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The introduction of metamaterials has provided new possibilities to manipulate the propagation of waves in different fields of physics, ranging from electromagnetism to acoustics. However, despite the variety of configurations proposed so far, most solutions lack dynamic tunability, i.e. their functionality cannot be altered post-fabrication. Our work overcomes this limitation by employing a photo-responsive polymer to fabricate a simple metamaterial structure and enable tuning of its elastic properties using visible light. The structure of the metamaterial consists of graded resonators in the form of an array of pillars, each giving rise to different resonances and transmission band gaps. Selective laser illumination can then tune the resonances and their frequencies individually or collectively, thus yielding many degrees of freedom in the tunability of the filtered or transmitted wave frequencies, similar to playing a keyboard, where illuminating each pillar corresponds to playing a different note. This concept can be used to realize low-power active devices for elastic wave control, including beam splitters, switches and filters.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

The software for chemical interaction networks (SCINE) project aims at pushing the frontier of quantum chemical calculations on molecular structures to a new level. While calculations on individual structures as well as on simple relations between them have become routine in chemistry, new developments have pushed the frontier in the field to high-throughput calculations. Chemical relations may be created by a search for specific molecular properties in a molecular design attempt, or they can be defined by a set of elementary reaction steps that form a chemical reaction network. The software modules of SCINE have been designed to facilitate such studies. The features of the modules are (i) general applicability of the applied methodologies ranging from electronic structure (no restriction to specific elements of the periodic table) to microkinetic modeling (with little restrictions on molecularity), full modularity so that SCINE modules can also be applied as stand-alone programs or be exchanged for external software packages that fulfill a similar purpose (to increase options for computational campaigns and to provide alternatives in case of tasks that are hard or impossible to accomplish with certain programs), (ii) high stability and autonomous operations so that control and steering by an operator are as easy as possible, and (iii) easy embedding into complex heterogeneous environments for molecular structures taken individually or in the context of a reaction network. A graphical user interface unites all modules and ensures interoperability. All components of the software have been made available as open source and free of charge., (© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) license (https://creativecommons.org/licenses/by-nc-nd/4.0/).)

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.

Semi-empirical quantum chemical approaches are known to compromise accuracy for the feasibility of calculations on huge molecules. However, the need for ultrafast calculations in interactive quantum mechanical studies, high-throughput virtual screening, and data-driven machine learning has shifted the emphasis toward calculation runtimes recently. This comes with new constraints for the software implementation as many fast calculations would suffer from a large overhead of the manual setup and other procedures that are comparatively fast when studying a single molecular structure, but which become prohibitively slow for high-throughput demands. In this work, we discuss the effect of various well-established semi-empirical approximations on calculation speed and relate this to data transfer rates from the raw-data source computer to the results of the visualization front end. For the former, we consider desktop computers, local high performance computing, and remote cloud services in order to elucidate the effect on interactive calculations, for web and cloud interfaces in local applications, and in world-wide interactive virtual sessions. The models discussed in this work have been implemented into our open-source software SCINE Sparrow.

This broad review summarizes recent advances and "hot" research topics in nanophononics and elastic, acoustic, and mechanical metamaterials based on results presented by the authors at the EUROMECH 610 Colloquium held on April 25-27, 2022 in Benicássim, Spain. The key goal of the colloquium was to highlight important developments in these areas, particularly new results that emerged during the last two years. This work thus presents a "snapshot" of the state-of-the-art of different nanophononics- and metamaterial-related topics rather than a historical view on these subjects, in contrast to a conventional review article. The introduction of basic definitions for each topic is followed by an outline of design strategies for the media under consideration, recently developed analysis and implementation techniques, and discussions of current challenges and promising applications. This review, while not comprehensive, will be helpful especially for early-career researchers, among others, as it offers a broad view of the current state-of-the-art and highlights some unique and flourishing research in the mentioned fields, providing insight into multiple exciting research directions., (© 2023 the author(s), published by De Gruyter, Berlin/Boston.)

Spider webs are finely tuned multifunctional structures, widely studied for their prey capture functionalities such as impact strength and stickiness. However, they are also sophisticated sensing tools that enable the spider to precisely determine the location of impact and capture the prey before it escapes. In this paper, we suggest a new mechanism for this detection process, based on potential modal analysis capabilities of the spider, using its legs as distinct distributed point sensors. To do this, we consider a numerical model of the web structure, including asymmetry in the design, prestress, and geometrical nonlinearity effects. We show how vibration signals deriving from impacts can be decomposed into web eigenmode components, through which the spider can efficiently trace the source location. Based on this numerical analysis, we discuss the role of the web structure, asymmetry, and prestress in the imaging mechanism, confirming the role of the latter in tuning the web response to achieve an efficient prey detection instrument. The results can be relevant for efficient distributed impact sensing applications., (© 2022. The Author(s).)

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.

Carbon exhibits a remarkable range of structural forms, due to the availability of sp 3 , sp 2 and sp 1 chemical bonds. Contrarily to other group IV elements such as silicon and germanium, the formation of an amorphous phase based exclusively on sp 3 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 sp 3 -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-sp 3 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 sp 2 -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., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

Salmonella enterica serovar Typhimurium (S.Tm) infections of cultured cell lines have given rise to the ruffle model for epithelial cell invasion. According to this model, the Type-Three-Secretion-System-1 (TTSS-1) effectors SopB, SopE and SopE2 drive an explosive actin nucleation cascade, resulting in large lamellipodia- and filopodia-containing ruffles and cooperative S.Tm uptake. However, cell line experiments poorly recapitulate many of the cell and tissue features encountered in the host's gut mucosa. Here, we employed bacterial genetics and multiple imaging modalities to compare S.Tm invasion of cultured epithelial cell lines and the gut absorptive epithelium in vivo in mice. In contrast to the prevailing ruffle-model, we find that absorptive epithelial cell entry in the mouse gut occurs through "discreet-invasion". This distinct entry mode requires the conserved TTSS-1 effector SipA, involves modest elongation of local microvilli in the absence of expansive ruffles, and does not favor cooperative invasion. Discreet-invasion preferentially targets apicolateral hot spots at cell-cell junctions and shows strong dependence on local cell neighborhood. This proof-of-principle evidence challenges the current model for how S.Tm can enter gut absorptive epithelial cells in their intact in vivo context., Competing Interests: The authors have declared that no competing interests exist.

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.

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.

Physical structures built by animals challenge our understanding of biological processes and inspire the development of smart materials and green architecture. It is thus indispensable to understand the drivers, constraints, and dynamics that lead to the emergence and modification of building behavior. Here, we demonstrate that spider web diversification repeatedly followed strikingly similar evolutionary trajectories, guided by physical constraints. We found that the evolution of suspended webs that intercept flying prey coincided with small changes in silk anchoring behavior with considerable effects on the robustness of web attachment. The use of nanofiber based capture threads (cribellate silk) conflicts with the behavioral enhancement of web attachment, and the repeated loss of this trait was frequently followed by physical improvements of web anchor structure. These findings suggest that the evolution of building behavior may be constrained by major physical traits limiting its role in rapid adaptation to a changing environment., (© 2019 The Author(s). Evolution © 2019 The Society for the Study of Evolution.)

Acoustic filters and metamaterials have become essential components for elastic wave control in applications ranging from ultrasonics to noise abatement. Other devices have been designed in this field, emulating their electromagnetic counterparts. One such case is an acoustic diode or rectifier, which enables one-way wave transmission by breaking the wave equation-related reciprocity. Its achievement, however, has proved to be rather problematic, and current realizations display a number of shortcomings in terms of simplicity and versatility. Here, we present the design, fabrication and characterization of a device able to work as an acoustic diode, a switch and a transistor-like apparatus, exploiting symmetry-breaking nonlinear effects like harmonic generation and wave mixing, and the filtering capabilities of metamaterials. This device presents several advantages compared with previous acoustic diode realizations, including versatility, time invariance, frequency preserving characteristics and switchability. We numerically evaluate its efficiency and demonstrate its feasibility in a preliminary experimental realization. This work may provide new opportunities for the practical realization of structural components with one-way wave propagation properties.

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.

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.

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.

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.

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.

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.

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 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.

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.

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.

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.

It is well known that hierarchical structure is an important feature in biological materials to optimise various properties, including mechanical ones. It is however still unclear how these hierarchical architectures can improve material characteristics, for example strength. Also, the transposition of these structures from natural to artificial bioinspired materials remains to be perfected. In this paper, we introduce a numerical method to evaluate the strength of fibre-based heterogeneous biological materials and systematically investigate the role of hierarchy. Results show that hierarchy indeed plays an important role and that it is possible to "tune" the strength of bio-inspired materials in a wide range of values, in some cases improving the strength of non-hierarchical structures considerably., (Copyright © 2012 Elsevier Ltd. All rights reserved.)

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., (This journal is © The Royal Society of Chemistry 2012)

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.

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., (© 2012 American Physical Society)

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.

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.

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.

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.

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).