Cutting mechanics in soft solids have been a subject of study for several decades, an interest fuelled by the multitude of its applications, including material testing, manufacturing, and biomedical technology. Wire cutting is the simplest model system to analyze the cutting resistance of a soft material. However, even for this simple system, the complex failure mechanisms that underpin cutting are still not completely understood. Several models that connect the critical cutting force to the radius of the wire and the key mechanical properties of the cut material have been proposed. An almost ubiquitous simplifying assumption is a state of plane (and anti-plane) strain in the material. In this paper, we show that this assumption can lead to erroneous conclusions because even such a simple cutting problem is essentially three-dimensional. A planar approximation restricts the analysis to the stress distribution in the mid-plane. However, through finite element modeling, we reveal that the maximal tensile stress - and thus the likely location of cut initiation - is in fact located in the front plane. Friction reduces the magnitude of this stress, but this detrimental effect can be counteracted by large slice-to-push (shear-to-indentation) ratios. The introduction of these end effects helps reconcile a recent controversy around the role of friction in wire cutting, for it implies that slicing can indeed reduce required cutting forces, but only if the slice-push ratio and the friction coefficient are sufficiently large. Material strain-stiffening reduces the critical indentation depth required to initiate the cut further and thus needs to be considered when cutting non-linearly elastic materials.

中文翻译：

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进行切割：最终效果和切片的好处

几十年来，软固体中的切削力学一直是研究的主题，其众多应用（包括材料测试、制造和生物医学技术）激发了人们的兴趣。线切割是分析软材料切削阻力的最简单的模型系统。然而，即使对于这个简单的系统，支撑切割的复杂故障机制仍然没有被完全理解。已经提出了几种将临界切削力与线材半径和被切削材料的关键机械性能联系起来的模型。几乎普遍存在的简化假设是材料中的平面（和反平面）应变状态。在本文中，我们表明这种假设可能会导致错误的结论，因为即使如此简单的切割问题本质上也是三维的。平面近似将分析限制为中平面内的应力分布。然而，通过有限元建模，我们揭示了最大拉伸应力（以及因此可能的切割起始位置）实际上位于前平面。摩擦会降低这种应力的大小，但这种有害影响可以通过大的切片与推力（剪切与压痕）比率来抵消。这些末端效应的引入有助于调和最近关于在线切割中摩擦作用的争论，因为它意味着切片确实可以减少所需的切削力，但前提是切片推力比和摩擦系数足够大。材料应变强化降低了进一步开始切割所需的临界压痕深度，因此在切割非线性弹性材料时需要考虑。