Hierarchical simulations for the design of supertough nanofibers inspired by spider silk

Modeling and design of heterogeneous hierarchical bioinspired spider web structures using deep learning and additive manufacturing

Spider webs are incredible biological structures, comprising thin but strong silk filament and arranged into complex hierarchical architectures with striking mechanical properties (e.g., lightweight but high strength, achieving diverse mechanical responses). While simple 2D orb webs can easily be mimicked, the modeling and synthesis of 3D-based web structures remain challenging, partly due to the rich set of design features. Here, we provide a detailed analysis of the heterogeneous graph structures of spider webs and use deep learning as a way to model and then synthesize artificial, bioinspired 3D web structures. The generative models are conditioned based on key geometric parameters (including average edge length, number of nodes, average node degree, and others). To identify graph construction principles, we use inductive representation sampling of large experimentally determined spider web graphs, to yield a dataset that is used to train three conditional generative models: 1) an analog diffusion model inspired by nonequilibrium thermodynamics, with sparse neighbor representation; 2) a discrete diffusion model with full neighbor representation; and 3) an autoregressive transformer architecture with full neighbor representation. All three models are scalable, produce complex, de novo bioinspired spider web mimics, and successfully construct graphs that meet the design objectives. We further propose an algorithm that assembles web samples produced by the generative models into larger-scale structures based on a series of geometric design targets, including helical and parametric shapes, mimicking, and extending natural design principles toward integration with diverging engineering objectives. Several webs are manufactured using 3D printing and tested to assess mechanical properties.

Hybrid Spider Silk with Inorganic Nanomaterials

High-performance functional biomaterials are becoming increasingly requested. Numerous natural and artificial polymers have already demonstrated their ability to serve as a basis for bio-composites. Spider silk offers a unique combination of desirable aspects such as biocompatibility, extraordinary mechanical properties, and tunable biodegradability, which are superior to those of most natural and engineered materials. Modifying spider silk with various inorganic nanomaterials with specific properties has led to the development of the hybrid materials with improved functionality. The purpose of using these inorganic nanomaterials is primarily due to their chemical nature, enhanced by large surface areas and quantum size phenomena. Functional properties of nanoparticles can be implemented to macro-scale components to produce silk-based hybrid materials, while spider silk fibers can serve as a matrix to combine the benefits of the functional components. Therefore, it is not surprising that hybrid materials based on spider silk and inorganic nanomaterials are considered extremely promising for potentially attractive applications in various fields, from optics and photonics to tissue regeneration. This review summarizes and discusses evidence of the use of various kinds of inorganic compounds in spider silk modification intended for a multitude of applications. It also provides an insight into approaches for obtaining hybrid silk-based materials via 3D printing.

Strength of filament bundles - The role of bundle structure stochasticity

Most biological fibrous materials are hierarchical, in the sense that fibers of finite length assemble in bundles, which then form networks with structural role. Examples include collagen, silk, fibrin and microtubules. Some artificial fiber-based materials share this characteristic, examples including carbon nanotube (CNT) yarns and unidirectional composites. Here we study bundles in which filaments do not break, while bundle rupture happens by the failure of inter-filament crosslinks, followed by pull-out. In all cases, the crosslinks are randomly distributed along interfaces. The strength of such bundles depends on material parameters of the filaments and crosslinks, such as their stiffness and strength, and on the cross-link density. We focus on the dependence of the bundle strength on two parameters: filament waviness and filament staggering. Bundles with regular staggering are stronger than those with stochastic staggering. We identify the optimal regular staggering that maximizes the strength. Filament waviness increases the strength of stochastically staggered bundles at constant crosslink density but decreases the strength of regularly staggered bundles. Results for bundles with permanent crosslinks, which never reform once they break, as well as transient crosslinks capable of reforming during deformation are presented, and it is shown that the general trends are independent of the nature of the crosslinks. The results are discussed in the context of collagen and carbon nanotube bundles.

De Novo Design of Recombinant Spider Silk Proteins for Material Applications

Spider silks are well known for their superior mechanical properties that are stronger and tougher than steel despite being assembled at close to ambient conditions and using water as the solvent. However, it is a significant challenge to utilize spider silks for practical applications due to their limited sources. Fortunately, genetic engineering techniques offer a promising approach to produce useable amounts of spider silk variants. Starting from these recombinant spider silk proteins, a series of experiments and simulations strategies are developed to improve the recombinant spider silk proteins (RSSP) material design and fabrication with the aim of biomimicking the structure-property-function relationships of spider silks. Accordingly, in this review, the authors first introduce the structure-property-function relationship of spider silks. Then, the recent progress in the genetic synthesis of RSSPs is discussed and their related multiscale self-assembly behaviors is summarized. Finally, the authors outline works utilizing multiscale modeling to assist RSSP material design.

Compliant threads maximize spider silk connection strength and toughness

Millions of years of evolution have adapted spider webs to achieve a range of functionalities, including the well-known capture of prey, with efficient use of material. One feature that has escaped extensive investigation is the silk-on-silk connection joints within spider webs, particularly from a structural mechanics perspective. We report a joint theoretical and computational analysis of an idealized silk-on-silk fibre junction. By modifying the theory of multiple peeling, we quantitatively compare the performance of the system while systematically increasing the rigidity of the anchor thread, by both scaling the stress-strain response and the introduction of an applied pre-strain. The results of our study indicate that compliance is a virtue-the more extensible the anchorage, the tougher and stronger the connection becomes. In consideration of the theoretical model, in comparison with rigid substrates, a compliant anchorage enormously increases the effective adhesion strength (work required to detach), independent of the adhered thread itself, attributed to a nonlinear alignment between thread and anchor (contact peeling angle). The results can direct novel engineering design principles to achieve possible load transfer from compliant fibre-to-fibre anchorages, be they silk-on-silk or another, as-yet undeveloped, system.

Bioinspired structural materials

Natural structural materials are built at ambient temperature from a fairly limited selection of components. They usually comprise hard and soft phases arranged in complex hierarchical architectures, with characteristic dimensions spanning from the nanoscale to the macroscale. The resulting materials are lightweight and often display unique combinations of strength and toughness, but have proven difficult to mimic synthetically. Here, we review the common design motifs of a range of natural structural materials, and discuss the difficulties associated with the design and fabrication of synthetic structures that mimic the structural and mechanical characteristics of their natural counterparts.

Self-healing of hierarchical materials

We present a theoretical and numerical analysis of the mechanical behavior of self-healing materials using an analytical model and numerical calculations both based on a Hierarchical Fiber Bundle Model, and applying them to graphene- or carbon-nanotube-based materials. The self-healing process can be described essentially through a single parameter, that is, the healing rate, but numerical simulations also highlight the influence of the location of the healing process on the overall strengthening and toughening of the material. The role of hierarchy is discussed, showing that full-scale hierarchical structures can in fact acquire more favorable properties than smaller, nonhierarchical ones through interaction with the self-healing process, thus inverting the common notion in fracture mechanics that specimen strength increases with decreasing size. Further, the study demonstrates that the developed analytical and numerical tools can be useful to develop strategies for the optimization of strength and toughness of synthetic bioinspired materials.

Imperfections in a two-dimensional hierarchical structure

Hierarchical and fractal designs have been shown to yield high mechanical efficiency under a variety of loading conditions. Here a fractal frame is optimized for compressive loading in a two-dimensional space. We obtain the dependence of volume required for stability against loading for which the structure is optimized and a set of scaling relationships is found. We evaluate the dependence of the Hausdorff dimension of the optimal structure on the applied loading and establish the limit to which it tends under gentle loading. We then investigate the effect of a single imperfection in the structure through both analytical and simulational techniques. We find that a single asymmetric perturbation of beam thickness, increasing or decreasing the failure load of the individual beam, causes the same decrease in overall stability of the structure. A scaling relationship between imperfection magnitude and decrease in failure loading is obtained. We calculate theoretically the limit to which the single perturbation can effect the overall stability of higher generation frames.

Synergetic material and structure optimization yields robust spider web anchorages

Millions of years of evolution have adapted spider webs to achieve a range of properties, including the well-known capture of prey, with efficient use of materials. One feature that remains poorly understood is the attachment disc, a network of silk fibers that mechanically anchors a web to its environment. Experimental observations suggest that one possible attachment disc adheres to a substrate through multiple symmetrically branched structures composed of sub-micrometer scale silk fibers. Here, a theoretical model is used to explore the adaptation of the strength of attachment of such an anchorage, and complementary mesoscale simulations are applied to demonstrate a novel mechanism of synergetic material and structural optimization, such that the maximum anchorage strength can be achieved regardless of the initial anchor placement or material type. The optimal delamination (peeling) angle is facilitated by the inherent extensibility of silk, and is attained automatically during the process of delamination. This concept of self-optimizing peeling angle suggests that attachment discs do not require precise placement by the spider, irrespective of adhesion strength. Additional hierarchical branching of the anchorage increases efficiency, where both the delamination force and toughness modulus increase with a splitting of the cross-sectional area.

Brittle-to-ductile transition in a fiber bundle with strong heterogeneity

We analyze the failure process of a two-component system with widely different fracture strength in the framework of a fiber bundle model with localized load sharing. A fraction 0≤α≤1 of the bundle is strong and it is represented by unbreakable fibers, while fibers of the weak component have randomly distributed failure strength. Computer simulations revealed that there exists a critical composition α(c) which separates two qualitatively different behaviors: Below the critical point, the failure of the bundle is brittle, characterized by an abrupt damage growth within the breakable part of the system. Above α(c), however, the macroscopic response becomes ductile, providing stability during the entire breaking process. The transition occurs at an astonishingly low fraction of strong fibers which can have importance for applications. We show that in the ductile phase, the size distribution of breaking bursts has a power law functional form with an exponent μ=2 followed by an exponential cutoff. In the brittle phase, the power law also prevails but with a higher exponent μ=9/2. The transition between the two phases shows analogies to continuous phase transitions. Analyzing the microstructure of the damage, it was found that at the beginning of the fracture process cracks nucleate randomly, while later on growth and coalescence of cracks dominate, which give rise to power law distributed crack sizes.

Avalanche process of the fiber-bundle model with stick-slip dynamics and a variable Young modulus

In order to more accurately describe the fracture process of extensive biological fibers, a fiber-bundle model with stick-slip dynamics and a variable Young modulus is constructed. In this model, the Young modulus of a fiber is assumed to increase or decrease by multiplying with a changing ratio after local sliding events. So, the maximum number of stick-slip events of a single fiber and the changing ratio of the Young modulus are the two key parameters of the model. By means of analytical theory and numerical simulation, the constitutive law, the critical stress, the average size of the largest avalanche, and the avalanche size distribution are shown against the two parameters of the model. From a macroscopic viewpoint, the constitutive curves show different morphologies varying from a local plastic state to a unimodal parabola, while from a microscopic viewpoint, the avalanche size distributions can be well fitted into a power law relationship, which is in accord with the classical fiber-bundle model.

Healable thermoset polymer composite embedded with stimuli-responsive fibres

Severe wounds in biological systems such as human skin cannot heal themselves, unless they are first stitched together. Healing of macroscopic damage in thermoset polymer composites faces a similar challenge. Stimuli-responsive shape-changing polymeric fibres with outstanding mechanical properties embedded in polymers may be able to close macro-cracks automatically upon stimulation such as heating. Here, a stimuli-responsive fibre (SRF) with outstanding mechanical properties and supercontraction capability was fabricated for the purpose of healing macroscopic damage. The SRFs and thermoplastic particles (TPs) were incorporated into regular thermosetting epoxy for repeatedly healing macroscopic damages. The system works by mimicking self-healing of biological systems such as human skin, close (stitch) then heal, i.e. close the macroscopic crack through the thermal-induced supercontraction of the SRFs, and bond the closed crack through melting and diffusing of TPs at the crack interface. The healing efficiency determined using tapered double-cantilever beam specimens was 94 per cent. The self-healing process was reasonably repeatable.

Bioinspired, mechanical, deterministic fractal model for hierarchical suture joints

Many biological systems possess hierarchical and fractal-like interfaces and joint structures that bear and transmit loads, absorb energy, and accommodate growth, respiration, and/or locomotion. In this paper, an elastic deterministic fractal composite mechanical model was formulated to quantitatively investigate the role of structural hierarchy on the stiffness, strength, and failure of suture joints. From this model, it was revealed that the number of hierarchies (N) can be used to tailor and to amplify mechanical properties nonlinearly and with high sensitivity over a wide range of values (orders of magnitude) for a given volume and weight. Additionally, increasing hierarchy was found to result in mechanical interlocking of higher-order teeth, which creates additional load resistance capability, thereby preventing catastrophic failure in major teeth and providing flaw tolerance. Hence, this paper shows that the diversity of hierarchical and fractal-like interfaces and joints found in nature have definitive functional consequences and is an effective geometric-structural strategy to achieve different properties with limited material options in nature when other structural geometries and parameters are biologically challenging or inaccessible. This paper also indicates the use of hierarchy as a design strategy to increase design space and provides predictive capabilities to guide the mechanical design of synthetic flaw-tolerant bioinspired interfaces and joints.

Investigating the role of hierarchy on the strength of composite materials: evidence of a crucial synergy between hierarchy and material mixing

Natural materials are often organized in complex hierarchical architectures to optimize mechanical properties. Artificial bio-inspired materials, however, have thus far failed to successfully mimic how these architectures improve material characteristics, for example strength. Here, a method is proposed for evaluating the role of hierarchy on structural strength. To do this, we consider different hierarchical architectures of fiber bundles through analytical multiscale calculations based on a fiber bundle model at each hierarchical level. In general, we find that an increase in the number of hierarchy levels leads to a decrease in the strength of material. However, when a composite bundle with two different types of fibers is considered, an improvement in the mean strength is obtained for some specific hierarchical architectures, indicating that both hierarchy and material "mixing" are necessary ingredients to obtain improved mechanical properties. Results are promising for the improvement and "tuning" of the strength of bio-inspired materials.

Evidence of the most stretchable egg sac silk stalk, of the European spider of the year Meta menardi

Spider silks display generally strong mechanical properties, even if differences between species and within the same species can be observed. While many different types of silks have been tested, the mechanical properties of stalks of silk taken from the egg sac of the cave spider Meta menardi have not yet been analyzed. Meta menardi has recently been chosen as the "European spider of the year 2012", from the European Society of Arachnology. Here we report a study where silk stalks were collected directly from several caves in the north-west of Italy. Field emission scanning electron microscope (FESEM) images showed that stalks are made up of a large number of threads, each of them with diameter of 6.03 ± 0.58 µm. The stalks were strained at the constant rate of 2 mm/min, using a tensile testing machine. The observed maximum stress, strain and toughness modulus, defined as the area under the stress-strain curve, are 0.64 GPa, 751% and 130.7 MJ/m(3), respectively. To the best of our knowledge, such an observed huge elongation has never been reported for egg sac silk stalks and suggests a huge unrolling microscopic mechanism of the macroscopic stalk that, as a continuation of the protective egg sac, is expected to be composed by fibres very densely and randomly packed. The Weibull statistics was used to analyze the results from mechanical testing, and an average value of Weibull modulus (m) is deduced to be in the range of 1.5-1.8 with a Weibull scale parameter (σ(0)) in the range of 0.33-0.41 GPa, showing a high coefficient of correlation (R(2) = 0.97).

Hierarchical fiber bundle model to investigate the complex architectures of biological materials

The mechanics of fiber bundles has been widely studied in the literature, and fiber bundle models in particular have provided a wealth of useful analytical and numerical results for modeling ordinary materials. These models, however, are inadequate to treat bioinspired nanostructured materials, where hierarchy, multiscale, and complex properties play a decisive role in determining the overall mechanical characteristics. Here, we develop an ad hoc hierarchical theory designed to tackle these complex architectures, thus allowing the determination of the strength of macroscopic hierarchical materials from the properties of their constituents at the nanoscale. The roles of finite size, twisting angle, and friction are also included. Size effects on the statistical distribution of fiber strengths naturally emerge without invoking best-fit or unknown parameters. A comparison between the developed theory and various experimental results on synthetic and natural materials yields considerable agreement.

Crackling noise in three-point bending of heterogeneous materials

We study the crackling noise emerging during single crack propagation in a specimen under three-point bending conditions. Computer simulations are carried out in the framework of a discrete element model where the specimen is discretized in terms of convex polygons and cohesive elements are represented by beams. Computer simulations revealed that fracture proceeds in bursts whose size and waiting-time distributions have a power-law functional form with an exponential cutoff. Controlling the degree of brittleness of the sample by the amount of disorder, we obtain a scaling form for the characteristic quantities of crackling noise of quasibrittle materials. Analyzing the spatial structure of damage we show that ahead of the crack tip a process zone is formed as a random sequence of broken and intact mesoscopic elements. We characterize the statistics of the shrinking and expanding steps of the process zone and determine the damage profile in the vicinity of the crack tip.