Regimes of wrinkling in pressurized elastic shells

We consider the point-indentation of a pressurized elastic shell. It has previously been shown that such a shell is subject to a wrinkling instability as the indentation depth is quasi-statically increased. Here we present detailed analysis of this wrinkling instability using a combination of analytical techniques and finite element simulations. In particular, we study how the number of wrinkles observed at the onset of instability grows with increasing pressurization. We also study how, for fixed pressurization, the number of wrinkles changes both spatially and with increasing indentation depth beyond onset. This `Far from threshold' analysis exploits the largeness of the wrinkle wavenumber that is observed at high pressurization and leads to quantitative differences with the standard `Near threshold' stability analysis.Comment: 21 pages, 8 figs. Minor typos correcte

Curvature controls beading in soft coated elastic cylinders:Finite wavemode instability and localized modulations

Axisymmetric beading instabilities in soft, elongated cylinders have been observed in a plethora of scenarios, ranging from cellular nanotunnels and nerves in biology to swollen cylinders and electrospun fibers in polymer physics. One of the common geometrical features that can be seen in these systems is the finite wavelength of the emerging pattern. However, modelling studies often predict that the instability has an infinite wavelength, which can be associated with localized necking or bulging. In this paper, we consider a soft elastic cylinder with a thin coating that resists bending, as described by the Helfrich free energy functional. The bending stiffness and natural mean curvature of the coating are two novel features whose competition against bulk elasticity and capillarity is investigated. For intermediate values of the bending stiffness, a linear stability analysis reveals that the mismatch between the current and natural mean curvature of the coating can lead to patterns emerging with a finite wavelength. This analysis creates a continuous bridge between the classical solutions of the shape equation obtained from the Helfrich functional and a curvature-controlled zero-wavemode instability, similar to the one induced by the competition between bulk elasticity and capillarity. A weakly non-linear analysis predicts that the criticality of the bifurcation depends on the controlling parameter, with both supercritical and subcritical bifurcations possible. When capillarity is introduced, the criticality of the bifurcation changes in a non-trivial way

Static bistability of spherical caps

Depending on its geometry, a spherical shell may exist in one of two stable states without the application of any external force: there are two `self-equilibrated' states, one natural and the other inside out (or `everted'). Though this is familiar from everyday life -- an umbrella is remarkably stable, yet a contact lens can be easily turned inside out -- the precise shell geometries for which bistability is possible are not known. Here, we use experiments and finite element simulations to determine the threshold between bistability and monostability for shells of different solid angle. We compare these results with the prediction from shallow shell theory, showing that, when appropriately modified, this offers a very good account of bistability even for relatively deep shells. We then investigate the robustness of this bistability against pointwise indentation. We find that indentation provides a continuous route for transition between the two states for shells whose geometry makes them close to the threshold. However, for thinner shells, indentation leads to asymmetrical buckling before snap-through, while also making these shells more `robust' to snap-through. Our work sheds new light on the robustness of the `mirror buckling' symmetry of spherical shell caps.Comment: 24 pages, 8 figure

Snap-induced morphing:From a single bistable shell to the origin of shape bifurcation in interacting shells

The bistability of embedded elements provides a natural route through which to introduce reprogrammability to elastic meta-materials. One example of this is the soft morphable sheet, in which bistable elements that can be snapped up or down, are embedded within a soft sheet. The state of the sheet can then be programmed by snapping particular elements up or down, resulting in different global shapes. However, attempts to leverage this programmability have been limited by the tendency for the deformations induced by multiple elastic elements to cause large global shape bifurcations. We study the root cause of this bifurcation in the soft morphable sheet by developing a detailed understanding of the behaviour of a single bistable element attached to a flat ‘skirt’ region. We study the geometrical limitations on the bistability of this single element, and show that the structure of its deformation can be understood using a boundary layer analysis. Moreover, by studying the compressive strains that a single bistable element induces in the surrounding skirt we show that the shape bifurcation in the soft morphable sheet can be delayed by an appropriate design of the lattice on which bistable elements are placed

Debiased ambient vibrations optical coherence elastography to profile cell, organoid and tissue mechanical properties

The role of the mechanical environment in defining tissue function, development and growth has been shown to be fundamental. Assessment of the changes in stiffness of tissue matrices at multiple scales has relied mostly on invasive and often specialist equipment such as AFM or mechanical testing devices poorly suited to the cell culture workflow.In this paper, we have developed a unbiased passive optical coherence elastography method, exploiting ambient vibrations in the sample that enables real-time noninvasive quantitative profiling of cells and tissues. We demonstrate a robust method that decouples optical scattering and mechanical properties by actively compensating for scattering associated noise bias and reducing variance. The efficiency for the method to retrieve ground truth is validated in silico and in vitro, and exemplified for key applications such as time course mechanical profiling of bone and cartilage spheroids, tissue engineering cancer models, tissue repair models and single cell. Our method is readily implementable with any commercial optical coherence tomography system without any hardware modifications, and thus offers a breakthrough in on-line tissue mechanical assessment of spatial mechanical properties for organoids, soft tissues and tissue engineering

An overview of the Italian forest biodiversity and its conservation level, based on the first outcomes of the 4th Habitat Report ex-Art. 17

In 2019 the 4th Report ex-Art. 17 on the conservation status (CS) of Annex I Habitats of the 92/43/EEC Directive was expected by every EU/28 country, with reference to the period 2013-18. In Italy, the process was in charge to the Italian Institute for Environmental Protection and Research (ISPRA), on behalf of the Ministry for Environment, Land and Sea Protection (MATTM), with the scientific support of the Italian Botanical Society (SBI). A large group of thematic and territorial experts elaborated the available data concerning the 124 types of terrestrial and inland water Habitats present in Italy, 39 of which are represented by Forest Habitats (Group 9),. The main aim of the work was the evaluation of the overall CS of each Habitat by Biogeographic Region (Mediterranean, Continental and Alpine), for a total amount of 294 assessments. A high proportion of these (92, corresponding to 31% of the total) referred to Forest Habitats, including 20 marginal types for which the CS was not requested. The analysis was carried out at different scales: a) administrative territory, through the data contained in the ISPRA database, whose compilation was in charge to the Regions and Autonomous Provinces; b) Natura 2000 site, with the latest updates available (Standard Data Forms updated to 2018); c) national scale, implementing the distribution maps for each Habitat based on the European grid ETRS89-LAEA5210 (10x10 km2 mesh); d) Biogeographic Region, scale of the final assessment. Cartographic outcomes, associated databases and additional data used for the assessments will be available online on the ISPRA Portal as soon as the validation process by the European Commission will be completed. A dedicated archive named "HAB_IT" has been created in the national database "VegItaly" (1), managed by the Italian Society of Vegetation Science, where the phytosociological relevés representative of the various Annex I Habitats in Italy will be archived and freely accessible. An overview of the results regarding the Forest habitats is here provided, including a comparison with the outcomes of the former reporting cycle, the 3rd Report ex-Art. 17 (2). In several cases (e.g. 9120, 91L0), the distribution maps have been remarkably improved due to better knowledge and more fitful interpretation. The conservation status resulted as Favourable (FV) for 6,7%, Inadequate (U1) for 58,7% and Bad (U1) for 32,0% of the 72 assessed forest Habitat types. In no case there was an improvement of the conservation status, while in 6 cases a worsening of the conditions resulted from the data analysis, pointing out the Habitats types with a higher need of action. Similarly to other projects carried out as a team by the network of Annex I Habitat experts of the Italian Botanical Society and the Italian Society for Vegetation Science (e.g. 3, 4), this is another step in the direction of supporting the implementation of the 92/43/EEC "Habitat" Directive in Italy and Europe. On this ground, the high biodiversity of the Italian forest Habitats could be emphasized, however results pointed out that some rare or endemic types (e.g. Alnus cordata or Betula aetnensis-dominated forests) are still scarcely acknowledged by the most prominent EU conservation tools such as the Annex I to the "Habitat" Directive. 1) F. Landucci et al. (2012) Plant Biosyst., 146(4), 756-763 2) P. Genovesi et al. (2014) ISPRA, Serie Rapporti, 194/2014 3) E. Biondi et al. (2009) Società Botanica Italiana, MATTM, D.P.N., http://vnr.unipg.it/habitat/ 4) D. Gigante et al. (2016) Plant Sociology, 53(2), 77-8

Regimes of wrinkling in pressurized elastic shells

'File Information.pdf', included in this archive, contains the description of all the files in the folder and how they are related to the paper with the same titl

Regimes of wrinkling in pressurized elastic shells

'File Information.pdf', included in this archive, contains the description of all the files in the folder and how they are related to the paper with the same titl

Axisymmetric ridges and circumferential buckling of indented shells of revolution

When poking a thin shell-like structure, like a plastic water bottle, experience shows that an initial axisymmetric dimple forms around the indentation point. The ridge of this dimple, with increasing indentation, eventually buckles into a polygonal shape. The polygon order generally continues to increase with further indentation. In the case of spherical shells, both the underlying axisymmetric deformation and the buckling evolution have been studied in detail. However, little is known about the behaviour of general geometries. In this work we describe the geometrical and mechanical features of the axisymmet-ric ridge that forms in indented general shells of revolution with non-negative Gaussian curvature and the conditions for circumferential buckling of this ridge. We show that, under the assumption of 'mirror buckling' a single unified description of this ridge can be written if the problem is non-dimensionalised using the local slope of the undeformed shell mid-profile at the ridge radial location. However, in dimensional form the ridge properties evolve in quite different ways for different mid-profiles. Focusing on the indentation of shallow shells of revolution with constant Gaussian curvature, we use our theoretical framework to study the properties of the ridge at the circumferential buckling threshold and evaluate the validity of the mirror buckling assumption against a linear stability analysis on the shallow shell equations, showing very good agreement. Our results highlight that circumferential buckling in indented thin shells is controlled by a complex interplay between the geometry and the stress state in the ridge. The results of our study will provide greater insight into the mechanics of thin shells. This could enable indentation to be used as a means to measure the mechanical properties of a wide range of shell geometries or used to design shells with specific mechanical behaviours