Negative Poisson's ratios in tendons: An unexpected mechanical response

2-dimensional impact-damping electrostatic actuators with elastomer-enhanced auxetic structure

Biomimetic robots yearn for compliant actuators that are comparable to biological muscle in both functions and structural properties. For that, electrostatic actuators have been developed to imitate bio-muscle in features of fast response, high power, energy-efficiency, etc. However, those actuators typically lack impact damping performance, making them vulnerable and unstable in real applications. Here, we present auxetic electrostatic actuators that address this issue and demonstrate muscle-like performance by using elastomer-enhanced auxetics and electrostatic zipping mechanism. The proposed actuators contract linearly on applied voltage, producing large actuation strength (15 N) and contraction ratio (59%). Fabricated from readily available materials, our prototypes can quickly attenuate vibrations caused by impacts and absorb shock energy in 0.3 s. Furthermore, leveraging their 2-dimensional working mode and self-locking mechanism, a stiffness-changing muscle for a robotic arm and an active tensegrity device exemplify the potential applications of auxetic electrostatic actuators to a wide range of bionic robots.

Auxetic Biomedical Metamaterials for Orthopedic Surgery Applications: A Comprehensive Review

Poisson's ratio in auxetic materials shifts from typically positive to negative, causing lateral expansion during axial tension. This scale-independent characteristic, originating from tailored architectures, exhibits specific physical properties, including energy adsorption, shear resistance, and fracture resistance. These metamaterials demonstrate exotic mechanical properties with potential applications in several engineering fields, but biomedical applications seem to be one of the most relevant, with an increasing number of articles published in recent years, which present opportunities ranging from cellular repair to organ reconstruction with outstanding mechanical performance, mechanical conduction, and biological activity compared with traditional biomedical metamaterials. Therefore, focusing on understanding the potential of these structures and promoting theoretical and experimental investigations into the benefits of their unique mechanical properties is necessary for achieving high-performance biomedical applications. Considering the demand for advanced biomaterial implants in surgical technology and the profound advancement of additive manufacturing technology that are particularly relevant to fabricating complex and customizable auxetic mechanical metamaterials, this review focuses on the fundamental geometric configuration and unique physical properties of negative Poisson's ratio materials, then categorizes and summarizes auxetic material applications across some surgical departments, revealing efficacy in joint surgery, spinal surgery, trauma surgery, and sports medicine contexts. Additionally, it emphasizes the substantial potential of auxetic materials as innovative biomedical solutions in orthopedics and demonstrates the significant potential for comprehensive surgical application in the future.

The anisotropic and region-dependent mechanical response of wrap-around tendons under tensile, compressive and combined multiaxial loads

The present work reports on the multiaxial region and orientation-dependent mechanical properties of two porcine wrap-around tendons under tensile, compressive and combined loads based on an extensive study with n=175 samples. The results provide a detailed dataset of the anisotropic tensile and compressive longitudinal properties and document a pronounced tension-compression asymmetry. Motivated by the physiological loading conditions of these tendons, which include transversal compression at bony abutments in addition to longitudinal tension, we systematically investigated the change in axial tension when the tendon is compressed transversally along one or both perpendicular directions. The results reveal that the transversal compression can increase axial tension (proximal-distal direction) in both cases to orders of 30%, yet by a larger amount in the first case (transversal compression in anterior-posterior direction), which seems to be more relevant for wrap-around tendons in-vivo. These quantitative measurements are in line with earlier findings on auxetic properties of tendon tissue, but show for the first time the influence of this property on the stress response of the tendon, and may thus reveal an important functional principle within these essential elements of force transmission in the body. STATEMENT OF SIGNIFICANCE: The work reports for the first time on multiaxial region and orientation-dependent mechanical properties of wrap-around tendons under various loads. The results indicate that differences in the mechanical properties exist between zones that are predominantly in a uniaxial tensile state and those that experience complex load states. The observed counterintuitive increase of the axial tension upon lateral compression points at auxetic properties of the tendon tissue which may be pivotal for the function of the tendon as an element of the musculoskeletal system. It suggests that the tendon's performance in transmitting forces is not diminished but enhanced when the action line is deflected by a bony pulley around which the tendon wraps, representing an important functional principle of tendon tissue.

Auxetic polymer networks: The role of crosslinking, density, and disorder

Low-crosslinked polymer networks have recently been found to behave auxetically when subjected to small tensions, that is, their Poisson's ratio ν becomes negative. In addition, for specific state points, numerical simulations revealed that diamond-like networks reach the limit of mechanical stability, exhibiting values of ν = -1, a condition that we define as hyper-auxeticity. This behavior is interesting per se for its consequences in materials science but is also appealing for fundamental physics because the mechanical instability is accompanied by evidence of criticality. In this work, we deepen our understanding of this phenomenon by performing a large set of equilibrium and stress-strain simulations in combination with phenomenological elasticity theory. The two approaches are found to be in good agreement, confirming the above results. We also extend our investigations to disordered polymer networks and find that the hyper-auxetic behavior also holds in this case, still manifesting a similar critical-like behavior as in the diamond one. Finally, we highlight the role of the number density, which is found to be a relevant control parameter determining the elastic properties of the system. The validity of the results under disordered conditions paves the way for an experimental investigation of this phenomenon in real systems, such as hydrogels.

Fiber orientation and crimp level might control the auxetic effect of biological tissues

We propose an analytical micromechanical model for studying the lamellar-composite-like structure of fibrous soft tissue. The tissue under consideration is made up of several lamellae, and is designed to resemble the annulus fibrosus (AF) tissue or media layer of arterial tissue, for example. The collagen fibers are arranged in parallel in each lamella and the fiber orientation differs from one lamella to its neighbors. The parallel fibers in each lamella of AF tissue, for example, have been observed to have a crimped microstructure. The proposed model incorporates this quality, considering fiber waviness as a sinusoidal shape and taking into account the fiber dispersion in different layers, where both fiber and matrix are considered as solid phases. We find that collagen-fiber waviness and layer orientation have a significant influence on Poisson's ratio. The effective Poisson's ratio predicted by the proposed model demonstrates that the crimped collagen fiber microstructure might weaken the auxetic effect of fibrous soft tissue, which might explain why, as the literature suggests, the auxetic behavior is more difficult to observe than large Poisson's ratios. As opposed to the many studies that use the well-known hyperelastic fiber-based constitutive model, in which out-of-plane expansion is often observed, the present work explains the auxetic response found in modeling and in experimental data from the perspective of collagen fiber microstructure.

Edible Origami Actuators Using Gelatin-Based Bioplastics

The potential of ingestible medical devices can be greatly enhanced through the use of smart structures made from stimuli-responsive materials. While hydration is a convenient stimulus for inducing shape changes in biomaterials, finding robust materials that can achieve rapid actuation, facile manufacturability, and biocompatibility suitable for ingestible medical devices poses practical challenges. Hydration is a convenient stimulus to induce shape changes in smart biomaterials; however, there are many practical challenges to identifying materials that can achieve rapid actuation and facile manufacturability while satisfying constraints associated with biocompatibility requirements and mechanical properties that are suitable for ingestible medical devices. Herein, we illustrate the formulation and processability of a moisture-responsive genipin-crosslinked gelatin bioplastic system, which can be processed into complex three-dimensional shapes. Mechanical characterization of bioplastic samples showed Young's Modulus values as high as 1845 MPa and toughness values up to 52 MJ/m3, using only food-safe ingredients. Custom molds and UV-laser processing enabled the fabrication of centimeter-scale structures with over 150 independent actuating joints. These self-actuating structures soften and unfold in response to surrounding moisture, eliminating the need for additional stimuli or actuating elements.

Auxeticity as a Mechanobiological Tool to Create Meta-Biomaterials

Mechanical and morphological design parameters, such as stiffness or porosity, play important roles in creating orthopedic implants and bone substitutes. However, we have only a limited understanding of how the microarchitecture of porous scaffolds contributes to bone regeneration. Meta-biomaterials are increasingly used to precisely engineer the internal geometry of porous scaffolds and independently tailor their mechanical properties (e.g., stiffness and Poisson's ratio). This is motivated by the rare or unprecedented properties of meta-biomaterials, such as negative Poisson's ratios (i.e., auxeticity). It is, however, not clear how these unusual properties can modulate the interactions of meta-biomaterials with living cells and whether they can facilitate bone tissue engineering under static and dynamic cell culture and mechanical loading conditions. Here, we review the recent studies investigating the effects of the Poisson's ratio on the performance of meta-biomaterials with an emphasis on the relevant mechanobiological aspects. We also highlight the state-of-the-art additive manufacturing techniques employed to create meta-biomaterials, particularly at the micrometer scale. Finally, we provide future perspectives, particularly for the design of the next generation of meta-biomaterials featuring dynamic properties (e.g., those made through 4D printing).

Analytical relationships for 2D Re-entrant auxetic metamaterials: An application to 3D printing flexible implants

Both 2D and 3D re-entrant designs are among the well-known prevalent auxetic structures exhibiting negative Poisson's ratio. The present study introduces novel analytical relationships for 2D re-entrant hexagonal honeycombs for both negative and positive ranges of the cell interior angle θ (θ<0 showing a negative Poisson's ratio). The derived analytical solutions are validated against finite element method (FEM) and experimental results. The results show that, compared to the analytical solutions available in the literature, the analytical relationships presented in this study provide the most accurate results for elastic modulus, Poisson's ratio, and yield stress. The analytical/computational tools are then implemented for designing Kinesio taping (KT) structures applicable to treatment of Achilles tendon injuries. One of the main features of the Achilles tendon is a natural auxetic behavior. Poisson's ratio distribution of an Achilles tendon is obtained using longitudinal and transverse strains and are then used to design and 3D print thermoplastic polyurethane (TPU) KT structures with non-uniform distribution of auxetic unit cells. The presented novel KT shows that it is capable of replicating the deformation and global and local Poisson's ratio distributions, similar to those of the Achilles tendon. Due to the absence of similar formulations and procedures in the literature, the results are expected to be instrumental for designing and 3D printing of flexible implants with unusual auxeticity.

Tuning the Poisson's ratio of poly(ethylene glycol) diacrylate/cellulose nanofibril aerogel scaffold precisely for cultivation of bone marrow mesenchymal stem cell

Tissue engineering (TE) scaffolds with appropriate Poisson's ratio (PR) are suitable for mimicking the environment of native tissues on which cells could survive and thrive better. Herein, cellular structured scaffolds are made by a new composite poly(ethylene glycol) diacrylate/cellulose nanofibril aerogel, with prototypes of the hexagonal, reentrant, and semireentrant models. Scaffolds with different geometry parameters (l, t, α) are designed and simulated by COMSOL to enable precise regulation of their PR. Then, nine groups of scaffolds with different PRs ranging from -0.5 to 0.85 are designed by adjusting geometry parameters and fabricated by using stereolithography and freeze-drying techniques. Subsequently, bone marrow mesenchymal stem cells (BMSc) are cultured on these scaffolds for 21 days, during which CCK8 assay, fluorescence microscope observation, and real-time polymerase chain reaction experiments are performed to characterize the proliferation and differentiation of BMSc. The results reflect that the scaffolds with different PR can provide various stress environments for cells, and the scaffold with zero PR is the most suitable for BMSc differentiating into chondrocytes during early culture experiments. This study suggests that tuning PR precisely is an attractive and effective strategy to provide a cells-suitable environment for scaffold fabrication for TE.

On the Kinematics of the Forward-Facing Venetian-Style Rowing Technique

This work presents a qualitative and quantitative pilot study which explores the kinematics of Venetian style forward-facing standing rowing as practised by able-bodied competitive athletes. The technique, made famous by the gondoliers, was replicated in a biomechanics laboratory by a cohort of four experienced rowers who compete in this style at National Level events in Malta. Athletes were marked with reflective markers following the modified Helen Hayes model and asked to row in a manner which mimics their on-water practise and recorded using a Vicon optoelectronic motion capture system. Data collected were compared to its equivalent using a standard sliding-seat ergometer as well as data collated from observations of athletes rowing on water, thus permitting the documentation of the manner of how this technique is performed. It was shown that this rowing style is characterised by rather asymmetric and complex kinematics, particularly upper-body movements which provides the athlete with a total-body workout involving all major muscle groups working either isometrically, to provide stability, or actively.

The rise of mechanical metamaterials: Auxetic constructs for skin wound healing

Auxetic materials are known for their unique ability to expand/contract in multiple directions when stretched/compressed. In other words, they exhibit a negative Poisson's ratio, which is usually positive for most of materials. This behavior appears in some biological tissues such as human skin, where it promotes wound healing by providing an enhanced mechanical support and facilitating cell migration. Skin tissue engineering has been a growing research topic in recent years, largely thanks to the rapid development of 3D printing techniques and technologies. The combination of computational studies with rapid manufacturing and tailored designs presents a huge potential for the future of personalized medicine. Overall, this review article provides a comprehensive overview of the current state of research on auxetic constructs for skin healing applications, highlighting the potential of auxetics as a promising treatment option for skin wounds. The article also identifies gaps in the current knowledge and suggests areas for future research. In particular, we discuss the designs, materials, manufacturing techniques, and also the computational and experimental studies on this topic.

Influence of walking on knee ligament response in car-to-pedestrian collisions

Pedestrians are likely to experience walking before accidents. The walking process imposes cyclic loading on knee ligaments and increases knee joint temperature. Both cyclic loading and temperature affect the material properties of ligaments, which further influence the risk of ligament injury. However, the effect of such walking-induced material property changes on pedestrian ligament response has not been considered. Therefore, in this study, we investigated the influence of walking on ligament response in car-to-pedestrian collisions. Using Total Human Model for Safety (THUMS) model, knee ligament responses (i.e., cross-sectional force and local strain) were evaluated under several crash scenarios (i.e., two impact speeds, two knee contact heights, and three pedestrian postures). In worst case scenarios, walking-induced changes in ligament material properties led to a 10% difference in maximum local strain and a 6% difference in maximum cross-sectional force. Further considering the material uncertainty caused by experimental dispersion, the ligament material property changes due to walking resulted in a 28% difference in maximum local strain and a 26% difference in maximum cross-sectional force. This study demonstrates the importance of accounting for walking-induced material property changes for the reliability of safety assessments and injury analysis.

Direct Observation of Biaxial Nematic Order in Auxetic Liquid Crystal Elastomers

Auxetic materials exhibit a negative Poisson's ratio, i.e., they become thicker rather than thinner in at least one dimension when strained. Recently, a nematic liquid crystal elastomer (LCE) was shown to be the first synthetic auxetic material at a molecular level. Understanding the mechanism of the auxetic response in LCEs is clearly important, and it has been suggested through detailed Raman scattering studies that it is related to the reduction of uniaxial order and emergence of biaxial order on strain. In this paper, we demonstrate direct observation of the biaxial order in an auxetic LCE under strain. We fabricated ~100 μm thick LCE strips with complementary geometries, exhibiting either planar or homeotropic alignment, in which the auxetic response is seen in the thickness or width of the sample, respectively. Polarized Raman scattering measurements on the planar sample show directly the reduction in the uniaxial order parameters on strain and suggest the emergence of biaxial order to mediate the auxetic response in the sample thickness. The homeotropic sample is studied via conoscopy, allowing direct observation of both the auxetic response in the width of the sample and increasing biaxiality in the LCE as it is strained. We verified that the mechanism of the auxetic response in auxetic LCEs is due to the emergence of the biaxial order and conclude such materials can be added to the small number of biaxial nematic systems that have been observed. Importantly, we also show that the mechanical Frèedericksz transition seen in some LCEs is consistent with a strain-induced transition from an optically positive to an optically negative biaxial system under strain, rather than a director rotation in a uniaxial system.

Limpet teeth microstructure unites auxeticity with extreme strength and high stiffness

Materials displaying negative Poisson's ratio, referred to as auxeticity, have been found in nature and created in engineering through various structural mechanisms. However, uniting auxeticity with high strength and high stiffness has been challenging. Here, combining in situ nanomechanical testing with microstructure-based modeling, we show that the leading part of limpet teeth successfully achieves this combination of properties through a unique microstructure consisting of an amorphous hydrated silica matrix embedded with bundles of single-crystal iron oxide hydroxide nanorods arranged in a pseudo-cholesteric pattern. During deformation, this microstructure allows local coordinated displacement and rotation of the nanorods, enabling auxetic behavior while maintaining one of the highest strengths among natural materials. These findings lay a foundation for designing biomimetic auxetic materials with extreme strength and high stiffness.

Design, Fabrication, and Characterization of an Impact Dissipative Layer for Fiber-Reinforced Polymer Composites

This study presents the option of an effective low-impact energy dissipating material applied to GFRP (glass fiber reinforced plastic) composite laminates using auxectic technology in the case of planing hull vessels that use the same high-speed light materials that repeatedly impact the surface of the water when sailing, producing a slamming phenomenon. Research shows that the option to modify the laminate with an auxectic layer protects the laminate from damage. This work proposes the manufacturing of dissipative layers, introduced in laminates made with a polymeric matrix and fiberglass reinforcement, which are evaluated with weight drop tests under different impact energies. The data are collected and processed by a unidirectional gravitometer that gives the acceleration values of the impactor. The tests compare unmodified panels with modified panels, showing that the energy absorbed by the unmodified panel is greater at equal energy levels. The returned energy comparison curve is shown, and the benefits of its use are presented.

Additive Manufacturing of Biomaterials-Design Principles and Their Implementation

Additive manufacturing (AM, also known as 3D printing) is an advanced manufacturing technique that has enabled progress in the design and fabrication of customised or patient-specific (meta-)biomaterials and biomedical devices (e.g., implants, prosthetics, and orthotics) with complex internal microstructures and tuneable properties. In the past few decades, several design guidelines have been proposed for creating porous lattice structures, particularly for biomedical applications. Meanwhile, the capabilities of AM to fabricate a wide range of biomaterials, including metals and their alloys, polymers, and ceramics, have been exploited, offering unprecedented benefits to medical professionals and patients alike. In this review article, we provide an overview of the design principles that have been developed and used for the AM of biomaterials as well as those dealing with three major categories of biomaterials, i.e., metals (and their alloys), polymers, and ceramics. The design strategies can be categorised as: library-based design, topology optimisation, bio-inspired design, and meta-biomaterials. Recent developments related to the biomedical applications and fabrication methods of AM aimed at enhancing the quality of final 3D-printed biomaterials and improving their physical, mechanical, and biological characteristics are also highlighted. Finally, examples of 3D-printed biomaterials with tuned properties and functionalities are presented.

An Experimental Study of Auxetic Tubular Structures

Auxetic tubular structures are widely known structures, characterized by a negative Poisson’s ratio upon stretching and deformation in the axial and transverse directions, which have numerous application possibilities. In this paper, tubular structures were realized by rolling up planar auxetic structures and using rigid square frames as unit cells. Planar and tubular structures were built from square frames that were 3D printed with plastic or laser-cut from metal. The changes in linear dimensions of the studied structures were based on a hinge mechanism, the functioning of which was experimentally verified on different solutions leading to square unit cells. To connect the square frames of the structure, an innovative solution was used in the form of rotation axes on their surface at a preset distance from the edge of the square frame. The geometric parameter thus introduced was used to determine the relative change in the size of the structure when stretched (i.e., when moving from the closed to the open position).

Review: Auxetic Polymer-Based Mechanical Metamaterials for Biomedical Applications

Over the last three decades but more particularly during the last 5 years, auxetic mechanical metamaterials constructed from precisely architected polymer-based materials have attracted considerable attention due to their fascinating mechanical properties. These materials present a negative Poisson's ratio and therefore unusual mechanical behavior, which has resulted in enhanced static modulus, energy adsorption, and shear resistance, as compared with the bulk properties of polymers. Novel advanced polymer processing and fabrication techniques, and in particular additive manufacturing, allow one to design complex and customizable polymer architectures that are particularly relevant to fabricate auxetic mechanical metamaterials. Although these metamaterials exhibit exotic mechanical properties with potential applications in several engineering fields, biomedical applications seem to be one of the most relevant with a growing number of articles published over recent years. As a result, special focus is needed to understand the potential of these structures and foster theoretical and experimental investigations on the potential benefits of the unusual mechanical properties of these materials on the way to high performance biomedical applications. The present Review provides up to date information on the recent progress of polymer-based auxetic mechanical metamaterials mainly fabricated using additive manufacturing methods with a special focus toward biomedical applications including tissue engineering as well as medical devices including stents and sensors.

In Vitro Cellular Strain Models of Tendon Biology and Tenogenic Differentiation

Research has shown that the surrounding biomechanical environment plays a significant role in the development, differentiation, repair, and degradation of tendon, but the interactions between tendon cells and the forces they experience are complex. In vitro mechanical stimulation models attempt to understand the effects of mechanical load on tendon and connective tissue progenitor cells. This article reviews multiple mechanical stimulation models used to study tendon mechanobiology and provides an overview of the current progress in modelling the complex native biomechanical environment of tendon. Though great strides have been made in advancing the understanding of the role of mechanical stimulation in tendon development, damage, and repair, there exists no ideal in vitro model. Further comparative studies and careful consideration of loading parameters, cell populations, and biochemical additives may further offer new insight into an ideal model for the support of tendon regeneration studies.

Onset of criticality in hyper-auxetic polymer networks

Against common sense, auxetic materials expand or contract perpendicularly when stretched or compressed, respectively, by uniaxial strain, being characterized by a negative Poisson's ratio ν. The amount of deformation in response to the applied force can be at most equal to the imposed one, so that ν = - 1 is the lowest bound for the mechanical stability of solids, a condition here defined as "hyper-auxeticity". In this work, we numerically show that ultra-low-crosslinked polymer networks under tension display hyper-auxetic behavior at a finite crosslinker concentration. At this point, the nearby mechanical instability triggers the onset of a critical-like transition between two states of different densities. This phenomenon displays similar features as well as important differences with respect to gas-liquid phase separation. Since our model is able to faithfully describe real-world hydrogels, the present results can be readily tested in laboratory experiments, paving the way to explore this unconventional phase behavior.

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 Hybrid Microstructural-Continuum Multiscale Approach for Modeling Hyperelastic Fibrous Soft Tissue

The heterogeneous, nonlinear, anisotropic material behavior of biological tissues makes precise definition of an accurate constitutive model difficult. One possible solution to this issue would be to define microstructural elements and perform fully coupled multiscale simulation. However, for complex geometries and loading scenarios, the computational costs of such simulations can be prohibitive. Ideally then, we should seek a method that contains microstructural detail, but leverages the speed of classical continuum-based finite-element (FE) modeling. In this work, we demonstrate the use of the Holzapfel-Gasser-Ogden (HGO) model [1, 2] to fit the behavior of microstructural network models. We show that Delaunay microstructural networks can be fit to the HGO strain energy function by calculating fiber network strain energy and average fiber stretch ratio. We then use the HGO constitutive model in a FE framework to improve the speed of our hybrid model, and demonstrate that this method, combined with a material property update scheme, can match a full multiscale simulation. This method gives us flexibility in defining complex FE simulations that would be impossible, or at least prohibitively time consuming, in multiscale simulation, while still accounting for microstructural heterogeneity.

Application of textile technology in tissue engineering: A review

One of the key elements in tissue engineering is to design and fabricate scaffolds with tissue-like properties. Among various scaffold fabrication methods, textile technology has shown its unique advantages in mimicking human tissues' properties such as hierarchical, anisotropic, and strain-stiffening properties. As essential components in textile technology, textile patterns affect the porosity, architecture, and mechanical properties of textile-based scaffolds. However, the potential of various textile patterns has not been fully explored when fabricating textile-based scaffolds, and the effect of different textile patterns on scaffold properties has not been thoroughly investigated. This review summarizes textile technology development and highlights its application in tissue engineering to facilitate the broader application of textile technology, especially various textile patterns in tissue engineering. The potential of using different textile methods such as weaving, knitting, and braiding to mimic properties of human tissues is discussed, and the effect of process parameters in these methods on fabric properties is summarized. Finally, perspectives on future directions for explorations are presented. STATEMENT OF SIGNIFICANCE: Recently, biomedical engineers have applied textile technology to fabricate scaffolds for tissue engineering applications. Various textile methods, especially weaving, knitting, and braiding, enables engineers to customize the physical, mechanical, and biological properties of scaffolds. However, most textile-based scaffolds only use simple textile patterns, and the effect of different textile patterns on scaffold properties has not been thoroughly investigated. In this review, we cover for the first time the effect of process parameters in different textile methods on fabric properties, exploring the potential of using different textile methods to mimic properties of human tissues. Previous advances in textile technology are presented, and future directions for explorations are presented, hoping to facilitate new breakthroughs of textile-based tissue engineering.

Shearing Deformations of β-Cristobalite-Like Boron Arsenate

Boron arsenate, BAsO4, is crystalline material (I4¯ group) that was recently shown to be auxetic in its (001) plane for loading in any direction in this plane, and, which exhibits negative linear compressibility at elevated pressured in its [001] direction. This work presents and discusses the results of extensive density functional theory (DFT) based simulations aimed at studying deformations that such crystals undergo when subjected to shear loading in an attempt to obtain a better insight into the manner in which this material responds to mechanical loads. The deformations for shearing in the (001) plane are described in terms of the ‘rotating squares’ model, which was used to explain the auxeticity in the same plane where it was shown that shear loading results primarily in deformations which make the ‘squares’ become ‘parallelogram-like’ rather than rotate. This lack of rigidity in projected ‘squares’ was discussed by looking at changes in bond lengths and bond angles.

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.

Idealized 3D Auxetic Mechanical Metamaterial: An Analytical, Numerical, and Experimental Study

Mechanical metamaterials are man-made rationally-designed structures that present unprecedented mechanical properties not found in nature. One of the most well-known mechanical metamaterials is auxetics, which demonstrates negative Poisson's ratio (NPR) behavior that is very beneficial in several industrial applications. In this study, a specific type of auxetic metamaterial structure namely idealized 3D re-entrant structure is studied analytically, numerically, and experimentally. The noted structure is constructed of three types of struts-one loaded purely axially and two loaded simultaneously flexurally and axially, which are inclined and are spatially defined by angles θ and φ. Analytical relationships for elastic modulus, yield stress, and Poisson's ratio of the 3D re-entrant unit cell are derived based on two well-known beam theories namely Euler-Bernoulli and Timoshenko. Moreover, two finite element approaches one based on beam elements and one based on volumetric elements are implemented. Furthermore, several specimens are additively manufactured (3D printed) and tested under compression. The analytical results had good agreement with the experimental results on the one hand and the volumetric finite element model results on the other hand. Moreover, the effect of various geometrical parameters on the mechanical properties of the structure was studied, and the results demonstrated that angle θ (related to tension-dominated struts) has the highest influence on the sign of Poisson's ratio and its extent, while angle φ (related to compression-dominated struts) has the lowest influence on the Poisson's ratio. Nevertheless, the compression-dominated struts (defined by angle φ) provide strength and stiffness for the structure. The results also demonstrated that the structure could have zero Poisson's ratio for a specific range of θ and φ angles. Finally, a lightened 3D re-entrant structure is introduced, and its results are compared to those of the idealized 3D re-entrant structure.

Fiber splay precludes the direct identification of ligament material properties: Implications for ACL graft selection

Anterior cruciate ligament (ACL) injuries typically require surgical reconstruction to restore adequate knee stability. The middle third of an injured patient's patellar tendon (PT) is a commonly used graft for ACL reconstruction. However, many clinicians and researchers question whether it is the best option, as several studies have suggested that it is a stiffer material than the ACL. Still, there is little to no consensus on even the most basic material property of ligaments/tendons: the tangent modulus in the fiber direction, or slope of the linear portion of the uniaxial stress-strain curve. In this study, we investigate the effect of fiber splay (the tendency of collagen fibers to spread out near the enthesis) on the apparent tangent modulus. Using a simplified theoretical model, we establish a quantity we call the splay ratio, which describes the relationship between splay geometry and the apparent tangent modulus. We then more rigorously investigate the effect of the splay ratio on the apparent tangent modulus of the ovine PT and anteromedial and posterolateral regions of the ACL using experimental and computational methods. Both approaches confirmed that splay geometry significantly affects the apparent material behavior. Because true material properties are independent of geometry, we conclude that the macroscopic response of ligaments and tendons is not sufficient for the characterization of their material properties, but rather is reflective of both material and structural properties. We further conclude that the PT is probably not a stiffer material than ACL, but that the PT graft is likely a stiffer structure than either ACL region.

A biomechanical study of clamping technique on patellar tendon surface strain and material properties using digital image correlation

Several clamping techniques exist for ex vivo mechanical testing of tendon. For the patellar tendon, one can choose to clamp directly to the bony attachment sites, the tendon itself, or a combination of the two; however, the influence of these techniques on localized strains and gross material properties is unknown. To this end, uniaxial tensile tests were performed on eleven porcine patellar tendons in three clamping setups while digital image correlation was used to measure axial and transverse strains, Young's modulus, and Poisson's ratio. The setups involved clamping to: 1) the patella and tibia, 2) the patella and the dissected distal tendon, and 3) the dissected proximal and distal tendon. Axial strains in the tendon-tendon clamping setup were 181% higher than patella-tibia clamping (p = 0.002) and 131% higher than patella-tendon clamping (p = 0.006). Transverse strains were not significantly different between clamping conditions (p ≥ 0.118). Young's modulus was 50% (p < 0.001) greater for patella-tibia clamping and 42% (p < 0.001) greater for patella-tendon clamping when compared to tendon-tendon clamping. For all clamping setups, the tendon illustrated auxetic behaviour (i.e., negative Poisson's ratio); however, the Poisson's ratios were 80% smaller in the patella-tibia setup (p = 0.006) and 71% smaller patella-tendon setup (p = 0.007) compared to the tendon-tendon setup. These results illustrate that discretion should be utilized when reporting material properties derived from mechanical tests involving direct clamping to the dissected patellar tendon at both ends, as this clamping technique significantly increases axial strains, reduces Young's modulus, and alters the tendon's natural auxetic behaviour.

4D Printing of NiTi Auxetic Structure with Improved Ballistic Performance

Auxetic structures have attracted attention in energy absorption applications owing to their improved shear modulus and enhanced resistance to indentation. On the other hand, four-dimensional (4D) printing is an emerging technology that is capable of 3D printing smart materials with additional functionality. This paper introduces the development of a NiTi negative-Poisson's-ratio structure with superelasticity/shape memory capabilities for improved ballistic applications. An analytical model was initially used to optimize the geometrical parameters of a re-entrant auxetic structure. It was found that the re-entrant auxetic structure with a cell angle of -30° produced the highest Poisson's ratio of -2.089. The 4D printing process using a powder bed fusion system was used to fabricate the optimized NiTi auxetic structure. The measured negative Poisson's ratio of the fabricated auxetic structure was found in agreement with both the analytical model and the finite element simulation. A finite element model was developed to simulate the dynamic response of the optimized auxetic NiTi structure subjected to different projectile speeds. Three stages of the impact process describing the penetration of the top plate, auxetic structure, and bottom plate have been identified. The results show that the optimized auxetic structures affect the dynamic response of the projectile by getting denser toward the impact location. This helped to improve the energy absorbed per unit mass of the NiTi auxetic structure to about two times higher than that of the solid NiTi plate and five times higher than that of the solid conventional steel plate.

Osmo-inelastic response of the intervertebral disc annulus fibrosus tissue

The aim of this article is to provide some insights on the osmo-inelastic response under stretching of annulus fibrosus of the intervertebral disc. Circumferentially oriented specimens of square cross section, extracted from different regions of bovine cervical discs (ventral-lateral and dorsal-lateral), are tested under different strain-rates and saline concentrations within normal range of strains. An accurate optical strain measuring technique, based upon digital image correlation, is used in order to determine the full-field displacements in the lamellae and fibers planes of the layered soft tissue. Annulus stress-stretch relationships are measured along with full-field transversal strains in the two planes. The mechanical response is found hysteretic, rate-dependent and osmolarity-dependent with a Poisson's ratio higher than 0.5 in the fibers plane and negative (auxeticity) in the lamellae plane. While the stiffness presents a regional-dependency due to variations in collagen fibers content/orientation, the strain-rate sensitivity of the response is found independent on the region. A significant osmotic effect is found on both the auxetic response in the lamellae plane and the stiffness rate-sensitivity. These local experimental observations will result in more accurate chemo-mechanical modeling of the disc annulus and a clearer multi-scale understanding of the disc intervertebral function.

Role of Biomaterials and Controlled Architecture on Tendon/Ligament Repair and Regeneration

Engineering synthetic scaffolds to repair and regenerate ruptured native tendon and ligament (T/L) tissues is a significant engineering challenge due to the need to satisfy both the unique biological and biomechanical properties of these tissues. Long-term clinical outcomes of synthetic scaffolds relying solely on high uniaxial tensile strength are poor with high rates of implant rupture and synovitis. Ideal biomaterials for T/L repair and regeneration need to possess the appropriate biological and biomechanical properties necessary for the successful repair and regeneration of ruptured tendon and ligament tissues.

The use of auxetic materials in tissue engineering

A number of biological tissues have been reported as behaving in an auxetic manner, defined by a negative Poisson's ratio. This describes the deformation of tissue which expands in the axial and the transverse directions simultaneously while under uniaxial tension; and contracts axially and transversely upon uniaxial compression. The discovery of auxetic behaviour within biological tissues has implications for the recreation of the auxetic loading environment within tissue engineering. Tissue engineers strive to recreate the natural properties of biological tissue and in order to recreate the unique loading environment of cells from auxetic tissue, an auxetic scaffold is required. A number of studies have used a variety of auxetic scaffolds within tissue engineering. Investigation into the effect of auxetic micro-environments created by auxetic scaffolds on cellular behaviour has demonstrated an increased cellular proliferation and enhanced differentiation. Here, we discuss studies which have identified auxetic behaviour within biological tissues, and where cells have been cultured within auxetic scaffolds, bringing together current knowledge of the potential use of auxetic materials in tissue engineering applications and biomedical devices.

Meta-biomaterials

Meta-biomaterials are designer biomaterials with unusual and even unprecedented properties that primarily originate from their geometrical designs at different (usually smaller) length scales.

Interlamellar-induced time-dependent response of intervertebral disc annulus: A microstructure-based chemo-viscoelastic model

The annulus fibrosus of the intervertebral disc exhibits an unusual transversal behavior for which a constitutive representation that considers as well regional effect, chemical sensitivity and time-dependency has not yet been developed, and it is hence the aim of the present contribution. A physically-based model is proposed by introducing a free energy function that takes into account the actual disc annulus structure in relation with the surrounding biochemical environment. The response is assumed to be dominated by the viscoelastic contribution of the extracellular matrix, the elastic contribution of the oriented collagen fibers and the osmo-induced volumetric contribution of the internal fluid content variation. The regional dependence of the disc annulus response due to variation in fibers content/orientation allows a micromechanical treatment of the soft tissue. A finite element model of the annulus specimen is designed while taking into consideration the 'interlamellar' ground substance zone between lamellae of the layered soft tissue. The kinetics is designed using full-field strain measurements performed on specimens extracted from two disc annulus regions and tested under different osmotic conditions. The time-dependency of the tissue response is reported on stress-free volumetric changes, on hysteretic stress and transversal strains during quasi-static stretching at different strain-rates and on their temporal changes during an interrupted stretching. Considering the effective contributions of the internal fluid transfer and the extracellular matrix viscosity, the microstructure-based chemo-mechanical model is found able to successfully reproduce the significant features of the macro-response and the unusual transversal behavior including the strong regional dependency from inner to outer parts of the disc: Poisson's ratio lesser than 0 (auxetic) in lamellae plane, higher than 0.5 in fibers plane, and their temporal changes towards usual values (between 0 and 0.5) at chemo-mechanical equilibrium. The underlying time-dependent mechanisms occurring in the tissue are analyzed via the local numerical fields and important insights about the effective role of the interlamellar zone are revealed for the different disc localizations. STATEMENT OF SIGNIFICANCE: The structural complexity of the annulus fibrosus has only been appreciated through recent experimental contributions and a constitutive representation that considers as well regional effect, chemical sensitivity and time-dependency of the unusual transversal behavior has not yet been developed. Here, a microstructure-based chemo-viscoelastic model is developed to highlight the interlamellar-induced time-dependent response by means of a two-scale strategy. The model provides important insights about the origin of the time-dependent phenomena in disc annulus along with regional dependency, essential for understanding disc functionality.

An experimental and numerical study on the transverse deformations in tensile test of tendons

The transverse deformations of tendons assessed in tensile tests seems to constitute a controversial issue in literature. On the one hand, large positive variations of the Poisson's ratio have been reported, indicating volume reduction under tensile states. On the other hand, negative values were also observed, pointing out an auxetic material response. Based on these experimental observations, the following question is raised: Are these large and discrepant transverse deformations intrinsically related to the constitutive response of tendons or they result from artifacts of the mechanical test setup? In order to provide further insights to this question, an experimental and numerical study on the transverse kinematics of tendons was carried out. Tensile experiments were performed in branches of deep digital flexor tendons of domestic porcine, where the transverse displacements were measured by two high-speed, high-accuracy optical digital micrometers placed transversely to one another. Aiming at a better understanding of the effects of the mechanical test setup in the transverse measurements, a three-dimensional finite element model is proposed to resemble the tensile experiment. The main achieved results strongly support the following hypotheses regarding tensile tests of tendons: the clamping region considerably affects the kinematics of the specimen even at a large distance from the clamps; the transverse deformations are mainly ruled by stiff fibers embedded in a soft matrix; the generalization of the Poisson's ratio to draw conclusions about changes in volume of tendons may lead to misinterpretations.

Mechanical performance of additively manufactured meta-biomaterials

Additive manufacturing (AM) (=3D printing) and rational design techniques have enabled development of meta-biomaterials with unprecedented combinations of mechanical, mass transport, and biological properties. Such meta-biomaterials are usually topologically ordered and are designed by repeating a number of regular unit cells in different directions to create a lattice structure. Establishing accurate topology-property relationships is of critical importance for these materials. In this paper, we specifically focus on AM metallic meta-biomaterials aimed for application as bone substitutes and orthopaedic implants and review the currently available evidence regarding their mechanical performance under quasi-static and cyclic loading conditions. The topology-property relationships are reviewed for regular beam-based lattice structures, sheet-based lattice structures including those based on triply periodic minimal surface, and graded designs. The predictive models used for establishing the topology-property relationships including analytical and computational models are covered as well. Moreover, we present an overview of the effects of the AM processes, material type, tissue regeneration, biodegradation, surface bio-functionalization, post-manufacturing (heat) treatments, and loading profiles on the quasi-static mechanical properties and fatigue behavior of AM meta-biomaterials. AM meta-biomaterials exhibiting unusual mechanical properties such as negative Poisson's ratios (auxetic meta-biomaterials), shape memory behavior, and superelasitcity as well as the potential applications of such unusual behaviors (e.g. deployable implants) are presented too. The paper concludes with some suggestions for future research. STATEMENT OF SIGNIFICANCE: Additive manufacturing enables fabrication of meta-biomaterials with rare combinations of topological, mechanical, and mass transport properties. Given that the micro-scale topological design determines the macro-scale properties of meta-biomaterials, establishing topology-property relationships is the central research question when rationally designing meta-biomaterials. The interest in understanding the relationship between the topological design and material type on the one hand and the mechanical properties and fatigue behavior of meta-biomaterials on the other hand is currently booming. This paper presents and critically evaluates the most important trends and findings in this area with a special focus on the metallic biomaterials used for skeletal applications to enable researchers better understand the current state-of-the-art and to guide the design of future research projects.

Tenogenically differentiated adipose-derived stem cells are effective in Achilles tendon repair in vivo

The purpose of this study was to characterize rat adipose-derived stem cells, induce adipose-derived stem cell tenogenesis, and analyze adipose-derived stem cell effects on tendon repair in vivo. Adipose-derived stem cells demonstrated an immunomodulatory, pro-angiogenic, and pro-proliferatory profile in vitro. Tenogenesis was induced for 1, 7, 14, and 21 days with 24 combinations of growth differentiation factor-5, 6, and 7 and platelet-derived growth factor–BB. Adipose-derived stem cells expression of scleraxis and collagen type I increased the most after 14 days of induction with growth differentiation factor-6 and platelet-derived growth factor–BB. Achilles excision defects injected with hydrogel alone (Gp2), with undifferentiated (Gp3) adipose-derived stem cells, or tenogenically differentiated (Gp4) adipose-derived stem cells exhibited improved tissue repair compared with untreated tendons (Gp1). Addition of adipose-derived stem cells improved tissue cytoarchitecture and increased expression of collagen type I and III, scleraxis, and tenomodulin. Adipose-derived stem cells significantly improved biomechanical properties (ultimate load and elastic toughness) over time more than hydrogel alone, while tenogenically differentiated adipose-derived stem cells improved the mean histological score and collagen fiber dispersion range closest to normal tendon. In addition, tendon sections treated with GFP-adipose-derived stem cells exhibited green fluorescence and positive GFP immunostaining on microscopy confirming the in vivo survival of adipose-derived stem cells that were injected into tendon defects to support the effects of adipose-derived stem cells on tissue up to 4.5 weeks post injury.

Viscoelastic shear lag model to predict the micromechanical behavior of tendon under dynamic tensile loading

Owing to its viscoelastic nature, tendon exhibits stress rate-dependent breaking and stiffness function. A Kelvin-Voigt viscoelastic shear lag model is proposed to illustrate the micromechanical behavior of the tendon under dynamic tensile conditions. Theoretical closed-form expressions are derived to predict the deformation and stress transfer between fibrils and interfibrillar matrix while tendon is dynamically stretched. The results from the analytical solutions demonstrate that how the fibril overlap length and fibril volume fraction affect the stress transfer and mechanical properties of tendon. We find that the viscoelastic property of interfibrillar matrix mainly results in collagen fibril failure under fast loading rate or creep rupture of tendon. However, discontinuous fibril model and hierarchical structure of tendon ensure relative sliding under slow loading rate, helping dissipate energy and protecting fibril from damage, which may be a key reason why regularly staggering alignment microstructure is widely selected in nature. According to the growth, injury, healing and healed process of tendon observed by many researchers, the conclusions presented in this paper agrees well with the experimental findings. Additionally, the emphasis of this paper is on micromechanical behavior of tendon, whereas this analytical viscoelastic shear lag model can be equally applicable to other soft or hard tissues, owning the similar microstructure.

Digital image correlation-aided mechanical characterization of the anteromedial and posterolateral bundles of the anterior cruciate ligament

The anterior cruciate ligament (ACL) is one of the most commonly injured soft tissue structures in the articular knee joint, often requiring invasive surgery for patients to restore pre-injury knee kinematics. There is a pressing need to understand the role of the ACL in knee function, in order to select proper replacements. Digital image correlation (DIC), a non-contact full field displacement measurement technique, is an established tool for evaluating non-biological materials. The application of DIC to soft tissues has been in the nascent stages, largely due to patterning challenges of such materials. The ACL is notoriously difficult to mechanically characterize, due to the complex geometry of its two bundles and their insertions. This paper examines the use of DIC to determine the tensile mechanical properties of the AM and PL bundles of ovine ACLs in a well-known loading state. Homogenous loading in the mid-substance of the bundles provides for accurate development of stress/strain curves using DIC. Animal to animal variability is reduced, and the bundles are stiffer than previously thought when tissue-level strains are accurately measured.

STATEMENT OF SIGNIFICANCE

The anterior cruciate ligament (ACL), a major stabilizing ligament of the articular knee joint, is one of the most commonly injured soft tissue structures in the knee. Often, invasive surgery is required to restore pre-injury knee kinematics, and there are several long-term consequences of ACL reconstructions, including early-onset osteoarthritis. The role of the ACL in knee stability and motion has received much attention in the biomechanics community. This paper examines the use of a non-contact full-field displacement measurement technique, digital image correlation, to determine the tensile mechanical properties of the ACL. The focus of this work is to investigate the intrinsic mechanical properties of the ACL, as new knowledge in these areas will aid clinicians in selecting ACL replacements.

3D-printed biomaterials with regional auxetic properties

Tissue engineering is replete with methods for inducing and mediating cell differentiation, which are crucial for ensuring proper regrowth of desired tissues. In this study, we developed a 3D-printed, non-positive Poisson's Ratio (NPPR) scaffold intended for future use in stretch-mediated cell differentiation applications, such as in muscle and tendon regeneration. We utilized dynamic optical projection stereolithography (DOPsL) to fabricate multi-layered, cell-laden NPPR scaffolds - these scaffolds can not only support aggregate cell growth, but can also be printed with locally-tunable force-displacement properties at length scales appropriate for tissue interaction. These NPPR multilayered mesh scaffolds can be embedded into highly elastic hydrogels in order to couple a reduced NPPR behavior to a normally Positive Poisson's Ratio (PPR) solid bulk material. This hybrid structure may potentially enable induced 'auxetic' behavior at the single-cell scale while tuning the Poisson's Ratio to a more isolated value. This would be uniquely suited for providing stretch-mediated effects for various cell-types within the tendon-to-muscle tissue transition.

Auxetic mechanical metamaterials

We review the topology–property relationship and the spread of Young's modulus–Poisson's ratio duos in three main classes of auxetic metamaterials.