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The spreading of respiratory diseases through deposited saliva droplets is strongly dependent on the water evaporation process that may determine the virus viability due to the increase in concentration of nonvolatile compounds that are harmful for the virus. The drying time of a virus-laden droplet is influenced by environmental conditions, such as relative humidity and temperature, physical properties, such as the features of the surface on which it is deposited, and the wetting regime. Under this perspective, we addressed the modeling of an evaporating sessile droplet resting on a flat smooth surface, extending a previous diffusion-based model from the same authors. The evaporation behavior of sessile droplets of aqueous sodium chloride solutions and the virus viability of a surrogate virus (MS2) have been simulated considering different wetting regimes to account for different types of surfaces, ranging from highly hydrophilic to highly hydrophobic, as well as different ambient conditions, in terms of temperature and relative humidity. The results of calculations were given in terms of time evolution of contact angle, contact radius, mixture volume, and salt concentration, unveiling the importance of different wetting regimes for evaporation behavior and drying time. Longer evaporation times have been observed as temperature decreases and relative humidity increases. With reference to a surrogate virus, we evaluated the virus viability at different selected conditions, observing the classical U-shape of relative viability as a function of relative humidity of the environment at a certain temperature.

We study the equilibrium configurations related to the growth of an elastic fibre in a confining flexible ring. This system represents a paradigm for a variety of biological, medical, and engineering problems. We consider a simplified geometry in which initially the container is a circular ring of radius $R$. Quasi-static growth is then studied by solving the equilibrium equations as the fibre length $l$ increases, starting from $l = 2R$. Considering both the fibre and the ring as inextensible and unshearable, we find that beyond a critical length, which depends on the relative bending stiffness, the fibre buckles. Furthermore, as the fibre grows further it folds, distorting the ring until it induces a break in mirror symmetry at $l>2 \pi R$. We get that the equilibrium shapes depend only on two dimensionless parameters: the length ratio $\mu = l/R$ and the bending stiffnesses ratio $\kappa$. These findings are also supported by finite element simulation. Finally we experimentally validate the theoretical results showing a very good quantitative prediction of the observed buckling and folding regimes at variable geometrical parameters.

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

In the present work, we present a linear poroelastic model for a quasi-static oscillating bilayer beam made by two thick strata in perfect bond at their interface, characterized by different elastic moduli and permeability, both directly influenced by porosity. The solution is built up by considering the structure as a three-dimensional object and is obtained analytically for the full coupling of mass balance and mechanical equations, by imposing weak boundary conditions on the sole forces emerging at the lateral outermost surfaces, neglecting the inertial effects. After verifying the accuracy of the solution by comparing theoretical outcomes and numerical results from Finite Element simulations, ad hoc sensitivity analyses were then carried out in order to investigate the effects on the stress distribution and fluid flow due to prescribed inhomogeneities related to variations of material and geometrical parameters across the beam thickness, by keeping constant the total volume of the porous solid skeleton and applying self-equilibrated and oscillating in time axial forces and bending moments at two opposite sides of the structure. Some dynamic analyses were also performed to highlight proper periods and frequencies ranges where pulse loadings ensured the quasi-static response of the system, however discussing interferences due to transient regimes for selected cases on the basis of numerical analyses. Finally, we show that, by playing with ratios between elastic moduli, thickness and porosity of the two layers, a number of counterintuitive or even non-conventional behaviors can be observed, which give rise to unexpected back-flow phenomena and anomalous fluid content distributions, as well as to stress peaks kindled by moving the layer interface and overall stiffening that could be all exploited for the design of new multi-objective poroelastic metamaterials.

Langmuir monolayers at gas/liquid interfaces provide a rich framework to investigate the interplay between multiscale geometry and mechanics. Monolayer collapse is investigated at a topological and geometric level by building a scale space M from experimental imaging data. We present a general lipid monolayer collapse phase diagram, which shows that wrinkling, folding, crumpling, shear banding, and vesiculation are a continuous set of mechanical states that can be approached by either tuning monolayer composition or temperature. The origin of the different mechanical states can be understood by investigating the monolayer geometry at two scales: fluorescent vs atomic force microscopy imaging. We show that an interesting switch in continuity occurs in passing between the two scales, C

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.

Even with the most recent advances in rock mechanics, the stability assessment of underground tunnels continues to involve many uncertainties in the parameters which can significantly affect the calculated factors of safety. In the present work, a straight characterization which can help to evaluate the risk of a tunnel collapse with respect to the depth of excavation is proposed. Following a consolidated Limit Analysis approach and by means of the Hoek-Brown failure criterion, the galleries are divided into shallow, intermediate and deep according to the variability of the mechanical parameters of the rock mass with depth. A solution to the problem of impending collapse in the case of variable rock properties is proposed and examples are presented and discussed both from an analytical and a numerical standpoint.

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.

In this paper, a first insight into the role that non-conventional structural patterns might play in the design of tall buildings is presented. The idea is to explore the mechanical properties of selected non-conventional structural patterns, in the form of both regular (Hexagrid) and irregular (Voronoi tessellation inspired) arrays, in order to assess their actual applicability in tall building design. For this aim, the concept of Representative Volume Element (RVE) and a classical homogenization-based micromechanical approach are employed for identifying the pattern units and deriving the relevant generalized stress-strain relationships. In the case of irregular patterns based on Voronoi diagrams, obtained by perturbing prescribed key geometrical features of hexagrids, a statistically significant sample of RVEs is defined on the basis of sensitivity analyses, and the related mechanical characterization is developed in statistical terms. Finally, a preliminary stiffness-based design procedure is proposed and applied to a tall building model with Voronoi exoskeleton. In conclusion, a discussion on the effectiveness of the design procedure and on the structural efficiency of the Voronoi patterns for tall buildings is presented.

Langmuir monolayers at gas/liquid interfaces provide a rich framework to investigate the interplay between multiscale geometry and mechanics. Monolayer collapse is investigated at a topological and geometric level by building a scale space M from experimental imaging data. We present a general lipid monolayer collapse phase diagram, which shows that wrinkling, folding, crumpling, shear banding, and vesiculation are a continuous set of mechanical states that can be approached by either tuning monolayer composition or temperature. The origin of the different mechanical states can be understood by investigating the monolayer geometry at two scales: fluorescent vs atomic force microscopy imaging. We show that an interesting switch in continuity occurs in passing between the two scales, C A F M ∈ M A F M ≠ C F M ∈ M . Studying the difference between monolayers that fold vs shear band, we show that shear banding is correlated to the persistence of a multi-length scale microstructure within the monolayer at all surface pressures. A detailed analytical geometric formalism to describe this microstructure is developed using the theory of structured deformations. Lastly, we provide the first ever finite element simulation of lipid monolayer collapse utilizing a direct mapping from the experimental image space M into a simulation domain P . We show that elastic dissipation in the form of bielasticity is a necessary and sufficient condition to capture loss of in-plane stability and shear banding.

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 progressive falling of barriers among disciplines is opening unforeseen scenarios in diagnosis and treatment of cancer diseases. By sharing models and mature knowledge in physics, engineering, computer sciences and molecular biology, synergistic efforts have in fact contributed in the last years to re-think still unsolved problems, shedding light on key roles of mechanobiology in tumors and envisaging new effective strategies for a precise medicine. The use of ultrasounds for altering cancer cells’ program is one of the most attracting grounds to be explored in oncophysics, although how to administer mechanical energy to impair selected cell structures and functions simultaneously overcoming the critical trade-off between the impact of the cure and the patient risk still remains an open issue. Within this framework, by starting from the theoretical possibility of selectively attacking malignant cells by exploiting the stiffness discrepancies between tumor and healthy single cells, first proposed by Fraldi et al. (2015), we here investigate the in-frequency response of an overall spherical close-packing of geometrically equal polyhedral cells to gain insights into how mechanical resonance and vibration-induced failure phenomena can be oriented to destroy specific target units when both the cell populations coexist, as it happens for in vivo cases. Inspired by the dynamic action of earthquakes – which fracture only selected elements among adjacent ones in the same structure or damage individual constructions in contiguous buildings – we study the harmonic response of hierarchically architectured cell agglomerates, inhabited by both tumor and healthy cells that interact mutually throughout the extra-cellular matrix and whose cytoskeleton is modeled as a nonlinear soft-tensegrity structure. Numerical Finite Element results show that, at frequencies compatible with low intensity therapeutic ultrasounds, mechanical resonance and possible fatigue cycles of the pre-stressed actin filaments and microtubules can be selectively induced in cancer cells as a function of the global volume fraction of the cell species, paving the way for future engineered treatment protocols.

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.

Adherent cells are able to actively generate internal forces, channelled by cytoskeletal protein filaments and transmitted through transmembrane receptors to the surrounding environment by means of focal adhesions. Cells also dynamically interact with extracellular matrix by sensing external chemo-mechanical stimuli and then inducing formation of stress fibres mediated by polymerization/de-polymerization processes which continuously redesign the interplay between structural organization and contractility activities in the cytoskeleton, so orchestrating selected signal pathways at the basis of many important cell’s physiological functions like adhesion, migration and division. Despite chemo- and duro-taxis have been intensively studied in the last years to understand how cells move on a substrate, their polarization and reorientation – observed during gastrulation, wound healing and morphogenesis – are only partially understood. By starting from the evidence highlighted in some recent studies that cells reorient in response to substrata deformation by essentially obeying a pure mechanical interaction, we propose to interpret the seeming overall cells’ rotation resulting from the reconfiguration of their cytoskeleton – here named mechanotropism – as a nonlinear optimization problem in which the adherent cell aims to align along directions leading it to minimize a physically coherent measure of work spent to deform the elastic substrate while retaining a prescribed level of homeostatic contractile force. To do this, the single-cell is simply modelled as a finite size contractile force dipole that acts on the boundary of a half-space perturbed by applied point loads. The effects of fences of forces acting orthogonally and tangentially on the boundary of the adhesion medium and encircling the cell are then investigated, so obtaining solutions that predict multiple non-trivial cell polarizations as functions of number, direction, relative magnitude and distance from the cell-dipole of the forces, as well as of the substrate’s Poisson ratio, with unprecedented outcomes under the hypothesis of auxetic (i.e. negative Poisson ratio) materials. The results lead to envisage that the proposed theoretical model might contribute to unveil the mechanobiological principles ruling in vivo cells orientation processes by guiding the design of novel experimental strategies and to conceive new mechanics-based markers for guessing cells’ pathological conditions from their mechanotropism.

In the present paper a mathematical model able to reproduce the mechanical response of a shape memory alloy (SMA) helical spring is presented. The proposed model is based on a simplified but effective theory of the helix that assumes small strains and large displacements. The kinematics of the helix and the related generalized strain measures are introduced, with stress resultants conjugated to them and the corresponding equilibrium equations of the curved beam. A specific constitutive law for this structural model is then presented for the SMA material, which accounts for the phase transformation due to the coupling of the shear and axial strains and to the effect of the temperature variation as well. Then, a numerical procedure, based on the backward Euler time integration algorithm and the prediction-correction technique for solving the nonlinear time step, is developed. Several numerical applications are presented to assess the reliability of the proposed SMA helix model and the implemented numerical procedure, and to investigate the response of the helix. Initially, the behavior of a circular SMA cross-section is studied, comparing the results obtained by the proposed modeling approach with the ones carried out by finite element analyses. Then, the helix structural element is considered and results are again compared with finite element outcomes. Finally, a sensitivity analysis is performed varying the pitch of the helix.

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.

Complex mechanical behaviours are generally met in macroscopically homogeneous media as effects of inelastic responses or as results of unconventional material properties, which are postulated or due to structural systems at the meso/micro-scale. Examples are strain localization due to plasticity or damage and metamaterials exhibiting negative Poisson’s ratios resulting from special porous, eventually buckling, sub-structures. In this work, through ad hoc conceived mechanical paradigms, we show that several non-standard behaviours can be obtained simultaneously by accounting for kinematical discontinuities, without invoking inelastic laws or initial voids. By allowing mutual sliding among rigid tesserae connected by pre-stressed hyperelastic links, we find several unusual kinematics such as localized shear modes and tensile buckling-induced instabilities, leading to deck-of-cards deformations—uncapturable with classical continuum models—and unprecedented ‘bulky’ auxeticity emerging from a densely packed, geometrically symmetrical ensemble of discrete units that deform in a chiral way. Finally, after providing some analytical solutions and inequalities of mechanical interest, we pass to the limit of an infinite number of tesserae of infinitesimal size, thus transiting from discrete to continuum, without the need to introduce characteristic lengths. In the light of the theory of structured deformations, this result demonstrates that the proposed architectured material is nothing else than the first biaxial paradigm of structured continuum —a body that projects, at the macroscopic scale, geometrical changes and disarrangements occurring at the level of its sub-macroscopic elements.

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.

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.

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.

The focus of the present work is to present an analytical approach for buckling and free vibrations analysis of thick functionally graded nanoplates embedded in a Winkler-Pasternak medium. The equations of motion are derived according to both the third-order shear deformation theory, proposed by Reddy, and the nonlocal elasticity Eringen's model. For the first time, the equations are solved analytically for plates with two simply supported opposite edges, the solutions also turning helpful as shape functions in the analysis of structures with more complex geometries and boundary conditions. Sensitivity analyses are finally performed to highlight the role of nonlocal parameters, aspect and side-to-thickness ratios, boundary conditions, and functionally graded material properties in the overall response of plates and cylindrical shells. It is felt that the proposed strategy could be usefully adopted as benchmark solutions in numerical routines as well as for predicting some unexpected behaviors, for instance, in terms of buckling load, in thick nanoplates on elastic foundations.

Optimization of materials and structures is a crucial step in the design of man-made mechanical components for a wide field of engineering applications. It also plays a key role in mechanobiology of living systems, being involved by nature across the scales, from single-cell to tissues and organs, as a strategy to minimize metabolic cost and maximize biomechanical performances. The synergy between thecontinuously increasing developmentof high-resolution 3D printing technologies andthe possibility to predict chemical and physical properties through molecular dynamics-based numerical analyses hasrecently contributed to boost the use of both design and topology optimization procedures. They are employed in ab initio simulations as key strategies for deciding microstructures to improve mechanical performances and, concretely, to achieve prototypes of new material components. With this in mind, we here proposeto abandon the classical approach of using a single scalar objective function employed in the classical design and topology optimization strategies, to introduce multiple quantities to be minimized, identified as the differences between material yield stress and the maximum von Mises stress. After mathematically justifying the well-posedness of thisunconventionalchoicefor the case at hand, it is highlightedthat the proposedstrategy is based on the concept of "equalizing" a proper stress measure at any point of the body and, for this reason, it is baptized as Galilei’s optimization, in honor of the Italian scholar who somehow first wondered about the possibility of changing sizes of beams to have uniform internal forces and, in turn, minimum weight. By exploiting analytical solutions and ad hoc implementing a parametric finite element algorithm to be applied to a wide variety of solids with arbitrary complex structural geometries, including nested or hierarchically organized architectures, it is firstdemonstrated that the proposed optimization strategy roughlyretraces principles invoked by nature to guide growth, remodeling and shaping of biomaterials. More importantly, by means of several benchmark examples, we finally show the proposed procedure might be also helpfully employed to conceive a new class of micro-structured, eventually 3D-printed materials exhibiting surprising post-elastic properties, such as high overall resilience and toughness, in particular obtaining a decrease of stress concentration and a slowing down ofcrack propagation as direct effects of the optimization, which de facto minimizesstress gradients wherever in the solid domain.

In the last years, due to their exceptional mechanical properties (elastic modulus of about 1 TPa and tensile strength of 130–150 GPa), single and multi-wall carbon nanotubes (CNTs and MWCNTs) have encountered an increasing interest among scientists. More recently, a number of studies have also envisaged the possibility of building up a new generation of composites with elastomeric or polymeric matrix, reinforced with MWCNTs, to gain high mechanical performances and other physical properties. However, independently from problems related to accuracy and costs associated to the processing and the production of MWCNTS and some difficulties in exactly controlling their dimensions, distribution and geometry, a detailed micromechanical description of the overall elastic response of these complex structures—that appear to be constituted by several layers organized as hollow cylindrical phases wrapped around a central core—is still at the center of a vivid debate, because it is expected that their chirality induces an anisotropic (e.g. trigonal/monoclinic) elastic behavior, which is characterized by a coupling between torsion and axial deformations. This is a relevant aspect for the developing of stresses inside the reinforcements and, importantly, for predicting the actual stress regimes at the interfaces and in turn the overall mechanical behavior of these composites, with transferring of spurious shear stresses and size effects. In this framework, due to the difficulties of deriving analytical results for the mechanical response of these multi-wall elastically monoclinic cylinders, the vast majority of the literature efforts have presented numerical results, for example by performing Finite Element (FE) analyses or by estimating the stiffness of these structures, at different scale levels, through molecular dynamics (MD) strategies. The present contribution is therefore aimed to furnish new closed-form elastic solutions for general compound cylinders, made by n hallow monoclinic/trigonal phases and a possible central core, under prescribed boundary conditions of interest for applications, to be implemented in computational FE algorithms for faithfully replicating the actual mechanical response of composites reinforced with MWCNTs.

Clustering of ligand-binding receptors of different types on thickened isles of the cell membrane, namely lipid rafts, is an experimentally observed phenomenon. Although its influence on cell's response is deeply investigated, the role of the coupling between mechanical processes and multiphysics involving the active receptors and the surrounding lipid membrane during ligand-binding has not yet been understood. Specifically, the focus of this work is on G-protein-coupled receptors (GPCRs), the widest group of transmembrane proteins in animals, which regulate specific cell processes through chemical signalling pathways involving a synergistic balance between the cyclic Adenosine Monophosphate (cAMP) produced by active GPCRs in the intracellular environment and its efflux, mediated by the Multidrug Resistance Proteins (MRPs) transporters. This paper develops a multiphysics approach based on the interplay among energetics, multiscale geometrical changes and mass balance of species, i.e. active GPCRs and MRPs, including diffusion and kinetics of binding and unbinding. Because the obtained energy depends upon both the kinematics and the changes of species densities, balance of mass and of linear momentum are coupled and govern the space-time evolution of the cell membrane. The mechanobiology involving remodelling and change of lipid ordering of the cell membrane allows to predict dynamics of transporters and active receptors -in full agreement with experimentally observed cAMP levels- and how the latter trigger rafts formation and cluster on such sites. Within the current scientific debate on Severe Acute Respiratory Syndrome CoronaVirus 2 (SARS-CoV-2) and on the basis of the ascertained fact that lipid rafts often serve as an entry port for viruses, it is felt that approaches accounting for strong coupling among mechanobiological aspects could even turn helpful in better understanding membrane-mediated phenomena such as COVID-19 virus-cell interaction.

Mechanical stress accumulating during growth in solid tumors plays a crucial role in the tumor mechanobiology. Stresses arise as a consequence of the spatially inhomogeneous tissue growth due to the different activity of healthy and cancer cells inhabiting the various districts of the tissue, an additional piling up effect, induced by stress transferring across the scales, contributing to determine the total stress occurring at the macroscopic level. The spatially inhomogeneous growth rates accompany nonuniform and time-propagating stress profiles, which constitute mechanical barriers to nutrient transport and influence the intratumoral interstitial flow, in this way deciding the starved/feeded regions, with direct aftereffects on necrosis, angiogenesis, cancer aggressiveness and overall tumor mass size. Despite their ascertained role in tumor mechanobiology, stresses cannot be directly appraised neither from overall tumor size nor through standard non-invasive measurements. To date, the sole way for qualitatively revealing their presence within solid tumors is ex vivo, by engraving the excised masses and then observing opening between the cut edges. Therefore, to contribute to unveil stresses and their implications in tumors, it is first proposed a multiscale model where Volterra-Lotka (predator/prey-like) equations describing the interspecific (environment-mediated) competitions among healthy and cancer cells are coupled with equations of nonlinear poroelasticity. Then, an experimental study on mice injected subcutaneously with a suspension of two different cancer cell lines (MiaPaCa-2 and MDA.MB231) was conducted to provide experimental evidences that gave qualitative and some new quantitative confirmations of the theoretical model predictions.

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.

OBJECTIVES Reinforcements for the pulmonary autograft (PA) in the Ross operation have been introduced to avoid the drawback of conduit expansion and failure. With the aid of an in silico simulation, the biomechanical boundaries applied to a healthy PA during the operation were studied to tailor the best implant technique to prevent reoperation. METHODS Follow-up echocardiograms of 66 Ross procedures were reviewed. Changes in the dimensions and geometry of reinforced and non-reinforced PAs were evaluated. Miniroot and subcoronary implantation techniques were used in this series. Mechanical stress tests were performed on 36 human pulmonary and aortic roots explanted from donor hearts. Finite element analysis was applied to obtain high-fidelity simulation under static and dynamic conditions of the biomechanical properties and applied stresses on the PA root and leaflet and the similar components of the native aorta. RESULTS The non-reinforced group showed increases in the percentages of the mean diameter that were significantly higher than those in the reinforced group at the level of the Valsalva sinuses (3.9%) and the annulus (12.1%). The mechanical simulation confirmed geometrical and dimensional changes detected by clinical imaging and demonstrated the non-linear biomechanical behaviour of the PA anastomosed to the aorta, a stiffer behaviour of the aortic root in relation to the PA and similar qualitative and quantitative behaviours of leaflets of the 2 tissues. The annulus was the most significant constraint to dilation and affected the distribution of stress and strain within the entire complex, with particular strain on the sutured regions. The PA was able to evenly absorb mechanical stresses but was less adaptable to circumferential stresses, potentially explaining its known dilatation tendency over time. CONCLUSIONS The absence of reinforcement leads to a more marked increase in the diameter of the PA. Preservation of the native geometry of the PA root is crucial; the miniroot technique with external reinforcement is the most suitable strategy in this context.

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.

Ischemic mitral regurgitation (IMR) is a form of mitral insufficiency that is characterized by papillary muscle (PM) displacement, leaflet tethering, reduced closing forces, and different degree of annular dilatation. Treatment of this condition includes mitral valve replacement or mitral valve repair with restrictive annuloplasty. Recent evidences in mitral valve repair showed that addressing only the annulus and neglecting the subvalvular apparatus provides a suboptimal operation with poor long-term results. However, the complexity of the geometrical aberrances occurring in IMR demands for more accurate analysis also involving the biomechanics underlying the failing mitral valve and subvalvular apparatus. Finite element analysis (FEA) is a powerful tool in this context and we developed a biomechanical model of mitral valve and subvalvular unit using 3D geometry of the leaflets, annulus, chordae and PM. After the application of structural properties of materials to these elements and simulation of systemic pressure loading, FEA could be used to directly determine biomechanical changes and geometry variations. We believe this approach can provide valuable information to better address the surgical treatment of IMR and answer some of the questions still pending in IMR management.

The failure of mitral valve repair procedures revealed in the outcomes of the recent randomized studies is suggesting the necessity for a better understanding of the biomechanical mechanisms underlying the failure of the surgical approaches. Use of biomechanical modelling and finite element analysis (FEA) in cardiovascular research is an important aid in this context. In our group we developed a biomechanical model taking into account all the component of the mitral valve functional unit including the valve leaflets, the annulus, the papillary muscles, the chordae tendinea and the ventricular geometry. The two-dimensional mathematical model was capable to predict some of the actual geometrical and mechanical features of the valvular and subvalvular apparatuses in physiological and pathological conditions providing the engineering quantitative relations between closing and tethering forces and the mechanisms governing the mitral valve unit function. This model might further become patient-specific by means of 3D reconstruction of clinical imaging. Images are first converted in a standard vector format (DICOM, etc.), then automatically translated in a "structural" finite element model and finally implemented in a finite element code. This allows for in silico simulations to virtually explore the effects of different surgical approaches at an early stage after the procedure, to help the operative decision processes, or to optimize the design of surgical implants.

Acoustophoresis devices are proposed as tools for manipulation and diagnostic in microfluidic environments. We demonstrate that their diffusion can be supported and enhanced by Digital Holography. Indeed, this technique covers all the current imaging needs and can stimulate the development of novel applications thanks to its unique features. The numerical refocusing is exploited to control the manipulation during acoustic focusing and acoustic-driven aggregation and to retrieve the 3D trajectories of tracer beads for the ultrasound field calibration. Besides tracking, DH displays its full potential when USs are used to directly manipulate or deform cells. In this case, numerical processing provides information on the sample movement and morphology, with potential applications in the field of diagnostic.

We introduce a time memory formalism in the flux-pressure constitutive relation, ruling the fluid diffusion phenomenon occurring in several classes of porous media. The resulting flux-pressure law is adopted into the Biot’s formulation of the poroelasticity problem. The time memory formalism, useful to capture non-Darcy behavior, is modeled by the Caputo’s fractional derivative. We show that the time-evolution of both the degree of settlement and the pressure field is strongly influenced by the order of Caputo’s fractional derivative. Also a numerical experiment aiming at simulating the confined compression test poroelasticity problem of a sand sample is performed. In such a case, the classical Darcy equation may lead to inaccurate estimates of the settlement time.

The combination of Digital holography and acoustofluidics provides distinct advantages. While a transparent piezo assures optical investigation through the microchannel, we employ holographic imaging to assess the acoustic manipulation and to calibrate bulk acoustic waves.

Strategies to reduce leakage based on integrated systems of monitoring and management of the pressure levels and related anomalies are acknowledged as the most reliable and cost-effective techniques to improve the efficiency of water networks. Because of their relevant impact at the large scale and the crucial roles currently played by programs envisaging ideas of smart cities capable to control/solve problems of homeland security and prevention and early monitoring of disasters and natural hazards, assessment and optimization of water networks have gained interest in recent years, overcoming the scientific fences of civil and hydraulic engineering and now being at the center of a wider vivid debate on how to maximize theoretical and experimental methods to increase security, reliability, and the so-called resilience of urban centers. Within this general scenario, this paper approaches the problem of the monitoring of leakage phenomena by focusing on the possibility of tracing the effects of the presence of not-necessarily circular holes on pipes subjected to combined water pressure and bending regimes, conceiving a parametric model which includes size, shape, orientation, and positioning of the hole, as well as different boundary conditions in the analyses to establish how they influence the final leakage. Sensitivity finite-element–based analyses are conducted to derive curves which could in principle serve, in combination with other consolidated strategies, to better identify position and amount of leakage phenomena. The outcomes are compared with the literature and in-house full-scale experimental findings, demonstrating good agreement between theoretical outcomes and laboratory results and gaining insight into advantages and limitations of the proposed strategy. It is felt that the developed approach, integrated with consolidated monitoring systems, might be useful to scientists and civil engineers in the management of existing hydraulic networks to estimate leakage volumes and predict more-realistic scenarios and related solutions for designing and planning practical interventions. This paper principally focuses on the hole geometry and position aspects, without addressing the hydraulic topic of discharge coefficient, in order to better understand the behavior of a leaking pipe.

This article outlines the methods and applications of threshold-based techniques to assess in vivo muscle and bone tissue distribution in normal and pathological conditions using computed tomography imaging. The approaches described here use medical imaging processing techniques and computational methods to study bone mechanical proprieties, analyze and quantify muscle morphology, visualize changes with 3-D models, develop subject-specific numerical profiles, and assess muscle and bone changes during clinical treatments.