How friction and adhesion affect the mechanics of deep penetration in soft solids

Abstract

The mechanics of puncture and soft solid penetration is commonly explored with the assumption of frictionless contact between the needle (penetrator) and the specimen. This leads to the hypothesis of...

Modelling biological puncture: a mathematical framework for determining the energetics and scaling

“…Complications arise for quantification of W f in determination of the friction force per unit area, f , as an interfacial parameter (equation (2.7)). Alternatively, f can be expressed as f = ηp app [15,26], where p app is the average interfacial pressure between the puncture tool and the material, and η is the friction coefficient. It can be shown from the general form of the puncture energy presented by equation (2.22) that regardless of the constitutive model implemented, p app can be generally expressed as, normalized by the shear modulus, μ, papp=normal∂ΔEknormal∂d⋅1μAnormalproj=A+Bℓcd,where A proj = π tan 2 θd 2 is the projection area of the puncture cone at d ; and A and B are dimensionless functions of θ and material failure properties.…”

“…Experimental work has shown that η is highly sensitive to surface roughness, and such dependence is governed by a ‘true’ contact area at a microscale [62]. In biological tissues, contact mechanics can be even more complicated when the effects of surface adhesion [26,63], hierarchical structures [63], ornamentation [7,9,11,48] or lubrication [57] are introduced. Organic puncture tools such as mosquito proboscis [11], stingray barbs [9], parasitic wasp ovipositor [14], porcupine quill [48] and cactus spine [7] often exhibit morphological ornamentations or microstructured serrations.…”

“…Understanding the morphology of the damage in a puncture system is important as it directly reflects the failure response of the tested material and provides a basis for quantifying the puncture performance. However, despite the abundance of previous studies on experimental and numerical puncture mechanics in soft polymers and biomaterials [5,16,17,19,21,23,26,28,36,[42][43][44], only a handful of literature has explored the morphology of a post-puncture fracture surface following the removal of the tool; and the focus was mostly on the puncture failure caused by cylindrical or similar shaped tools. There is no guarantee that the conical-shaped puncture system ubiquitous in living organisms will exhibit similar failure responses.…”

“…We denote the elastic energy required for the first step as Δ U el,0 (figure 3). To estimate the magnitude of Δ U el,0 , we adopt an approach similar to the one proposed by Shergold and Fleck for a cylindrical punch [22,26]. We introduce a dimensionless function f ( a / R ) to describe the normalized elastic energy associated with a symmetric problem where a planar crack having length 2 a in an elastic substrate is wedge opened by a rigid circle having radius R under plane strain (electronic supplementary material, figure S3).…”

“…Since the early work by Stevenson & Maleck [21], there have been a limited number of theoretical investigations and modelling attempts on puncture mechanics in soft solids and bio-tissues [16,20,[22][23][24][25][26]. These studies often focus on specific puncture cases where damage is produced by either a flat punch or a cylindrical-like tool [16,20,22,26] and are mostly related to medical needle injection [20,22,23] and material characterization [16,24,25]. However, biological puncture tools such as teeth [1], fangs [4] and stingers [15] often resemble tapered, conical shapes, at least at their tips.…”