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Moving masses are of interest in many applications of structural dynamics, soliciting in the last decades a vast debate in the scientific literature. However, despite the attention devoted to the subject, to the best of the authors’ knowledge, there is a lack of analysis about the fate of a movable mass when it rolls or slips with friction on a structure. With the aim of elucidating the dynamics of the simplest paradigm of this system and to investigate its asymptotic response, we make reference to a two-degree-of-freedom model made of an elastically vibrating carriage surmounted by a spherical mass, facing the problem both theoretically and experimentally. In case of linear systems, the analytical solutions and the laboratory tests performed on ad hoc constructed prototypes highlighted a counterintuitive asymptotic dynamics, here called binary: in the absence of friction at the interface of the bodies’ system, the mass holds its initial position or, if nonzero damping acts, at the end of the motion it is in a position that exactly recovers the initial relative distance carriage–sphere. While the first result might be somewhat obvious, the second appears rather surprising. Such a binary behaviour is also confirmed for a Duffing-like system, equipped with cubic springs, while it can be lost when non-smooth friction phenomena occur, as well as in the case of elastic springs restraining the motion of the sphere. The obtained analytical results and the numerical findings, also confirmed by experimental evidences, contribute to the basic understanding of the role played by the damping parameters governing the systems’ dynamics with respect to its asymptotic behaviour and could pave the way for designing active or passive vibration controllers of interest in engineering.

Building up and maintenance of cytoskeletal structure in living cells are force-dependent processes involving a dynamic chain of polymerization and depolymerization events, which are also at the basis of cells’ remodelling and locomotion. All these phenomena develop by establishing cell–matrix interfaces made of protein complexes, known as focal adhesions, which govern mechanosensing and mechanotransduction mechanisms mediated by stress transmission between cell interior and external environment. Within this framework, by starting from a work by Cao et al. (Biophys J 109:1807–1817, 2015), we here investigate the role played by actomyosin contractility of stress fibres in nucleation, growth and disassembling of focal adhesions. In particular, we propose a tensegrity model of an adherent cell incorporating nonlinear elasticity and unstable behaviours, which provides a new kinematical interpretation of cellular contractile forces and describes how stress fibres, microtubules and adhesion plaques interact mechanobiologically. The results confirm some experimental evidences and suggest how the actomyosin contraction level could be exploited by cells to actively control their adhesion, eventually triggering cytoskeleton reconfigurations and migration processes observed in both physiological conditions and diseases.

Background The aim of the study was to compare the bone mineral density changes between unmatched patients undergoing total hip arthroplasty receiving uncemented and cemented type of implants. Previous studies have used DEXA or a two dimensional analysis to estimate the bone quality following total joint replacement, whereas this study presents the changes in three dimensions. Methods Fifty subjects both male and females receiving both cemented and uncemented type of implant were recruited. Two CT scans were taken of each subject, the first at 24 h post surgery and the second one 1 year after surgery. The scans were calibrated using a phantom converting the Hounsfield units to bone mineral density values in g/cm3. The two scans were registered together using anatomical landmarks and resliced to compare the two femurs in the identical frame of reference. The bone density gain and loss was calculated by comparing density values between the two sets of scans. Findings The results showed that most of the bone loss was located around the Lesser Trochanter and some bone density gain at the distal tip of the implant. The three dimensional density changes occur differently between individuals and the study showed no correlation of bone loss with age. Interpretation The bone loss occurred mostly at the proximal femur, which is in agreement with previously presented studies. By carrying out three dimensional analysis on the bone gain and loss on the femur, it is possible to identify the patients that are showing high degree of bone loss.

Urban densification represents one of the biggest universal challenges of contemporary cities: the increase of urban population requires new spaces to accommodate the growing demand for housing, working and tertiary activities. However, the land available for new constructions in highly urbanized areas is very limited. In this framework, the vertical extension of existing buildings is the most sustainable strategy and fascinating. Masonry structures , constituting a major part of the built stock in the historical city centres of several European countries, are particularly suitable for vertical addition of extra-floors, since they generally exhibit an adequate overstrength for bearing an increase of gravity loads, although seismic retrofit interventions are usually required. In this paper, starting from the case study of the historical town of Pozzuoli, in South Italy, an “antifragile” approach, based on the intermediate isolation system, is suggested to rise the height of the masonry building , while reducing the global seismic demand. For this aim, in this paper are analysed the architectural-functional and structural design issues related to a vast-scale application of vertical additions isolated on the top of existing structures. Further, the feasibility and effectiveness of the strategy are discussed, and benefits in terms of seismic performance are evaluated.

Abstract Poromechanics plays a key role in modelling hard and soft tissue behaviours, by providing a thermodynamic framework in which chemo-mechanical mutual interactions among fluid and solid constituents can be consistently rooted, at different scale levels. In this context, how different biological species (including cells, extra-cellular components and chemical metabolites) interplay within complex environments is studied for characterizing the mechanobiology of tumor growth, governed by intratumoral residual stresses that initiate mechanotransductive processes deregulating normal tissue homeostasis and leading to tissue remodelling. Despite the coupling between tumor poroelasticity and interspecific competitive dynamics has recently highlighted how microscopic cells and environment interactions influence growth-associated stresses and tumor pathophysiology, the nonlinear interlacing among biochemical factors and mechanics somehow hindered the possibility of gaining qualitative insights into cells dynamics. Motivated by this, in the present work we recover the linear poroelasticity in order to benefit of a reduced complexity, so first deriving the well-known Lyapunov stability criterion from the thermodynamic dissipation principle and then analysing the stability of the mechanical competition among cells fighting for common space and resources during cancer growth and invasion. At the end, the linear poroelastic model enriched by interspecific dynamics is also exploited to show how growth anisotropy can alter the stress field in spherical tumor masses, by thus indirectly affecting cell mechano-sensing. GraphicAbstract

Grounded in the interdisciplinary crosstalk among physics and biological sciences, precision medicine-based diagnosis and treatment strategies have recently gained great attention for the actual applicability of new engineered approaches in many medical fields, particularly in oncology. Within this framework, the use of ultrasounds employed to attack cancer cells in tumors to induce possible mechanical damage at different scales has received growing attention from scholars and scientists worldwide. With these considerations in mind, on the basis of ad hoc elastodynamic solutions and numerical simulations, we propose a pilot study for in silico modeling of the propagation of ultrasound waves inside tissues, with the aim of selecting proper frequencies and powers to be irradiated locally through a new teragnostic platform based on Lab-on-Fiber technology, baptized as a hospital in the needle and already the object of a patent. It is felt that the outcomes and the related biophysical insights gained from the analyses could pave the way for envisaging new integrated diagnostic and therapeutic approaches that might play a central role in future applications of precise medicine, starting from the growing synergy among physics, engineering and biology.

We demonstrate that several key aspects of the contractile activity of a cell interacting with the substrate can be captured by means of a non linear elastic tensegrity mechanical system made of a tensile element in parallel with a buckling-prone component, and exchanging forces with the surroundings through an extracellular matrix-focal adhesion complex. Mechanosensitivity of the focal adhesion plaque is triggered by pre-strain-driven buckling of the system induced either by pre-contraction or pre-polymerization of the constituents. The impact of pre-polymerization on the mechanical force and the implications of using linear and nonlinear elasticity for the focal adhesion plaque are assessed.

The mechanical performance of reinforced composites is strongly influenced at different scales by the stress transferred at the matrix-fibre interfaces and at any surface where material discontinuity occurs. In particular, the mechanical response of elastomeric composites where the reinforcement is composed by cords with helically wound fibres is heavily compromised by fatigue and delamination phenomena occurring at cord-rubber as well as at the ply interfaces, since rubber and polymeric matrices are mainly vulnerable to the accumulation of deviatoric energy due to the shear stresses transferred across the surfaces. Despite the large diffusion of composites in a vast field of applications and the mature knowledge of their behaviour, some key mechanical aspects underlying failure mechanisms are still partially unclear. For example, stress amplification and strain localization are often difficult to predict by means of analytical solutions and averaging techniques that usually conceal stress gradients. In this work, we analyse coupling between torsional and tensile loads in twisted cords, which are adopted in many cases to reinforce composites and rubbers in tire applications. We provide a model characterized by an enriched cord-matrix mechanical interplay able to theoretically explain and predict actual stress distributions responsible for the onset of delamination and fatigue-guided phenomena that are experimentally observed in these composites. In particular, we demonstrate that the assumption of a monoclinic/trigonal behaviour for the mechanical response of the hierarchical strands allows to estimate, by means of analytical formulas and a homogenization approach, hitherto neglected shear stresses at the matrix-reinforcement interface. These stresses are transferred to the neighbouring regions, leading to post-elastic behaviour and failure events. Finite Element simulation results for rubber/cord composites under various boundary conditions highlight the discrepancies in mechanical behaviour between the proposed model and standard approaches in the literature, while experimental tests performed on composite rubber pads confirm theoretical predictions, providing qualitative evidence of the onset of cracks.

Growing biological media develop residual stresses to make compatible elastic and inelastic growth-induced deformations, which in turn remodel the tissue properties modifying the actual elastic moduli and transforming an initially isotropic and homogeneous material into a spatially inhomogeneous and anisotropic one. This process is crucial in solid tumor growth mechanobiology, the residual stresses directly influencing tumor aggressiveness, nutrients walkway, necrosis and angiogenesis. With this in mind, we here analyze the problem of a hyperelastic sphere undergoing finite heterogeneous growth, in cases of different boundary conditions and spherical symmetry. By following an analytical approach, we obtain the explicit expression of the tangent elasticity tensor at any point of the material body as a function of the prescribed growth, by involving a small-on-large procedure and exploiting exact solutions for layered media. The results allowed to gain several new insights into how growth-guided mechanical stresses and remodeling processes can influence the solid tumor development. In particular, we highlight that— under hypotheses consistent with mechanical and physiological conditions—auxetic (negative Poisson ratio) transformations of the elastic response of selected growing mass districts could occur and contribute to explain some not yet completely understood phenomena associated to solid tumors. The general approach proposed in the present work could be also helpfully employed to conceive composite materials where ad hoc pre-stress distributions can be designed to obtain auxetic or other selected mechanical properties.

The paper proposes a mixed strain- and stress-based topology optimization method for designing the ideal geometry of carbon fibers in composite laminates subjected to either applied tractions or prescribed displacements. On the basis of standard micromechanical approaches, analytical elastic solutions for a single cell, assumed to be a Representative Volume Element (RVE), are ad hoc constructed by involving anisotropy induced by fiber orientation and volume fraction, also taking into account inter-laminar stresses and strains. The analytical solutions are then implemented in a Finite Element (FE) custom-made topology optimization-based procedure rewritten to have as output the best curves the reinforcing fibers have to draw in any composite laminate layer to maximize the overall panel stiffness or to minimize the elastic energy. To verify the effectiveness of the proposed strategy, different structures undergoing either in-plane or out-plane boundary conditions have been selected and theoretically investigated, determining the optimal fibers' maps and showing the related results in comparison to standard sequences of alternate fibers disposition for the same composites. Two optimized panels were at the end actually produced using an innovative Automated Fiber Placement (AFP) machine and consolidating the materials by means of autoclave curing processes, in this way replicating the fiber paths obtained from theoretical outcomes. As a control, two corresponding composite structures were also built without employing the fiber optimization strategy. The panels have been tested in laboratory and the theoretical results have been compared with the experimental findings, showing a very good agreement with our predictions and confirming the capability of the proposed algorithm in suggesting the arrangement of the fibers to obtain enhanced mechanical performances. It is felt that the hybrid analytical-FE topology optimization strategy, in conjunction with the possibilities offered by AFP devices, could pave the way for a new generation of ultra-lightweight composites for aerospace, automotive and many industrial applications.

The modeling of the viability decay of viruses in sessile droplets is addressed considering a droplet sitting on a smooth surface characterized by a specific contact angle. To investigate, at prescribed temperature, how surface energy of the material and ambient humidity cooperate to determine the virus viability, we propose a model which involves the minimum number of thermodynamically relevant parameters. In particular, by considering a saline water droplet (one salt) as the simplest approximation of real solutions (medium and natural/artificial saliva), the evaporation is described by a first-order time-dependent nonlinear differential equation properly rearranged to obtain the contact angle evolution as the sole unknown function. The analyses were performed for several contact angles and two typical droplet sizes of interest in real situations by assuming constant ambient temperature and relative humidity in the range 0–100%. The results of the simulations, given in terms of time evolution of salt concentration, vapor pressure, and droplet volume, elucidate some previously not yet well-understood dynamics, demonstrating how three main regimes—directly implicated in nontrivial trends of virus viability and to date only highlighted experimentally—can be recognized as the function of relative humidity. By recalling the concept of cumulative dose of salts (CD), to account for the effect of the exposition of viruses to salt concentration on virus viability, we show how the proposed approach could suggest a chart of a virus fate by predicting its survival time at a given temperature as a function of the relative humidity and contact angle. We found a good agreement with experimental data for various enveloped viruses and predicted in particular for the Phi6 virus, a surrogate of coronavirus, the characteristic U-shaped dependence of viability on relative humidity. Given the generality of the model and once experimental data are available that link the vulnerability of a certain virus, such as SARS-CoV-2, to the concentrations of salts or other substances in terms of CD, it is felt that this approach could be employed for antivirus strategies and protocols for the prediction/reduction of human health risks associated with SARS-CoV-2 and other viruses. © Copyright © 2021 Di Novo, Carotenuto, Mensitieri, Fraldi and Pugno.

Composites are experiencing a new era. The spatial resolution at which is to date possible to build up complex architectured microstructures through additive manufacturing-based and sintering of powder metals 3D printing techniques, as well as the recent improvements in both filament winding and automated fiber deposition processes, are opening new unforeseeable scenarios for applying optimization strategies to the design of high-performance structures and metamaterials that could previously be only theoretically conceived. Motivated by these new possibilities, the present work, by combining computational methods, analytical approaches and experimental analysis, shows how finite element Design Optimization algorithms can be ad hoc rewritten by identifying as design variables the orientation of the reinforcing fibers in each ply of a layered structure for redesigning fiber-reinforced composites exhibiting at the same time high stiffness and toughening, two features generally in competition each other. To highlight the flexibility and the effectiveness of the proposed strategy, after a brief recalling of the essential theoretical remarks and the implemented procedure, selected example applications are finally illustrated on laminated plates under different boundary conditions, cylindrical layered shells with varying curvature subjected to point loads and composite tubes made of carbon fiber-reinforced polymers, recently employed as structural components in advanced aerospace engineering applications.

The stability of equilibrium is a fundamental topic in mechanics and applied sciences. Apart from its central role in most engineering fields, it also arises in many natural systems at any scale, from folding/unfolding processes of macromolecules and growth-induced wrinkling in biological tissues to meteorology and celestial mechanics. As such, a few key models represent essential benchmarks in order to gain significant insights into more complex physical phenomena. Among these models, a cornerstone is represented by a structure made of two straight axially deformable bars, connected by an elastic hinge and simply supported at the ends, which are capable of buckling under a compressive axial force. This classical example has been proposed and analysed in some depth by Feodosyev but the attention is here focused on an apparently paradoxical result given by this model, i.e. the existence of a lower bound for the axial-to-flexural stiffness ratio in order for the bifurcation to take place. This enigma is solved theoretically by showing that, differently from other classical stability problems, constitutive and geometric nonlinearities cannot be a priori disconnected and an ideal linearized axial constitutive law cannot be employed in this case. The theory is validated with an experiment, and post-buckling and energy extrema of the proposed solution are discussed as well, highlighting possible snap-back and snap-through phenomena. Finally, the results are extended to the complementary case of tensile buckling.

Materials that are lightweight yet exhibit superior mechanical properties are of compelling importance for several technological applications that range from aircrafts to household appliances. Lightweight materials allow energy saving and reduce the amount of resources required for manufacturing. Researchers have expended significant efforts in the quest for such materials, which require new concepts in both tailoring material microstructure as well as structural design. Architectured materials, which take advantage of new engineering paradigms, have recently emerged as an exciting avenue to create bespoke combinations of desired macroscopic material responses. In some instances, rather unique structures have emerged from advanced geometrical concepts (e.g. gyroids, menger cubes, or origami/kirigami-based structures), while in others innovation has emerged from mimicking nature in bio-inspired materials (e.g. honeycomb structures, nacre, fish scales etc.). Beyond design, additive manufacturing has enabled the facile fabrication of complex geometrical and bio-inspired architectures, using computer aided design models. The combination of simulations and experiments on these structures has led to an enhancement of mechanical properties, including strength, stiffness and toughness. In this review, we provide a perspective on topologically engineered architectured materials that exhibit optimal mechanical behaviour and can be readily printed using additive manufacturing.

Extreme adhesion mechanisms are shown in a wide number of situations in nature, from structures of single cells and spider web anchorages to hierarchical organization of ends and pads of insects and reptiles. With this in mind, we here propose a general formulation of multiple peeling theory accounting for geometrical and constitutive nonlinearities, i.e. large deformations and hyperelasticity. Pre-stress of adherent tracts and different initial V-shaped configurations of the tapes have been also included in the modelling. By following an analytical approach, closed-form solutions and explicit formulas were given for predicting pull-off critical forces and optimality conditions maximizing the adhesion strength, as well as for tracing the evolution of the delamination process, from the detaching onset to its progressive behaviour. Kendall and previous constitutively linear multiple peeling theory approaches were all recovered as limit cases, gaining insights into the role played by nonlinearities and pre-stress and also demonstrating – with mathematically rigorous arguments – the asymptotic character of the detaching phenomenon observed experimentally. Example applications and simple key tests were provided to show the effectiveness of the approach, which could help to interpret peeling in nature and to design materials with enhanced adhesive properties.

Total Hip Arthroplasty has been one of the most successful surgical procedure in terms of patient outcomes and satisfaction. However, due to increase in life expectancy and the related incidence of age-dependent bone diseases, a growing number of cases of intra-operative fractures lead to revision surgery with high rates of morbidity and mortality. Surgeons choose the type of the implant, either cemented or cementless prosthesis, on the basis of the age, the quality of the bone and the general medical conditions of the patients. Generally, no quantitative measures are available to assess the intra-operative fracture risk. Consequently, the decision-making process is mainly based on surgical operators&rsquo, expertise and qualitative information obtained from imaging. Motivated by this scenario, we here propose a mechanical-supported strategy to assist surgeons in their decisions, by giving intelligible maps of the risk fracture which take into account the interplay between the actual mechanical strength distribution inside the bone tissue and its response to the forces exerted by the implant. In the presented study, we produce charts and patient-specific synthetic &ldquo, traffic-light&rdquo, indicators of fracture risk, by making use of ad hoc analytical solutions to predict the stress levels in the bone by means of Computed Tomography-based mechanical and geometrical parameters of the patient. We felt that if implemented in a friendly software or proposed as an app, the strategy could constitute a practical tool to help the medical decision-making process, in particular with respect to the choice of adopting cemented or cementless implant.

The evolution of species is governed by complex phenomena in which biological and environmental features may interact dynamically. Subterranean mammals dig tunnels whose diameter minimizes energetic costs during excavations and display anatomical adaptations in order to burrow structurally stable tunnels according to specific features of the soil. These animals weight from less than 50 g up to 1–2 kg, and dig tunnels with diameters from 3 to 15 cm. The use of allometric laws has enabled these data to be correlated. However, since tunnels need to be stable with respect to the geomechanical characteristics of the resident soils, a mathematical treatment linking the admissible dimensions of tunnels to the environment here suggests a mechanically grounded correlation between the body mass of subterranean mammals and the maximum dimensions of tunnels. Remarkably, such theoretical findings reflect very well the empirical allometric relationship and contribute to explain the wide differences observed in body sizes of subterranean mammals. In this respect, a far from ancillary role of environmental mechanics on the morphological evolution of subterranean mammals can be hypothesized.