力。 显示英文摘要

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 {\mu}/\k{appa}, where {\mu} and \k{appa} are the shear and bulk moduli, indicates the material's degree of compressibility, where incompressible materials have {\mu}/\k{appa}=0, and larger {\mu}/\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.