Multiscale static and dynamic mechanical study of the Turritella terebra and Turritellinella tricarinata seashells

Marine shells are designed by nature to ensure mechanical protection from predators and shelter for molluscs living inside them. A large amount of work has been done to study the multiscale mechanical properties of their complex microstructure and to draw inspiration for the design of impact-resistant biomimetic materials. Less is known regarding the dynamic behaviour related to their structure at multiple scales. Here, we present a combined experimental and numerical study of the shells of two different species of gastropod sea snail belonging to the Turritellidae family, featuring a peculiar helicoconic shape with hierarchical spiral elements. The proposed procedure involves the use of micro-computed tomography scans for the accurate determination of geometry, atomic force microscopy and nanoindentation to evaluate local mechanical properties, surface morphology and heterogeneity, as well as resonant ultrasound spectroscopy coupled with finite element analysis simulations to determine global modal behaviour. Results indicate that the specific features of the considered shells, in particular their helicoconic and hierarchical structure, can also be linked to their vibration attenuation behaviour. Moreover, the proposed investigation method can be extended to the study of other natural systems, to determine their structure-related dynamic properties, ultimately aiding the design of bioinspired metamaterials and of structures with advanced vibration control.

Robust substrate anchorages of silk lines with extensible nano-fibres

Living systems are built of multiscale-composites: materials formed of components with different properties that are assembled in complex micro- and nano-structures. Such biological multiscale-composites often show outstanding physical properties that are unachieved by artificial materials. A major scientific goal is thus to understand the assembly processes and the relationship between structure and function in order to reproduce them in a new generation of biomimetic high-performance materials. Here, we tested how the assembly of spider silk nano-fibres (i.e. glue coated 0.5 μm thick fibres produced by so-called piriform glands) into different micro-structures correlates with mechanical performance by empirically and numerically exploring the mechanical behaviour of line anchors in an orb weaver, a hunting spider and two ancient web builders. We demonstrate that the anchors of orb weavers exhibit outstanding mechanical robustness with minimal material use by the indirect attachment of the silk line to the substrate through a soft domain ('bridge'). This principle can be used to design new artificial high-performance attachment systems.

Creation of pure non-crystalline diamond nanostructures via room-temperature ion irradiation and subsequent thermal annealing

Carbon exhibits a remarkable range of structural forms, due to the availability of sp³, sp² and sp¹ chemical bonds. Contrarily to other group IV elements such as silicon and germanium, the formation of an amorphous phase based exclusively on sp³ bonds is extremely challenging due to the strongly favored formation of graphitic-like structures at room temperature and pressure. As such, the formation of a fully sp³-bonded carbon phase requires an extremely careful (and largely unexplored) definition of the pressure and temperature across the phase diagram. Here, we report on the possibility of creating full-sp³ amorphous nanostructures within the bulk crystal of diamond with room-temperature ion-beam irradiation, followed by an annealing process that does not involve the application of any external mechanical pressure. As confirmed by numerical simulations, the (previously unreported) radiation-damage-induced formation of an amorphous sp²-free phase in diamond is determined by the buildup of extremely high internal stresses from the surrounding lattice, which (in the case of nanometer-scale regions) fully prevent the graphitization process. Besides the relevance of understanding the formation of exotic carbon phases, the use of focused/collimated ion beams discloses appealing perspectives for the direct fabrication of such nanostructures in complex three-dimensional geometries.

The role of hairs in the adhesion of octopus suckers: a hierarchical peeling approach

Organisms like the octopus or the clingfish are a precious source of inspiration for the design of innovative adhesive systems based on suction cups, but a complete mechanical description of their attachment process is still lacking. In this paper, we exploit the recent discovery of the presence of hairs in the acetabulum roof of octopus suction cups to revise the current model for its adhesion to the acetabulum wall. We show how this additional feature, which can be considered an example of a hierarchical structure, can lead to an increase of adhesive strength, based on the analysis of the cases of a simple tape and an axisymmetrical membrane adhering to a substrate. Using peeling theory, we discuss in both cases the influence of hierarchical structure and the resulting variation of geometry on the adhesive energy, highlighting how an increase in number of hierarchical levels contributes to its increment, with a corresponding improvement in functionality for the octopus suckers.

Competition between delamination and tearing in multiple peeling problems

Adhesive attachment systems consisting of multiple tapes or strands are commonly found in nature, for example in spider web anchorages or in mussel byssal threads, and their structure has been found to be ingeniously architected in order to optimize mechanical properties: in particular, to maximize dissipated energy before full detachment. These properties emerge from the complex interplay between mechanical and geometric parameters, including tape stiffness, adhesive energy, attached and detached lengths and peeling angles, which determine the occurrence of three main mechanisms: elastic deformation, interface delamination and tape fracture. In this paper, we introduce a formalism to evaluate the mechanical performance of multiple tape attachments in different parameter ranges, where an optimal (not maximal) adhesion energy emerges. We also introduce a numerical model to simulate the multiple peeling behaviour of complex structures, illustrating its predictions in the case of the staple-pin architecture. Finally, we present a proof-of-principle experiment to illustrate the predicted behaviour. We expect the presented formalism and the numerical model to provide important tools for the design of bioinspired adhesive systems with tuneable or optimized detachment properties.

Evidence of friction reduction in laterally graded materials

In many biological structures, optimized mechanical properties are obtained through complex structural organization involving multiple constituents, functional grading and hierarchical organization. In the case of biological surfaces, the possibility to modify the frictional and adhesive behaviour can also be achieved by exploiting a grading of the material properties. In this paper, we investigate this possibility by considering the frictional sliding of elastic surfaces in the presence of a spatial variation of the Young's modulus and the local friction coefficients. Using finite-element simulations and a two-dimensional spring-block model, we investigate how graded material properties affect the macroscopic frictional behaviour, in particular, static friction values and the transition from static to dynamic friction. The results suggest that the graded material properties can be exploited to reduce static friction with respect to the corresponding non-graded material and to tune it to desired values, opening possibilities for the design of bio-inspired surfaces with tailor-made tribological properties.

Emergence of the interplay between hierarchy and contact splitting in biological adhesion highlighted through a hierarchical shear lag model

Contact unit size reduction is a widely studied mechanism as a means to improve adhesion in natural fibrillar systems, such as those observed in beetles or geckos. However, these animals also display complex structural features in the way the contact is subdivided in a hierarchical manner. Here, we study the influence of hierarchical fibrillar architectures on the load distribution over the contact elements of the adhesive system, and the corresponding delamination behaviour. We present an analytical model to derive the load distribution in a fibrillar system loaded in shear, including hierarchical splitting of contacts, i.e. a "hierarchical shear-lag" model that generalizes the well-known shear-lag model used in mechanics. The influence on the detachment process is investigated introducing a numerical procedure that allows the derivation of the maximum delamination force as a function of the considered geometry, including statistical variability of local adhesive energy. Our study suggests that contact splitting generates improved adhesion only in the ideal case of extremely compliant contacts. In real cases, to produce efficient adhesive performance, contact splitting needs to be coupled with hierarchical architectures to counterbalance high load concentrations resulting from contact unit size reduction, generating multiple delamination fronts and helping to avoid detrimental non-uniform load distributions. We show that these results can be summarized in a generalized adhesion scaling scheme for hierarchical structures, proving the beneficial effect of multiple hierarchical levels. The model can thus be used to predict the adhesive performance of hierarchical adhesive structures, as well as the mechanical behaviour of composite materials with hierarchical reinforcements.

Tuning the strain-induced resonance shift in silicon racetrack resonators by their orientation

In this work, we analyze the role of strain on a set of silicon racetrack resonators presenting different orientations with respect to the applied strain. The strain induces a variation of the resonance wavelength, caused by the photoelastic variation of the material refractive index as well as by the mechanical deformation of the device. In particular, the mechanical deformation alters both the resonator perimeter and the waveguide cross-section. Finite element simulations taking into account all these effects are presented, providing good agreement with experimental results. By studying the role of the resonator orientation we identify interesting features, such as the tuning of the resonance shift from negative to positive values and the possibility of realizing strain insensitive devices.

The influence of substrate roughness, patterning, curvature, and compliance in peeling problems

Biological adhesion, in particular the mechanisms by which animals and plants 'stick' to surfaces, has been widely studied in recent years, and some of the structural principles have been successfully applied to bioinspired adhesives. However, modelling of adhesion, such as in single or multiple peeling theories, has in most cases been limited to ideal cases, and due consideration of the role of substrate geometry and mechanical properties has been limited. In this paper, we propose a numerical model to evaluate these effects, including substrate roughness, patterning, curvature, and deformability. The approach is validated by comparing its predictions with classical thin film peeling theoretical results, and is then used to predict the effects of substrate properties. These results can provide deeper insight into experiments, and the developed model can be a useful tool to design and optimize artificial adhesives with tailor-made characteristics.

Proof of Concept for an Ultrasensitive Technique to Detect and Localize Sources of Elastic Nonlinearity Using Phononic Crystals

The appearance of nonlinear effects in elastic wave propagation is one of the most reliable and sensitive indicators of the onset of material damage. However, these effects are usually very small and can be detected only using cumbersome digital signal processing techniques. Here, we propose and experimentally validate an alternative approach, using the filtering and focusing properties of phononic crystals to naturally select and reflect the higher harmonics generated by nonlinear effects, enabling the realization of time-reversal procedures for nonlinear elastic source detection. The proposed device demonstrates its potential as an efficient, compact, portable, passive apparatus for nonlinear elastic wave sensing and damage detection.

Refractive index variation in a free-standing diamond thin film induced by irradiation with fully transmitted high-energy protons

Ion irradiation is a widely employed tool to fabricate diamond micro- and nano-structures for applications in integrated photonics and quantum optics. In this context, it is essential to accurately assess the effect of ion-induced damage on the variation of the refractive index of the material, both to control the side effects in the fabrication process and possibly finely tune such variations. Several partially contradictory accounts have been provided on the effect of the ion irradiation on the refractive index of single crystal diamond. These discrepancies may be attributable to the fact that in all cases the ions are implanted in the bulk of the material, thus inducing a series of concurrent effects (volume expansion, stress, doping, etc.). Here we report the systematic characterization of the refractive index variations occurring in a 38 µm thin artificial diamond sample upon irradiation with high-energy (3 MeV and 5 MeV) protons. In this configuration the ions are fully transmitted through the sample, while inducing an almost uniform damage profile with depth. Therefore, our findings conclusively identify and accurately quantify the change in the material polarizability as a function of ion beam damage as the primary cause for the modification of its refractive index.

Hierarchical Spring-Block Model for Multiscale Friction Problems

A primary issue in biomaterials science is to design materials with ad hoc properties, depending on the specific application. Among these properties, friction is recognized as a fundamental aspect characterizing materials for many practical purposes. Recently, new and unexpected frictional properties have been obtained by exploiting hierarchical multiscale structures, inspired by those observed in many biological systems. In order to understand the emergent frictional behavior of these materials at the macroscale, it is fundamental to investigate their hierarchical structure, spanning across different length scales. In this article, we introduce a statistical multiscale approach, based on a one-dimensional formulation of the spring-block model, in which friction is modeled at each hierarchical scale through the classical Amontons-Coulomb force with statistical dispersion on the friction coefficients of the microscopic components. By means of numerical simulations, we deduce the global statistical distributions of the elementary structure at micrometric scale and use them as input distributions for the simulations at the next scale levels. We thus study the influence of microscopic artificial patterning on macroscopic friction coefficients. We show that it is possible to tune the friction properties of a hierarchical surface and provide some insight on the mechanisms involved at different length scales.

Static and dynamic friction of hierarchical surfaces

Hierarchical structures are very common in nature, but only recently have they been systematically studied in materials science, in order to understand the specific effects they can have on the mechanical properties of various systems. Structural hierarchy provides a way to tune and optimize macroscopic mechanical properties starting from simple base constituents and new materials are nowadays designed exploiting this possibility. This can be true also in the field of tribology. In this paper we study the effect of hierarchical patterned surfaces on the static and dynamic friction coefficients of an elastic material. Our results are obtained by means of numerical simulations using a one-dimensional spring-block model, which has previously been used to investigate various aspects of friction. Despite the simplicity of the model, we highlight some possible mechanisms that explain how hierarchical structures can significantly modify the friction coefficients of a material, providing a means to achieve tunability.

Numerical implementation of multiple peeling theory and its application to spider web anchorages

Adhesion of spider web anchorages has been studied in recent years, including the specific functionalities achieved through different architectures. To better understand the delamination mechanisms of these and other biological or artificial fibrillar adhesives, and how their adhesion can be optimized, we develop a novel numerical model to simulate the multiple peeling of structures with arbitrary branching and adhesion angles, including complex architectures. The numerical model is based on a recently developed multiple peeling theory, which extends the energy-based single peeling theory of Kendall, and can be applied to arbitrarily complex structures. In particular, we numerically show that a multiple peeling problem can be treated as the superposition of single peeling configurations even for complex structures. Finally, we apply the developed numerical approach to study spider web anchorages, showing how their function is achieved through optimal geometrical configurations.

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.

Hierarchical multiple peeling simulations

We model hierarchical multiple peeling through finite element simulations, quantifying how hierarchy optimizes the strength of the bioinspired attachment.

Direct measurement and modelling of internal strains in ion-implanted diamond

We present a phenomenological model and finite element simulations to describe the depth variation of mass density and strain of ion-implanted single-crystal diamond. Several experiments are employed to validate the approach: firstly, samples implanted with 180 keV B ions at relatively low fluences are characterized using high-resolution x-ray diffraction; secondly, the mass density variation of a sample implanted with 500 keV He ions, well above its amorphization threshold, is characterized with electron energy loss spectroscopy. At high damage densities, the experimental depth profiles of strain and density display a saturation effect with increasing damage and a shift of the damage density peak towards greater depth values with respect to those predicted by TRIM simulations, which are well accounted for in the model presented here. The model is then further validated by comparing transmission electron microscopy-measured and simulated thickness values of a buried amorphous carbon layer formed at different depths by implantation of 500 keV He ions through a variable-thickness mask to simulate the simultaneous implantation of ions at different energies.

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.

Spectroscopic measurement of the refractive index of ion-implanted diamond

We present the results of variable-angle spectroscopic ellipsometry and transmittance measurements to determine the variation of the complex refractive index of ion-implanted single-crystal diamond. An increase is found in both real and imaginary parts at increasing damage densities. The index depth variation is determined in the whole wavelength range between 250 and 1690 nm. The dependence from the vacancy density is evaluated, highlighting a deviation from linearity in the high-damage-density regime. A considerable increase (up to 5%) in the real part of the index is observed, attributed to an increase in polarizability, thus offering new microfabrication possibilities for waveguides and other photonic structures in diamond.

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.

Evidence of light guiding in ion-implanted diamond

We demonstrate the feasibility of fabricating light-waveguiding microstructures in bulk single-crystal diamond by means of direct ion implantation with a scanning microbeam, resulting in the modulation of the refractive index of the ion-beam damaged crystal. Direct evidence of waveguiding through such buried microchannels is obtained with a phase-shift micro-interferometric method allowing the study of the multimodal structure of the propagating electromagnetic field. The possibility of defining optical and photonic structures by direct ion writing opens a range of new possibilities in the design of quantum-optical devices in bulk single-crystal diamond.

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

Biological materials such as spider silk display hierarchical structures, from nano to macro, effectively linking nanoscale constituents to larger-scale functional material properties. Here, we develop a model that is capable of determining the strength and toughness of elastic-plastic composites from the properties, percentages, and arrangement of its constituents, and of estimating the corresponding dissipated energy during damage progression, in crack-opening control. Specifically, we adopt a fiber bundle model approach with a hierarchical multiscale self-similar procedure which enables to span various orders of magnitude in size and to explicitly take into account the hierarchical topology of natural materials. Hierarchical architectures and self-consistent energy dissipation mechanisms (including plasticity), both omitted in common fiber bundle models, are fully considered in our model. By considering one of the toughest known materials today as an example application, a synthetic fiber composed of single-walled carbon nanotubes and polyvinyl alcohol gel, we compute strength and specific energy absorption values that are consistent with those experimentally observed. Our calculations are capable of predicting these values solely based on the properties of the constituent materials and knowledge of the structural multiscale topology. Due to the crack-opening control nature of the simulations, it is also possible to derive a critical minimal percentage of plastic component needed to avoid catastrophic behavior of the material. These results suggest that the model is capable of helping in the design of new supertough materials.

Self-similarity of waiting times in fracture systems

Experimental and numerical results are presented for a fracture experiment carried out on a fiber-reinforced element under flexural loading, and a statistical analysis is performed for acoustic emission waiting-time distributions. By an optimization procedure, a recently proposed scaling law describing these distributions for different event magnitude scales is confirmed by both experimental and numerical data, thus reinforcing the idea that fracture of heterogeneous materials has scaling properties similar to those found for earthquakes. Analysis of the different scaling parameters obtained for experimental and numerical data leads us to formulate the hypothesis that the type of scaling function obtained depends on the level of correlation among fracture events in the system.

Phenomenological approach to mechanical damage growth analysis

The problem of characterizing damage evolution in a generic material is addressed with the aim of tracing it back to existing growth models in other fields of research. Based on energetic considerations, a system evolution equation is derived for a generic damage indicator describing a material system subjected to an increasing external stress. The latter is found to fit into the framework of a recently developed phenomenological universality (PUN) approach and, more specifically, the so-called U2 class. Analytical results are confirmed by numerical simulations based on a fiber-bundle model and statistically assigned local strengths at the microscale. The fits with numerical data prove, with an excellent degree of reliability, that the typical evolution of the damage indicator belongs to the aforementioned PUN class. Applications of this result are briefly discussed and suggested.

Multiscale stochastic simulations for tensile testing of nanotube-based macroscopic cables

Thousands of multiscale stochastic simulations are carried out in order to perform the first in-silico tensile tests of carbon nanotube (CNT)-based macroscopic cables with varying length. The longest treated cable is the space-elevator megacable but more realistic shorter cables are also considered in this bottom-up investigation. Different sizes, shapes, and concentrations of defects are simulated, resulting in cable macrostrengths not larger than approximately 10 GPa, which is much smaller than the theoretical nanotube strength (approximately 100 GPa). No best-fit parameters are present in the multiscale simulations: the input at level 1 is directly estimated from nanotensile tests of CNTs, whereas its output is considered as the input for the level 2, and so on up to level 5, corresponding to the megacable. Thus, five hierarchical levels are used to span lengths from that of a single nanotube (approximately 100 nm) to that of the space-elevator megacable (approximately 100 Mm).