On the relationship between cutting and tearing in soft elastic solids

Characterization of 3D printed micro-blades for cutting tissue-embedding material

Cutting soft materials on the microscale has emerging applications in single-cell studies, tissue microdissection for organoid culture, drug screens, and other analyses. However, the cutting process is complex and remains incompletely understood. Furthermore, precise control over blade geometries, such as the blade tip radius, has been difficult to achieve. In this work, we use the Nanoscribe 3D printer to precisely fabricate micro-blades (i.e., blades <1 mm in length) and blade grid geometries. This fabrication method enables a systematic study of the effect of blade geometry on the indentation cutting of paraffin wax, a common tissue-embedding material. First, we print straight micro-blades with tip radius ranging from ~100 nm to 10 μm. The micro-blades are mounted in a custom nanoindentation setup to measure the cutting energy during indentation cutting of paraffin. Cutting energy, measured as the difference in dissipated energy between the first and second loading cycles, decreases as blade tip radius decreases, until ~357 nm when the cutting energy plateaus despite further decrease in tip radius. Second, we expand our method to blades printed in unconventional configurations, including parallel blade structures and blades arranged in a square grid. Under the conditions tested, the cutting energy scales approximately linearly with the total length of the blades comprising the blade structure. The experimental platform described can be extended to investigate other blade geometries and guide the design of microscale cutting of soft materials.

Explaining the spread in measurement of PDMS elastic properties: influence of test method and curing protocol

Accuracy in the measurement of mechanical properties is essential for precision engineering and for the interrogation of composition-property relationships. Conventional methods of mechanical testing, such as uniaxial tension, compression, and nanoindentation, provide highly repeatable and reliable results for stiff materials, for which they were originally developed. However, when applied to the characterization of soft and biological materials, the same cannot be said, and the spread of reported properties of similar materials is vast. Polydimethylsiloxane (PDMS), commonly obtained from Dow as SYLGARD 184, is a ubiquitous such material, which has been integral to the rapid development of biocompatible microfluidic devices and flexible electronics in recent decades. However, reported shear moduli of this material range over 2 orders of magnitude for similar chemical compositions. Taking advantage of the increased mechanical scrutiny afforded to SYLGARD 184 in recent years, we combine both published and new experimental data obtained using 9 mechanical test methods. A statistical analysis then elucidates the significant bias induced by the test method itself, and distinguishes this bias from the influence of curing protocols on the mechanical properties. The goal of this work is thus two-fold: (i) it provides a quantitative understanding of the different factors that influence reported properties of this particular material, and (ii) it serves as a cautionary tale. As researchers in the field of mechanics strive to quantify the properties of increasingly complex soft and biological materials, converging on a standardized measurement of PDMS is a necessary first step.

Being thin-skinned can still reduce damage from dynamic puncture

The integumentary system in animals serves as an important line of defence against physiological and mechanical external forces. Over time, integuments have evolved layered structures (scales, cuticle and skin) with high toughness and strength to resist damage and prevent wound expansion. While previous studies have examined their defensive performance under low-rate conditions, the failure response and damage resistance of these thin layers under dynamic biological puncture remain underexplored. Here, we utilize a novel experimental framework to investigate the mechanics of dynamic puncture in both bilayer structures of synthetic tissue-mimicking composite materials and natural skin tissues. Our findings reveal the remarkable efficiency of a thin outer skin layer in reducing the overall extent of dynamic puncture damage. This enhanced damage resistance is governed by interlayer properties through puncture energetics and diminishes in strength at higher puncture rates due to rate-dependent effects in silicone tissue simulants. In addition, natural skin tissues exhibit unique material properties and failure behaviours, leading to superior damage reduction capability compared with synthetic counterparts. These findings contribute to a deeper understanding of the inherent biomechanical complexity of biological puncture systems with layered composite material structures. They lay the groundwork for future comparative studies and bio-inspired applications.

Curving expectations: The minimal impact of structural curvature in biological puncture mechanics

Living organisms have evolved various biological puncture tools, such as fangs, stingers, and claws, for prey capture, defense, and other critical biological functions. These tools exhibit diverse morphologies, including a wide range of structural curvatures, from straight cactus spines to crescent-shaped talons found in raptors. While the influence of such curvature on the strength of the tool has been explored, its biomechanical role in puncture performance remains untested. Here, we investigate the effect of curvature on puncture mechanics by integrating experiments with finite element simulations. Our findings reveal that within a wide biologically relevant range, structural curvature has a minimal impact on key metrics of damage initiation or the energies required for deep penetration in isotropic and homogeneous target materials. This unexpected result improves our understanding of the biomechanical pressures driving the morphological diversity of curved puncture tools and provides fundamental insights into the crucial roles of curvature in the biomechanical functions of living puncture systems.

Cutting soft matter: scaling relations controlled by toughness, friction, and wear

Cutting mechanics of soft solids is gaining rapid attention thanks to its promising benefits in material characterization and other applications. However, a full understanding of the physical phenomena is still missing, and several questions remain outstanding. E.g.: How can we directly and reliably measure toughness from cutting experiments? What is the role of blade sharpness? In this paper, we explore the simple problem of wire cutting, where blade sharpness is only defined by the wire radius. Through finite element analysis, we obtain a simple scaling relation between the wire radius and the steady-state cutting force per unit sample thickness. The cutting force is independent of the wire radius if the latter is below a transition length, while larger radii produce a linear force-radius correlation. The minimum cutting force, for small radii, is given by cleavage toughness, i.e., the surface energy required to break covalent bonds in the crack plane. The force-radius slope is instead given by the wear shear strength in the material. Via cutting experiments on polyacrylamide gels, we find that the magnitude of shear strength is close to the work of fracture of the material, i.e., the critical strain energy density required to break a pristine sample in uniaxial tension. The work of fracture characterizes the toughening contribution from the fracture process zone (FPZ), which adds to cleavage toughness. Our study provides two important messages, that answer the above questions: toughness can be estimated from wire-cutting experiments from the intercept of the force-radius linear correlation, as previously explored. However, as we discovered, this only estimates cleavage toughness. Additionally, the force-radius slope is correlated with the work of fracture, giving an estimation of the dissipative contributions from the FPZ.

Nano cells from fruit bunch residue: Nestling nanotechnology within the circular oil palm milling residue management

Nano-structured materials gain a vast market acceptance mainly due to their overarching endurance. Nanofibrillar cellulose (NFC) is one example of an augmenting agent unviable for production by small and medium enterprises (SMEs) due to the underlying process complexity. This study aims to characterise the NFC-alternative cells denoted as TRX-cellsⓇ, which is a mix of cellulose and non-cellulose components, ruling out its status as 'cellulose nanofibers, CNF'. The aim to test-fit the TRX-cells® production process into the circularity model was executed by deliberating on the usability of the byproduct. In doing so, fibrous oil palm empty fruit bunch (EFB) was treated with dioxydanyl radicals (DIOR) and homogenised. The rapid EFB-DIOR reaction at 70°C targeting dearomatisation reaction in a 10%-solid open system was performed before refining the DIOR-treated EFB to micro-scale fibres. Subjecting the micro-fibres to 17 kWh/mt PFI-milling yielded 85-95% of nano-scale fibrous mass. Relative to the stiff micro-fibres, the nano-scale cells web exhibit 34-41% softness enhancement judged from the web tear resistance profile associated with inter-fibre space reduction. Advanced chromatographic evidence for 27% xylan amongst TRX-cells®' total aldo-sugars was one form of the non-cellulose nano-component. High-resolution Transmission Electron Microscopy hyphenated to Energy Dispersive Analysis of X-ray (HRTEM-EDX) elemental mapping showed a 0.4 atomic percentage of nano-biominerals, confirming the presence of the redistributed dearomatised cells adjacent to cellulose held in the web of the hemicellulose. Shearing at the dearomatised inter-cell wall layers by PFI mill peeled 5 nm-100 nm thickness laminae. The smorgasbord of cellulose and non-celluloses resulted in crystallinity comparable to softwood NFC of approximately 60%, with unique preservation and precision-printing enabling properties. Given the non-recyclability of the DIOR-treated EFB microfibres, nestling the rapid waste transformation process into the circularity model shed light on circular bio-nanotechnology to the spectrum of opportunity for zero-waste, reduced emission and net zero carbon practices on top of an added value from waste transformation to a product.

Biomechanics of cutting: sharpness, wear sensitivity and the scaling of cutting forces in leaf-cutter ant mandibles

Herbivores large and small need to mechanically process plant tissue. Their ability to do so is determined by two forces: the maximum force they can generate, and the minimum force required to fracture the plant tissue. The ratio of these forces determines the relative mechanical effort; how this ratio varies with animal size is challenging to predict. We measured the forces required to cut thin polymer sheets with mandibles from leaf-cutter ant workers which vary by more than one order of magnitude in body mass. Cutting forces were independent of mandible size, but differed by a factor of two between pristine and worn mandibles. Mandibular wear is thus likely a more important determinant of cutting force than mandible size. We rationalize this finding with a biomechanical analysis, which suggests that pristine mandibles are ideally 'sharp'-cutting forces are close to a theoretical minimum, which is independent of tool size and shape, and instead solely depends on the geometric and mechanical properties of the cut tissue. The increase of cutting force due to mandibular wear may be particularly problematic for small ants, which generate lower absolute bite forces, and thus require a larger fraction of their maximum bite force to cut the same plant. This article is part of the theme issue 'Food processing and nutritional assimilation in animals'.

Slicing of a soft solid

Cutting of soft materials is a complex problem, which is still not well understood at the fundamental level, especially for soft materials. The cutting process we consider is slicing, which starts with indentation, followed by sliding of a knife on the material to be cut. Here, we describe cutting experiments on PDMS elastomers with three different moduli. Our experiments reveal typical stages of this cutting process, starting with indentation and ending at steady state cutting. The process starts with a pre-cutting phase in which the blade does not slip grossly relative to the solid to be cut, and deformation is mostly elastic. Slip of the blade initiates suddenly and is often accompanied by initiation of cutting. Cutting is relatively smooth in the next stage, which requires a continuous increase in shear force. For soft PDMS, this smooth cutting stage is followed by one in which folds or creases form on the cutting surface. The corresponding shear force response is no longer smooth as "steady" sliding occurs in a stick-slip fashion with oscillatory forces. The average shear force reaches a plateau and no longer increases with shear displacement. Experimental observations of the various cutting stages are interpreted quantitatively.

Deformation-dependent polydimethylsiloxane permeability measured using osmotic microactuators

In soft solids, large deformations significantly alter molecular structure and device geometry, which can impact other properties. In the case of mass transport, an interplay between flux and mechanical deformation results. Here we demonstrate a platform for the simultaneous characterization of mechano-permselectivity using the (slow) transport of water through polydimethylsiloxane (PDMS) as a challenging test case. The platform uses micron-sized, cylindrical, NaCl solution-filled PDMS chambers encapsulated by selectively-permeable PDMS thin film membranes. When placed in a high chemical potential environment (high water potential) the osmotic pressure difference between the chamber and environment induces water to flow through the PDMS membrane into the chamber, resulting in membrane bulging. A model combining membrane flux and nonlinear elasticity captures the time-dependent response well, but only when a deformation-dependent permeability is used. Notably, the permeability of water through PDMS decreases by nearly an order of magnitude, from 2 × 10-12 to 5 × 10-13 m2 s-1, due primarily to its thickness decreasing by nearly an order of magnitude as the average biaxial stretch increases from 1 to 2.75.

Investigation of the rate-mediated form-function relationship in biological puncture

Puncture is a vital mechanism for survival in a wide range of organisms across phyla, serving biological functions such as prey capture, defense, and reproduction. Understanding how the shape of the puncture tool affects its functional performance is crucial to uncovering the mechanics underlying the diversity and evolution of puncture-based systems. However, such form-function relationships are often complicated by the dynamic nature of living systems. Puncture systems in particular operate over a wide range of speeds to penetrate biological tissues. Current studies on puncture biomechanics lack systematic characterization of the complex, rate-mediated, interaction between tool and material across this dynamic range. To fill this knowledge gap, we establish a highly controlled experimental framework for dynamic puncture to investigate the relationship between the puncture performance (characterized by the depth of puncture) and the tool sharpness (characterized by the cusp angle) across a wide range of bio-relevant puncture speeds (from quasi-static to [Formula: see text] 50 m/s). Our results show that the sensitivity of puncture performance to variations in tool sharpness reduces at higher puncture speeds. This trend is likely due to rate-based viscoelastic and inertial effects arising from how materials respond to dynamic loads. The rate-dependent form-function relationship has important biological implications: While passive/low-speed puncture organisms likely rely heavily on sharp puncture tools to successfully penetrate and maintain functionalities, higher-speed puncture systems may allow for greater variability in puncture tool shape due to the relatively geometric-insensitive puncture performance, allowing for higher adaptability during the evolutionary process to other mechanical factors.

Puncturing of soft tissues: experimental and fracture mechanics-based study

The integrity of soft materials against puncturing is of great relevance for their performance because of the high sensitivity to local rupture caused by rigid sharp objects. In this work, the mechanics of puncturing is studied with respect to a sharp-tipped rigid needle with a circular cross section, penetrating a soft target solid. The failure mode associated with puncturing is identified as a mode-I crack propagation, which is analytically described by a two-dimensional model of the target solid, taking place in a plane normal to the penetration axis. It is shown that the force required for the onset of needle penetration is dependent on two energy contributions, that are, the strain energy stored in the target solid and the energy consumed in crack propagation. More specifically, the force is found to be dependent on the fracture toughness of the material, its stiffness and the sharpness of the penetrating tool. The reference case within the framework of small strain elasticity is first investigated, leading to closed-form toughness parameters related to classical linear elastic fracture mechanics. Then, nonlinear finite element analyses for an Ogden hyperelastic material are presented. Supporting the proposed theoretical framework, a series of puncturing experiments on two commercial silicones is presented. The combined experimental-theoretical findings suggest a simple, yet reliable tool to easily handle and assess safety against puncturing of soft materials.

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

Biological puncture systems use a diversity of morphological tools (stingers, teeth, spines etc.) to penetrate target tissues for a variety of functions (prey capture, defence, reproduction). These systems are united by a set of underlying physical rules which dictate their mechanics. While previous studies have illustrated form-function relationships in individual systems, these underlying rules have not been formalized. We present a mathematical model for biological puncture events based on energy balance that allows for the derivation of analytical scaling relations between energy expenditure and shape, size and material response. The model identifies three necessary energy contributions during puncture: fracture creation, elastic deformation of the material and overcoming friction during penetration. The theoretical predictions are verified using finite-element analyses and experimental tests. Comparison between different scaling relationships leads to a ratio of released fracture energy and deformation energy contributions acting as a measure of puncture efficiency for a system that incorporates both tool shape and material response. The model represents a framework for exploring the diversity of biological puncture systems in a rigorous fashion and allows future work to examine how fundamental physical laws influence the evolution of these systems.