Random auxetics from buckling fibre networks

Reduced stress propagation leads to increased mechanical failure resistance in auxetic materials

Materials with a negative Poisson ratio have the counterintuitive property of expanding laterally when they are stretched longitudinally. They are accordingly termed auxetic, from the Greek auxesis meaning to increase. Experimental studies have demonstrated auxetic materials to have superior material properties, compared with conventional ones. These include synclastic curvature, increased acoustic absorption, increased resilience to material fatigue, and increased resistance to mechanical failure. Until now, the latter observations have remained poorly understood theoretically. With this motivation, the contributions of this work are twofold. First, we elucidate analytically the way in which stress propagates spatially across a material following a localized plastic failure event, finding a significantly reduced stress propagation in auxetic materials compared with conventional ones. In this way, a plastic failure event occurring in one part of a material has a reduced tendency to trigger knock-on plastic events in neighboring regions. Second, via the numerical simulation of a lattice elastoplastic model, we demonstrate a key consequence of this reduced stress propagation to be an increased resistance to mechanical failure. This is seen not only via an increase in the externally measured yield strain, but also via a decreased tendency for plastic damage to percolate internally across a sample in catastrophic system-spanning clusters.

Humidity Response of a Capacitive Sensor Based on Auxeticity of Carbon Nanotube-Paper Composites

Auxetic materials showing a negative Poisson’s ratio can offer unusual sensing capabilities due to drastic percolation changes. This study presents the capacitive response of wet-fractured carbon nanotube paper composites in exposure to humidity. A strained composite strip is fractured to produce numerous cantilevers consisting of cellulose fibers coated with carbon nanotubes. During stretching, the thin composite buckles in the out-of-plane direction, which causes auxetic behavior to generate the radially structured electrodes. The crossbar junctions forming among the fractured electrodes significantly increase capacitance and its response to humidity as a function of sensor widths. The molecular junctions switch electric characteristics between predominantly resistive- and capacitive elements. The resulting capacitive response is characterized for humidity sensing without the need for an additional absorption medium. The normalized capacitance change (ΔC/C) exhibits a sensitivity of 0.225 within the range of 40~80 % relative humidity. The novel auxetic behavior of a water-printed paper-based nanocomposite paves the way for inexpensive humidity and sweat sensors.

Risky interpretations across the length scales: continuum vs. discrete models for soft tissue mechanobiology

Modelling and simulation in mechanobiology play an increasingly important role to unravel the complex mechanisms that allow resident cells to sense and respond to mechanical cues. Many of the in vivo mechanical loads occur on the tissue length scale, thus raising the essential question how the resulting macroscopic strains and stresses are transferred across the scales down to the cellular and subcellular levels. Since cells anchor to the collagen fibres within the extracellular matrix, the reliable representation of fibre deformation is a prerequisite for models that aim at linking tissue biomechanics and cell mechanobiology. In this paper, we consider the two-scale mechanical response of an affine structural model as an example of a continuum mechanical approach and compare it with the results of a discrete fibre network model. In particular, we shed light on the crucially different mechanical properties of the 'fibres' in these two approaches. While assessing the capability of the affine structural approach to capture the fibre kinematics in real tissues is beyond the scope of our study, our results clearly show that neither the macroscopic tissue response nor the microscopic fibre orientation statistics can clarify the question of affinity.

Tensile behavior of non-crosslinked networks of athermal fibers in the presence of entanglements and friction

Many biological and soft artificial materials contain a random network of non-crosslinked fibers as their main structural component. The excluded volume interactions (contact forces) at fiber contacts control the mechanical behavior of these systems. This physics has been studied extensively in compression, but little is known about the relation between network structure and its mechanical response in tension. In particular, although occasionally used conjecturally, the notion of fiber entanglements in athermal networks is not well defined, nor is it clear what role entanglements play in athermal network mechanics. The primary contribution of this work is the introduction of a measure of the degree of entanglement of a system of random athermal fibers, and the definition of its relationship with the mechanical behavior of the network. Entanglements confine the fibers during tensile loading, reduce the auxetic effect in mat-like networks, and maintain the inter-fiber contact density. In the absence of this contribution, reduction of the contact density during tensile loading due to auxeticity results in stress reduction. Entanglements stabilize the network via a tensegrity mechanism similar to that operating in woven materials and lead to network stiffening. The relation between the proposed measure of entanglements and the fiber volume fraction is defined. The effect of inter-fiber friction on the mechanics of entangled mat-like non-crosslinked fiber networks is also evaluated.

Tailoring the multiscale architecture of electrospun membranes to promote 3D cellular infiltration

Controlling the architecture of engineered scaffolds is of outmost importance to induce a targeted cell response and ultimately achieve successful tissue regeneration upon implantation. Robust, reliable and reproducible methods to control scaffold properties at different levels are timely and highly important. However, the multiscale architectural properties of electrospun membranes are very complex, in particular the role of fiber-to-fiber interactions on mechanical properties, and their effect on cell response remain largely unexplored. The work reported here reveals that the macroscopic membrane stiffness, observed by stress-strain curves, cannot be predicted solely based on the Young's moduli of the constituting fibers but is rather influenced by interactions on the microscale, namely the number of fiber-to-fiber bonds. To specifically control the formation of these bonds, solvent systems of the electrospinning solution were fine-tuned, affecting the membrane properties at every length-scale investigated. In contrast to dichloromethane that is characterized by a high vapor pressure, the use of trifluoroacetic acid, a solvent with a lower vapor pressure, favors the generation of fiber-to-fiber bonds. This ultimately led to an overall increased Young's modulus and yield stress of the membrane despite a lower stiffness of the constituting fibers. With respect to tissue engineering applications, an experimental setup was developed to investigate the effect of architectural parameters on the ability of cells to infiltrate and migrate within the scaffold. The results reveal that differences in fiber-to-fiber bonds significantly affect the infiltration of normal human dermal fibroblasts into the membranes. Membranes of loose fibers with low numbers of fiber-to-fiber bonds, as obtained from spinning solutions using dichloromethane, promote cellular infiltration and are thus promising candidates for the formation of a 3D tissue.

Auxeticity in biosystems: an exemplification of its effects on the mechanobiology of heterogeneous living cells

Auxeticity (negative Poisson's ratio) is the unique mechanical property found in an extensive variety of materials, such as metals, graphene, composites, polymers, foams, fibers, ceramics, zeolites, silicates and biological tissues. The enhanced mechanical features of the auxetic materials have motivated scientists to design, engineer and manufacture man-made auxetic materials to fully leverage their capabilities in different fields of research applications, including aeronautics, medical, protective equipments, smart sensors, filter cleaning, and so on. Atomic force microscopy (AFM) indentation is one of the most widely used methods for characterizing the mechanical properties and response of the living cells. In this contribution, we highlight main consequences of auxeticity for biosystems and provide a representative example to quantify the effect of nucleus auxeticity on the force response of the embryonic stem cells. A parametric study has been conducted on a heterogeneous stem cell to evaluate the effect of nucleus diameter, nucleus elasticity, indenter's shape and location on the force-indentation curve. The developed model has also been validated with the recently reported experimental studies available in the literature. Our results suggest that the nucleus auxeticity plays a profound role in cell mechanics especially for large size nucleus. We also report the mechanical stresses induced within the hyperelastic cell model under different loading conditions that would be quite useful in decoding the interrelations between mechanical stimuli and cellular behavior of auxetic biosystems. Finally, current and potential areas of applications of our findings for regenerative therapies, tissue engineering, 3 D/4D bioprinting, and the development of meta-biomaterials are discussed.

A computational framework for modeling cell-matrix interactions in soft biological tissues

Living soft tissues appear to promote the development and maintenance of a preferred mechanical state within a defined tolerance around a so-called set point. This phenomenon is often referred to as mechanical homeostasis. In contradiction to the prominent role of mechanical homeostasis in various (patho)physiological processes, its underlying micromechanical mechanisms acting on the level of individual cells and fibers remain poorly understood, especially how these mechanisms on the microscale lead to what we macroscopically call mechanical homeostasis. Here, we present a novel computational framework based on the finite element method that is constructed bottom up, that is, it models key mechanobiological mechanisms such as actin cytoskeleton contraction and molecular clutch behavior of individual cells interacting with a reconstructed three-dimensional extracellular fiber matrix. The framework reproduces many experimental observations regarding mechanical homeostasis on short time scales (hours), in which the deposition and degradation of extracellular matrix can largely be neglected. This model can serve as a systematic tool for future in silico studies of the origin of the numerous still unexplained experimental observations about mechanical homeostasis.

Mechanical homeostasis in tissue equivalents: a review

There is substantial evidence that growth and remodeling of load bearing soft biological tissues is to a large extent controlled by mechanical factors. Mechanical homeostasis, which describes the natural tendency of such tissues to establish, maintain, or restore a preferred mechanical state, is thought to be one mechanism by which such control is achieved across multiple scales. Yet, many questions remain regarding what promotes or prevents homeostasis. Tissue equivalents, such as collagen gels seeded with living cells, have become an important tool to address these open questions under well-defined, though limited, conditions. This article briefly reviews the current state of research in this area. It summarizes, categorizes, and compares experimental observations from the literature that focus on the development of tension in tissue equivalents. It focuses primarily on uniaxial and biaxial experimental studies, which are well-suited for quantifying interactions between mechanics and biology. The article concludes with a brief discussion of key questions for future research in this field.

Liquid Crystal Elastomers for Biological Applications

The term liquid crystal elastomer (LCE) describes a class of materials that combine the elastic entropy behaviour associated with conventional elastomers with the stimuli responsive properties of anisotropic liquid crystals. LCEs consequently exhibit attributes of both elastomers and liquid crystals, but additionally have unique properties not found in either. Recent developments in LCE synthesis, as well as the understanding of the behaviour of liquid crystal elastomers—namely their mechanical, optical and responsive properties—is of significant relevance to biology and biomedicine. LCEs are abundant in nature, highlighting the potential use of LCEs in biomimetics. Their exceptional tensile properties and biocompatibility have led to research exploring their applications in artificial tissue, biological sensors and cell scaffolds by exploiting their actuation and shock absorption properties. There has also been significant recent interest in using LCEs as a model for morphogenesis. This review provides an overview of some aspects of LCEs which are of relevance in different branches of biology and biomedicine, as well as discussing how recent LCE advances could impact future applications.