A physically consistent virtual crack closure technique accounting for contact and interpenetration

In some circumstances, the standard formulation of the virtual crack closure technique (VCCT) may yield negative values of the modal contributions to the energy release rate. To avoid such physically meaningless results, a revised formulation is available. However, the revised VCCT does not take into account possible interpenetration of the crack faces, that may be predicted by the linearly elastic solution. The present work extends the revised VCCT formulation by introducing suitable contact constraints to prevent local interpenetration of the crack-tip nodes. By considering open vs. interpenetrated cracks and tensile vs. compressive crack-tip forces, four cases emerge. For each case, a suitable two-step crack closure process is outlined with the two steps respectively corresponding to fracture modes II and I. The contact pressure force, if present, is evaluated and accounted for in the computation of the crack closure work. As a result, novel analytical expressions are derived for the modal contributions to the energy release rate accounting for contact and prevented interpenetration

A bimodal lognormal distribution model for the prediction of COVID-19 deaths

The paper presents a phenomenological epidemiological model for the description and prediction of the time trends of COVID-19 deaths worldwide. A bimodal distribution function—defined as the mixture of two lognormal distributions—is assumed to model the time distribution of deaths in a country. The asymmetric lognormal distribution enables better data fitting with respect to symmetric distribution functions. Besides, the presence of a second mode allows the model to also describe second waves of the epidemic. For each country, the model has six parameters, which are determined by fitting the available data through a nonlinear least-squares procedure. The fitted curves can then be extrapolated to predict the future trends of the total and daily number of deaths. Results for the six continents and the World are obtained by summing those computed for the 210 countries in the Our World in Data (OWID) dataset. To assess the accuracy of predictions, a validation study is first conducted. Then, based on data available as of 30 September 2020, the future trends are extrapolated until the end of year 2020

The ellipse of crack-tip flexibility for the partitioning of fracture modes

A crack in a solid body will generally propagate according to a combination of the three basic fracture modes (I or opening, II or sliding, and III or tearing). Thus, the energy release rate, G, will be the sum of three modal contributions, GI, GII, and GIII. In the finite element context, the virtual crack closure technique (VCCT) is widely used to calculate the energy release rate and its modal contributions. Accordingly, G is related to the work done by the forces, r and -r, applied at the crack-tip nodes to close up the crack, once propagated by a finite length, Da. In I/II mixed-mode fracture problems, the crack-tip relative displacement Ds = [Du, Dw]T = Fr, where F is the crack-tip flexibility matrix. The conic section associated to F turns out to be an ellipse, Gamma, named the ellipse of crack-tip flexibility, similar to Culmann’s ellipse of elasticity. The ellipse of crack-tip flexibility helps visualise the relationship between the crack-tip force, r, and relative displacement, Ds, whose directions correspond to conjugate diameters. Furthermore, the ellipse can be used to decompose the crack-tip force vector, r, into energetically orthogonal components, which enable a physically consistent partitioning of fracture modes

Non-gaussian probability distribution functions in two dimensional Magnetohydrodynamic turbulence

Intermittency in MHD turbulence has been analyzed using high resolution 2D numerical simulations. We show that the Probability Distribution Functions (PDFs) of the fluctuations of the Elsasser fields, magnetic field and velocity field depend on the scale at hand, that is they are self-affine. The departure of the PDFs from a Gaussian function can be described through the scaling behavior of a single parameter lambda_r^2 obtained by fitting the PDFs with a given curve stemming from the analysis of a multiplicative model by Castaing et al. (1990). The scaling behavior of the parameter lambda_r^2 can be used to extract informations about the intermittency. A comparison of intermittency properties in different MHD turbulent flows is also performed.Comment: 7 pages, with 5 figure

Habitat fragmentation and anthropogenic factors affect wildcat Felis silvestris silvestris occupancy and detectability on Mt Etna

Knowledge of patterns of occupancy is crucial for planning sound biological management and for identifying areas which require paramount conservation attention. The European wildcat Felis silvestris is an elusive carnivore and is classified as ‘least concern’ on the IUCN red list, but with a decreasing population trend in some areas. Sicily hosts a peculiar wildcat population, which deserves conservation and management actions, due to its isolation from the mainland. Patterns of occupancy for wildcats are unknown in Italy, and especially in Sicily. We aimed to identify which ecological drivers determined wildcat occurrence on Mt Etna and to provide conservation actions to promote the wildcats’ long-term survival in this peculiar environment. The genetic identity of the wildcat population was confirmed through a scat-collection which detected 22 different wildcat individuals. We analysed wildcat detections collected by 91 cameras using an occupancy frame work to assess which covariates influenced the detection (p) and the occupancy (ψ) estimates. We recorded 70 detections of the target species from 38 cameras within 3377 trap-days. Wildcat detection was positively influenced by the distance to the major paved roads and negatively affected by the presence of humans. Wildcat occupancy was positively associated with mixed forest and negatively influenced by pine forest, fragmentation of mixed forest and altitude. A spatially explicit predicted occupancy map, validated using an independent dataset of wildcat presence records, showed that higher occupancy estimates were scattered, mainly located on the north face and at lower altitude. Habitat fragmentation has been claimed as a significant threat for the wildcat and this is the first study that has ascertained this as a limiting factor for wildcat occurrence. Conservation actions should promote interconnectivity between areas with high predicted wildcat occupancy while minimising the loss of habitat

An Experimental Compliance Calibration Strategy for Mixed-mode Bending Tests

AbstractWe have developed an enhanced beam theory model of the mixed-mode bending (MMB) test, where the delaminated specimen is schematised as an assemblage of sublaminates connected by an elastic interface. We show how the interface parameters can be estimated through an experimental compliance calibration strategy. First, double cantilever beam (DCB) and end notched flexure (ENF) tests are conducted and the specimens’ compliance is measured. Then, a nonlinear least squares fitting procedure furnishes the values of the elastic interface constants. Such calibrated values can be used to interpret the results of MMB tests

Morphological variation of the newly confirmed population of the javelin sand boa, Eryx jaculus (Linnaeus, 1758) (Serpentes, erycidae) in Sicily, Italy

The presence of the Javelin sand boa in Sicily has recently been confirmed. Here the morphological characters and sexual dimorphism of the Sicilian population of Eryx jaculus are presented. Seven meristic and six metric characters in 96 specimens from Sicily were examined. The results show that tail length, snout-vent length, the distance between nostrils and the number of ventral and subcaudal scales are different between sexes. The characters found in the Sicilian population of the Javelin sand boa resemble those of the African population (ssp. jaculus) rather than the Eurasian population (ssp. turcicus), but biomolecular studies are necessary to understand its taxonomic identity

A mechanical model for FRP-strengthened beams in bending

We analyse the problem of a simply supported beam, strengthened with a fibre-reinforced polymer (FRP) strip bonded to its intrados and subjected to bending couples applied to its end sections. A mechanical model is proposed, whereby the beam and FRP strip are modelled according to classical beam theory, while the adhesive and its neighbouring layers are modelled as an interface having a piecewise linear constitutive law defined over three intervals (elastic response – softening response – debonding). The model is described by a set of differential equations with appropriate boundary conditions. An analytical solution to the problem is determined, including explicit expressions for the internal forces, displacements and interfacial stresses. The model predicts an overall non-linear mechanical response for the strengthened beam, ranging over several stages: from linearly elastic behaviour to damage, until the complete detachment of the FRP reinforcement

An elastic-interface model for the mixed-mode bending test under cyclic loads

AbstractWe have developed a mechanical model of the mixed-mode bending (MMB) test, whereby the specimen is considered as an assemblage of two identical sublaminates, modelled as Timoshenko beams. The sublaminates are partly connected by a linearly elastic–brittle interface, transmitting stresses along both the normal and tangential directions with respect to the interface plane. The model is described by a set of suitable differential equations and boundary conditions. Based on the explicit solution of this problem and following an approach already adopted to model buckling-driven delamination growth in fatigue, we analyse the response of the MMB test specimen under cyclic loads. Exploiting the available analytical solution, we apply a fracture mode-dependent fatigue growth law. As a result, the number of cycles needed for a delamination to extend to a given length can be predicted