Indentation of ellipsoidal and cylindrical elastic shells

Two-layer elastic models for single-yeast compressibility with flat microlevers

Unicellular organisms such as yeast can survive in very different environments, thanks to a polysaccharide wall that reinforces their extracellular membrane. This wall is not a static structure, as it is expected to be dynamically remodeled according to growth stage, division cycle, environmental osmotic pressure and ageing. It is therefore of great interest to study the mechanics of these organisms, but they are more difficult to study than other mammalian cells, in particular because of their small size (radius of a few microns) and their lack of an adhesion machinery. Using flat cantilevers, we perform compression experiments on single yeast cells (S. cerevisiae) on poly-L-lysine-coated grooved glass plates, in the limit of small deformation using an atomic force microscope (AFM). Thanks to a careful decomposition of force-displacement curves, we extract local scaling exponents that highlight the non-stationary characteristic of the yeast behavior upon compression. Our multi-scale nonlinear analysis of the AFM force-displacement curves provides evidence for non-stationary scaling laws. We propose to model these phenomena based on a two-component elastic system, where each layer follows a different scaling law..

Dehydration-induced corrugated folding in Rhapis excelsa plant leaves

Plant leaves, whose remarkable ability for morphogenesis results in a wide range of petal and leaf shapes in response to environmental cues, have inspired scientific studies as well as the development of engineering structures and devices. Although some typical shape changes in plants and the driving force for such shape evolution have been extensively studied, there remain many poorly understood mechanisms, characteristics, and principles associated with the vast array of shape formation of plant leaves in nature. Here, we present a comprehensive study that combines experiment, theory, and numerical simulations of one such topic-the mechanics and mechanisms of corrugated leaf folding induced by differential shrinking in Rhapis excelsa. Through systematic measurements of the dehydration process in sectioned leaves, we identify a linear correlation between change in the leaf-folding angle and water loss. Building on experimental findings, we develop a generalized model that provides a scaling relationship for water loss in sectioned leaves. Furthermore, our study reveals that corrugated folding induced by dehydration in R. excelsa leaves is achieved by the deformation of a structural architecture-the "hinge" cells. Utilizing such connections among structure, morphology, environmental stimuli, and mechanics, we fabricate several biomimetic machines, including a humidity sensor and morphing devices capable of folding in response to dehydration. The mechanisms of corrugated folding in R. excelsa identified in this work provide a general understanding of the interactions between plant leaves and water. The actuation mechanisms identified in this study also provide insights into the rational design of soft machines.

Inferring mechanical properties of the SARS-CoV-2 virus particle with nano-indentation tests and numerical simulations

The pandemic caused by the SARS-CoV-2 virus has claimed more than 6.5 million lives worldwide. This global challenge has led to accelerated development of highly effective vaccines tied to their ability to elicit a sustained immune response. While numerous studies have focused primarily on the spike (S) protein, less is known about the interior of the virus. Here we propose a methodology that combines several experimental and simulation techniques to elucidate the internal structure and mechanical properties of the SARS-CoV-2 virus. The mechanical response of the virus was analyzed by nanoindentation tests using a novel flat indenter and evaluated in comparison to a conventional sharp tip indentation. The elastic properties of the viral membrane were estimated by analytical solutions, molecular dynamics (MD) simulations on a membrane patch and by a 3D Finite Element (FE)-beam model of the virion's spike protein and membrane molecular structure. The FE-based inverse engineering approach provided a reasonable reproduction of the mechanical response of the virus from the sharp tip indentation and was successfully verified against the flat tip indentation results. The elastic modulus of the viral membrane was estimated in the range of 7-20 MPa. MD simulations showed that the presence of proteins significantly reduces the fracture strength of the membrane patch. However, FE simulations revealed an overall high fracture strength of the virus, with a mechanical behavior similar to the highly ductile behavior of engineering metallic materials. The failure mechanics of the membrane during sharp tip indentation includes progressive damage combined with localized collapse of the membrane due to severe bending. Furthermore, the results support the hypothesis of a close association of the long membrane proteins (M) with membrane-bound hexagonally packed ribonucleoproteins (RNPs). Beyond improved understanding of coronavirus structure, the present findings offer a knowledge base for the development of novel prevention and treatment methods that are independent of the immune system.

Geometric mapping from rectilinear material orthotropy to isotropy: Insights into plates and shells

Orthotropic shell structures are ubiquitous in biology and engineering, from bacterial cell walls to reinforced domes. We present a rescaling transformation that maps an orthotropic shallow shell to an isotropic one with a different local geometry. The mapping is applicable to any shell section for which the material orthotropy directions match the principal curvature directions, assuming the commonly used Huber form for the orthotropic shear modulus. Using the rescaling transformation, we derive exact expressions for the buckling pressure as well as the linear indentation response of orthotropic cylinders and general ellipsoids of revolution, which we verify against numerical simulations. Our analysis disentangles the separate contributions of geometric and material anisotropy to shell rigidity. In particular, we identify the geometric mean of orthotropic elastic constants as the key quantifier of material stiffness, playing a role akin to the Gaussian curvature which captures the geometric stiffness contribution. Besides providing insights into the mechanical response of orthotropic shells, our work rigorously establishes the validity of isotropic approximations to orthotropic shells and also identifies situations in which these approximations might fail.

Interfacial Nanoblisters Formed in Water Serving as Freestanding Platforms for Measuring Elastic Moduli of Polymeric Nanofilms

Polymeric nanofilms have been widely utilized in diverse cutting-edge technologies, yet accurately determining their elastic moduli remains challenging. Here we demonstrate that interfacial nanoblisters, which are produced by simply immersing substrate-supported nanofilms in water, represent natural platforms for assessing the mechanical properties of polymeric nanofilms using the sophisticated nanoindentation method. Nevertheless, high-resolution, quantitative force spectroscopy studies reveal that the indentation test must be performed on an effective freestanding region around the nanoblister apex and meanwhile under an appropriate loading force, to obtain load-independent, linear elastic deformations. The nanoblister stiffness increases with either decreasing its size or increasing its covering film thickness, and such size effects can be adequately rationalized by an energy-based theoretical model. The proposed model also enables an exceptional determination of the film elastic modulus. Given that interfacial blistering is a frequently occurring phenomenon for polymeric nanofilms, we envision that the presented methodology would stimulate broad applications in relevant fields.

Elastic shell theory for plant cell wall stiffness reveals contributions of cell wall elasticity and turgor pressure in AFM measurement

The stiffness of a plant cell in response to an applied force is determined not only by the elasticity of the cell wall but also by turgor pressure and cell geometry, which affect the tension of the cell wall. Although stiffness has been investigated using atomic force microscopy (AFM) and Young’s modulus of the cell wall has occasionally been estimated using the contact-stress theory (Hertz theory), the existence of tension has made the study of stiffness more complex. Elastic shell theory has been proposed as an alternative method; however, the estimation of elasticity remains ambiguous. Here, we used finite element method simulations to verify the formula of the elastic shell theory for onion (Allium cepa) cells. We applied the formula and simulations to successfully quantify the turgor pressure and elasticity of a cell in the plane direction using the cell curvature and apparent stiffness measured by AFM. We conclude that tension resulting from turgor pressure regulates cell stiffness, which can be modified by a slight adjustment of turgor pressure in the order of 0.1 MPa. This theoretical analysis reveals a path for understanding forces inherent in plant cells.

Dynamic Deformation and Perforation of Ellipsoidal Thin Shell Impacted by Flat-Nose Projectile

Experimental and theoretical studies were carried out on the dynamic deformation and penetration response characteristics of metal ellipsoidal thin curved shells under impact loads. The deformation characteristics of the impacted ellipsoid shell was investigated via the use of a light gas gun to carry out impact loading experiments at different speeds. Ten cases of experiments were conducted with the impact velocities distributed between 25.69 m/s and 118.97 m/s. Stereo digital image correlation (3D-DIC) technology was applied to capture the dynamic deformation and penetration process of the impacted shell. The recovered shells were measured, and the deformation characteristics were analyzed, along with the dynamic evolution, as observed through 3D-DIC analysis. Based on the experimental results, the displacement mode was summarized and the displacement distribution of the locally impacted ellipsoid shell was proposed. The governing equations were derived for the dynamic deformation and penetration of the impacted ellipsoid shell by means of the Lagrange equation. The proposed theoretical model was verified based on the experimental results. Finally, the influence of the curvature distribution on the impact resistance of ellipsoidal shells is discussed. The results indicated that the proposed theoretical model was effective in analyzing the large deformation and the penetration speed. Stretching the axial length of the ellipsoid shell in the impact direction improved its resistance to penetration. Stretching the axial length of the ellipsoid shell perpendicular to the impact direction improved its resistance to deformation, but reduced its resistance to penetration. Maintaining the triaxial ratio and appropriately reducing the size of the ellipsoidal shell improved its resistance to both deformation and penetration. The above research provides a reference for the analysis of the impact resistance of thin-walled curved shell structures in engineering.

Preliminary study of reliability of transcutaneous sensors in measuring intraabdominal pressure

Early recognition of elevated intraabdominal pressure (IAP) in critically ill patients is essential, since it can result in abdominal compartment syndrome, which is a life-threatening condition. The measurement of intravesical pressure is currently considered the gold standard for IAP assessment. Alternative methods have been proposed, where IAP assessment is based on measuring abdominal wall tension, which reflects the pressure in the abdominal cavity. The aim of this study was to evaluate the feasibility of using patch-like transcutaneous sensors to estimate changes in IAP, which could facilitate the monitoring of IAP in clinical practice. This study was performed with 30 patients during early postoperative care. All patients still had an indwelling urinary catheter postoperatively. Four wearable sensors were attached to the outer surface of the abdominal region to detect the changes in abdominal wall tension. Additionally, surface EMG was used to monitor the activity of the abdominal muscles. The thickness of the subcutaneous tissue was measured with ultrasound. Patients performed 4 cycles of the Valsalva manoeuvre, with a resting period in between (the minimal resting period was 30 s, with a prolongation as necessary to ensure that the fluid level in the measuring system had equilibrated). The IAP was estimated with intravesical pressure measurements during all resting periods and all Valsalva manoeuvres, while the sensors continuously measured changes in abdominal wall tension. The association between the subcutaneous thickness and tension changes on the surface and the intraabdominal pressure was statistically significant, but a large part of the variability was explained by individual patient factors. As a consequence, the predictions of IAP using transcutaneous sensors were not biased, but they were quite variable. The specificity of detecting intraabdominal pressure of 20 mmHg and above is 88%, with an NPV of 96%, while its sensitivity and PPV are currently far lower. There are inherent limitations of the chosen preliminary study design that directly caused the low sensitivity of our method as well as the poor agreement with the gold standard method; in spite of that, we have shown that these sensors have the potential to be used to monitor intraabdominal pressure. We are planning a study that would more closely resemble the intended clinical use and expect it to show more consistent results with a far smaller error.

Compression of a pressurized spherical shell by a spherical or flat probe

Measuring the mechanical properties of cells and tissues often involves indentation with a sphere or compression between two plates. Different theoretical approaches have been developed to retrieve material parameters (e.g., elastic modulus) or state variables (e.g., pressure) from such experiments. Here, we extend previous theoretical work on indentation of a spherical pressurized shell by a point force to cover indentation by a spherical probe or a plate. We provide formulae that enable the modulus or pressure to be deduced from experimental results with realistic contact geometries, giving different results that are applicable depending on pressure level. We expect our results to be broadly useful when investigating biomechanics or mechanobiology of cells and tissues.

Cell wall and cytoskeletal contributions in single cell biomechanics of Nicotiana tabacum

Studies on the mechanics of plant cells usually focus on understanding the effects of turgor pressure and properties of the cell wall (CW). While the functional roles of the underlying cytoskeleton have been studied, the extent to which it contributes to the mechanical properties of cells is not elucidated. Here, we study the contributions of the CW, microtubules (MTs) and actin filaments (AFs), in the mechanical properties of Nicotiana tabacum cells. We use a multiscale biomechanical assay comprised of atomic force microscopy and micro-indentation in solutions that (i) remove MTs and AFs and (ii) alter osmotic pressures in the cells. To compare measurements obtained by the two mechanical tests, we develop two generative statistical models to describe the cell's behaviour using one or both datasets. Our results illustrate that MTs and AFs contribute significantly to cell stiffness and dissipated energy, while confirming the dominant role of turgor pressure.

Stiffness Measurement of Drosophila Egg Chambers by Atomic Force Microscopy

Drosophila egg chamber development requires cellular and molecular mechanisms controlling morphogenesis. Previous research has shown that the mechanical properties of the basement membrane contribute to tissue elongation of the egg chamber. Here, we discuss how indentation with the microindenter of an atomic force microscope can be used to determine an effective stiffness value of a Drosophila egg chamber. We provide information on the preparation of egg chambers prior to the measurement, dish coating, the actual atomic force microscope measurement process, and data analysis. Furthermore, we discuss how to interpret acquired data and which mechanical components are expected to influence measured stiffness values.

Precise Thermoplastic Processing of Graphene Oxide Layered Solid by Polymer Intercalation

The processing capability is vital for the wide applications of materials to forge structures as-demand. Graphene-based macroscopic materials have shown excellent mechanical and functional properties. However, different from usual polymers and metals, graphene solids exhibit limited deformability and processibility for precise forming. Here, we present a precise thermoplastic forming of graphene materials by polymer intercalation from graphene oxide (GO) precursor. The intercalated polymer enables the thermoplasticity of GO solids by thermally activated motion of polymer chains. We detect a critical minimum containing of intercalated polymer that can expand the interlayer spacing exceeding 1.4 nm to activate thermoplasticity, which becomes the criteria for thermal plastic forming of GO solids. By thermoplastic forming, the flat GO-composite films are forged to Gaussian curved shapes and imprinted to have surface relief patterns with size precision down to 360 nm. The plastic-formed structures maintain the structural integration with outstanding electrical (3.07 × 10⁵ S m^-1) and thermal conductivity (745.65 W m^-1 K^-1) after removal of polymers. The thermoplastic strategy greatly extends the forming capability of GO materials and other layered materials and promises versatile structural designs for more broad applications.

Indentation responses of pressurized ellipsoidal and cylindrical elastic shells: Insights from shallow-shell theory

Pressurized elastic shells are ubiquitous in nature and technology, from the outer walls of yeast and bacterial cells to artificial pressure vessels. Indentation measurements simultaneously probe the internal pressure and elastic properties of thin shells and serve as a useful tool for strength testing and for inferring internal biological functions of living cells. We study the effects of geometry and pressure-induced stress on the indentation stiffness of ellipsoidal and cylindrical elastic shells using shallow-shell theory. We show that the linear indentation response reduces to a single integral with two dimensionless parameters that encode the asphericity and internal pressure. This integral can be numerically evaluated in all regimes and is used to generate compact analytical expressions for the indentation stiffness in various regimes of technological and biological importance. Our results provide theoretical support for previous scaling and numerical results describing the stiffness of ellipsoids, reveal a new pressure scale that dictates the large-pressure response, and give new insights to the linear indentation response of pressurized cylinders.

Sculpting Liquids with Ultrathin Shells

Thin elastic films can spontaneously attach to liquid interfaces, offering a platform for tailoring their physical, chemical, and optical properties. Current understanding of the elastocapillarity of thin films is based primarily on studies of planar sheets. We show that curved shells can be used to manipulate interfaces in qualitatively different ways. We elucidate a regime where an ultrathin shell with vanishing bending rigidity imposes its own rest shape on a liquid surface, using experiment and theory. Conceptually, the pressure across the interface "inflates" the shell into its original shape. The setup is amenable to optical applications as the shell is transparent, free of wrinkles, and may be manufactured over a range of curvatures.

Mechanical evaluation of 3D printed biomimetic non-Euclidean saddle geometries mimicking the mantis shrimp

Engineering design has drawn inspiration from naturally occurring structures to advance manufacturing processes and products, termed biomimetics. For example, the mantis shrimp, orderStomatopoda, is capable of producing one of the fastest appendage strikes in the world with marginal musculoskeletal displacement. The extreme speed of the mantis shrimp's raptorial appendage is due to the non-Euclidean hyperbolic paraboloid (i.e. saddle) shape within the dorsal region of the merus, which allows substantial energy storage through compression in the sagittal plane. Here, investigation of 3D printed synthetic geometries inspired by the mantis shrimp saddle geometry has revealed insights for elastic energy storage (i.e. spring-like) applications. Saddles composed of either astiffor aflexibleresin were investigated for spring response to explore the geometric effects. By modulating the saddle geometry and testing the spring response, it was found that, for thestiffresin, the spring constant was improved as the curvature of the contact and orthogonal faces were maximized and minimized, respectively. For theflexibleresin, it was found that the spring constant increased by less than 250 N mm^-1as the saddle geometry changed, substantiating that the flexible component of mantis saddles does not contribute to energy storage capabilities. The geometries of two saddles from the mantis shrimp speciesO. scyllaruswere estimated and exhibited similar trends to manufactured saddles, suggesting that modulating saddle geometry can be used for tailored energy storage moduli in spatially constrained engineering applications.

Shells of compacted DNA as nanocontainers transporting proteins in multiplexed delivery

Polyethyleneimine (PEI) polymers are known to compact DNA strands into spheroid, toroid, or rod structures. A formulation with mannose-grafted PEI (PEIm), however, was reported to compact DNA into ~100 nm spheroids that indented like thin-walled pressurized shells. The goal of the study is to understand why mannose bristles divert the traditional pathway of PEI-DNA compaction to produce shell-like structures, and to manipulate the process so that proteins can be packed into the core of the assembling shells for co-delivering DNA and proteins into cells. DLS, AFM, and TEM imaging provide a consistent picture that BSA proteins can be packed into the shells without altering the shell architecture, as long as the proteins were added during the time course of shell assembly. Force spectroscopy studies reveal that DNA shells that buckle also have a rich surface-coating of mannose, indicating that a micelle-like partitioning of hydrophobic and hydrophilic layers governs shell assembly. When HEK293T cells are spiked with BSA-laden DNA shells, co-transfection of DNA and BSA is observed at higher levels than control formulations. Distinct micron-sized features appear having both green fluorescence from BSA-FITC and blue fluorescence from NucBlue DNA stain, suggesting BSA release in nucleus and secretory granules. With DNA nanocontainers, proteins can take advantage of the efficiency of PEI-based DNA transfection for hitchhiking into cells while being shielded from the challenges of the intracellular route. DNA nanocontainers are rapid to assemble, not dependent on the DNA sequence, and can be adapted for different protein types; thereby having potential to serve as a high-throughput platform in scenarios where DNA and protein have to be released at the same site and time within cells (e.g., theranostics, multiplexed co-delivery, gene editing).

Electric-field-induced deformation, yielding, and crumpling of jammed particle shells formed on non-spherical Pickering droplets

Droplets covered with densely packed solid particles, often called Pickering droplets, are used in a variety of fundamental studies and practical applications. For many applications, it is essential to understand the mechanics of such particle-laden droplets subjected to external stresses. Several research groups have studied theoretically and experimentally the deformation, relaxation, rotation, and stability of Pickering droplets. Most of the research concerns spherical Pickering droplets. However, little is known about non-spherical Pickering droplets with arrested particle shells subjected to compressive stress. The experimental results presented here contribute to filling this gap in research. We deform arrested non-spherical Pickering droplets by subjecting them to electric fields, and study the effect of droplet geometry and size, as well as particle size and electric field strength, on the deformation and yielding of arrested non-spherical Pickering droplets. We explain why a more aspherical droplet and/or a droplet covered with a shell made of larger particles required higher electric stress to deform and yield. We also show that an armored droplet can absorb the electric stress differently (i.e., through either in-plane or out-of-plane particle rearrangements) depending on the strength of the applied electric field. Furthermore, we demonstrate that particle shells may fail through various crumpling instabilities, including ridge formation, folding, and wrinkling, as well as inward indentation.

3D mechanical characterization of single cells and small organisms using acoustic manipulation and force microscopy

Quantitative micromechanical characterization of single cells and multicellular tissues or organisms is of fundamental importance to the study of cellular growth, morphogenesis, and cell-cell interactions. However, due to limited manipulation capabilities at the microscale, systems used for mechanical characterizations struggle to provide complete three-dimensional coverage of individual specimens. Here, we combine an acoustically driven manipulation device with a micro-force sensor to freely rotate biological samples and quantify mechanical properties at multiple regions of interest within a specimen. The versatility of this tool is demonstrated through the analysis of single Lilium longiflorum pollen grains, in combination with numerical simulations, and individual Caenorhabditis elegans nematodes. It reveals local variations in apparent stiffness for single specimens, providing previously inaccessible information and datasets on mechanical properties that serve as the basis for biophysical modelling and allow deeper insights into the biomechanics of these living systems.

Indentation and bifurcation of inflated membranes

We study pneumatically inflated membranes indented by rigid indenters of different sizes and shapes. When the volume of the inflated membrane is beyond a critical value, a symmetric deformation mode becomes unstable and the system follows a path of asymmetric deformation. This bifurcation is analysed analytically for a two-dimensional membrane with either a line or plane indenter for which the stable deformation path is determined by computing the total system potential energy of different configurations. An axisymmetric membrane with indenters of different shapes and sizes is further investigated numerically. In this case, a cylindrical indenter can always trigger bifurcation while a small spherical indenter tends to be encapsulated rather than induce an asymmetric deformation mode. This result suggests that the observed bifurcation behaviour can be actively tuned and even triggered selectively by tuning indenter shape and size. We also demonstrate the effects of friction and biased bifurcation analytically through the example of a two-dimensional membrane with a line indenter.

First evidence of convergent lifestyle signal in reptile skull roof microanatomy

BACKGROUND

The study of convergently acquired adaptations allows fundamental insight into life's evolutionary history. Within lepidosaur reptiles-i.e. lizards, tuatara, and snakes-a fully fossorial ('burrowing') lifestyle has independently evolved in most major clades. However, despite their consistent use of the skull as a digging tool, cranial modifications common to all these lineages are yet to be found. In particular, bone microanatomy, although highly diagnostic for lifestyle, remains unexplored in the lepidosaur cranium. This constitutes a key gap in our understanding of their complexly interwoven ecology, morphology, and evolution. In order to bridge this gap, we reconstructed the acquisition of a fossorial lifestyle in 2813 lepidosaurs and assessed the skull roof compactness from microCT cross-sections in a representative subset (n = 99). We tested this and five macroscopic morphological traits for their convergent evolution.

RESULTS

We found that fossoriality evolved independently in 54 lepidosaur lineages. Furthermore, a highly compact skull roof, small skull diameter, elongate cranium, and low length ratio of frontal and parietal were repeatedly acquired in concert with a fossorial lifestyle.

CONCLUSIONS

We report a novel case of convergence that concerns lepidosaur diversity as a whole. Our findings further indicate an early evolution of fossorial modifications in the amphisbaenian 'worm-lizards' and support a fossorial origin for snakes. Nonetheless, our results suggest distinct evolutionary pathways between fossorial lizards and snakes through different contingencies. We thus provide novel insights into the evolutionary mechanisms and constraints underlying amniote diversity and a powerful tool for the reconstruction of extinct reptile ecology.

Gradient in cytoplasmic pressure in germline cells controls overlying epithelial cell morphogenesis

It is unknown how growth in one tissue impacts morphogenesis in a neighboring tissue. To address this, we used the Drosophila ovarian follicle, in which a cluster of 15 nurse cells and a posteriorly located oocyte are surrounded by a layer of epithelial cells. It is known that as the nurse cells grow, the overlying epithelial cells flatten in a wave that begins in the anterior. Here, we demonstrate that an anterior to posterior gradient of decreasing cytoplasmic pressure is present across the nurse cells and that this gradient acts through TGFβ to control both the triggering and the progression of the wave of epithelial cell flattening. Our data indicate that intrinsic nurse cell growth is important to control proper nurse cell pressure. Finally, we reveal that nurse cell pressure and subsequent TGFβ activity in the stretched cells combine to increase follicle elongation in the anterior, which is crucial for allowing nurse cell growth and pressure control. More generally, our results reveal that during development, inner cytoplasmic pressure in individual cells has an important role in shaping their neighbors.

Force microscopy of the Caenorhabditis elegans embryonic eggshell

Assays focusing on emerging biological phenomena in an animal's life can be performed during embryogenesis. While the embryo of Caenorhabditis elegans has been extensively studied, its biomechanical properties are largely unknown. Here, we demonstrate that cellular force microscopy (CFM), a recently developed technique that combines micro-indentation with high resolution force sensing approaching that of atomic force microscopy, can be successfully applied to C. elegans embryos. We performed, for the first time, a quantitative study of the mechanical properties of the eggshell of living C. elegans embryos and demonstrate the capability of the system to detect alterations of its mechanical parameters and shell defects upon chemical treatments. In addition to investigating natural eggshells, we applied different eggshell treatments, i.e., exposure to sodium hypochlorite and chitinase solutions, respectively, that selectively modified the multilayer eggshell structure, in order to evaluate the impact of the different layers on the mechanical integrity of the embryo. Finite element method simulations based on a simple embryo model were used to extract characteristic eggshell parameters from the experimental micro-indentation force-displacement curves. We found a strong correlation between the severity of the chemical treatment and the rigidity of the shell. Furthermore, our results showed, in contrast to previous assumptions, that short bleach treatments not only selectively remove the outermost vitelline layer of the eggshell, but also significantly degenerate the underlying chitin layer, which is primarily responsible for the mechanical stability of the egg.

Cellular Heterogeneity in Pressure and Growth Emerges from Tissue Topology and Geometry

Cell-to-cell heterogeneity prevails in many systems, as exemplified by cell growth, although the origin and function of such heterogeneity are often unclear. In plants, growth is physically controlled by cell wall mechanics and cell hydrostatic pressure, alias turgor pressure. Whereas cell wall heterogeneity has received extensive attention, the spatial variation of turgor pressure is often overlooked. Here, combining atomic force microscopy and a physical model of pressurized cells, we show that turgor pressure is heterogeneous in the Arabidopsis shoot apical meristem, a population of stem cells that generates all plant aerial organs. In contrast with cell wall mechanical properties that appear to vary stochastically between neighboring cells, turgor pressure anticorrelates with cell size and cell neighbor number (local topology), in agreement with the prediction by our model of tissue expansion, which couples cell wall mechanics and tissue hydraulics. Additionally, our model predicts two types of correlations between pressure and cellular growth rate, where high pressure may lead to faster- or slower-than-average growth, depending on cell wall extensibility, yield threshold, osmotic pressure, and hydraulic conductivity. The meristem exhibits one of these two regimes, depending on conditions, suggesting that, in this tissue, water conductivity may contribute to growth control. Our results unravel cell pressure as a source of patterned heterogeneity and illustrate links between local topology, cell mechanical state, and cell growth, with potential roles in tissue homeostasis.

Somatosensory neurons integrate the geometry of skin deformation and mechanotransduction channels to shape touch sensing

Touch sensation hinges on force transfer across the skin and activation of mechanosensitive ion channels along the somatosensory neurons that invade the skin. This skin-nerve sensory system demands a quantitative model that spans the application of mechanical loads to channel activation. Unlike prior models of the dynamic responses of touch receptor neurons in Caenorhabditis elegans (Eastwood et al., 2015), which substituted a single effective channel for the ensemble along the TRNs, this study integrates body mechanics and the spatial recruitment of the various channels. We demonstrate that this model captures mechanical properties of the worm’s body and accurately reproduces neural responses to simple stimuli. It also captures responses to complex stimuli featuring non-trivial spatial patterns, like extended or multiple contacts that could not be addressed otherwise. We illustrate the importance of these effects with new experiments revealing that skin-neuron composites respond to pre-indentation with increased currents rather than adapting to persistent stimulation.

Shallow shell theory of the buckling energy barrier: From the Pogorelov state to softening and imperfection sensitivity close to the buckling pressure

We study the axisymmetric response of a complete spherical shell under homogeneous compressive pressure p to an additional point force. For a pressure p below the classical critical buckling pressure p_{c}, indentation by a point force does not lead to spontaneous buckling but an energy barrier has to be overcome. The states at the maximum of the energy barrier represent a subcritical branch of unstable stationary points, which are the transition states to a snap-through buckled state. Starting from nonlinear shallow shell theory, we obtain a closed analytical expression for the energy barrier height, which facilitates its effective numerical evaluation as a function of pressure by continuation techniques. We find a clear crossover between two regimes: For p/p_{c}≪1 the postbuckling barrier state is a mirror-inverted Pogorelov dimple, and for (1-p/p_{c})≪1 the barrier state is a shallow dimple with indentations smaller than shell thickness and exhibits extended oscillations, which are well described by linear response. We find systematic expansions of the nonlinear shallow shell equations about the Pogorelov mirror-inverted dimple for p/p_{c}≪1 and the linear response state for (1-p/p_{c})≪1, which enable us to derive asymptotic analytical results for the energy barrier landscape in both regimes. Upon approaching the buckling bifurcation at p_{c} from below, we find a softening of an ideal spherical shell. The stiffness for the linear response to point forces vanishes ∝(1-p/p_{c})^{1/2}; the buckling energy barrier vanishes ∝(1-p/p_{c})^{3/2}; and the shell indentation in the barrier state vanishes ∝(1-p/p_{c})^{1/2}. This makes shells sensitive to imperfections which can strongly reduce p_{c} in an avoided buckling bifurcation. We find the same softening scaling in the vicinity of the reduced critical buckling pressure also in the presence of imperfections. We can also show that the effect of axisymmetric imperfections on the buckling instability is identical to the effect of a point force that is preindenting the shell. In the Pogorelov limit, the energy barrier maximum diverges ∝(p/p_{c})^{-3} and the corresponding indentation diverges ∝(p/p_{c})^{-2}. Numerical prefactors for proportionalities both in the softening and the Pogorelov regime are calculated analytically. This also enables us to obtain results for the critical unbuckling pressure and the Maxwell pressure.

Shell buckling: from morphogenesis of soft matter to prospective applications

Being one of the commonest deformation modes for soft matter, shell buckling is the primary reason for the growth and nastic movement of many plants, as well as the formation of complex natural morphology. On-demand regulation of buckling-induced deformation associated with wrinkling, ruffling, folding, creasing and delaminating has profound implications for diverse scopes, which can be seen in its broad applications in microfabrication, 4D printing, actuator and drug delivery. This paper reviews the recent remarkable developments in the shell buckling of soft matter to explain the most representative natural morphogenesis from the perspectives of theoretical analysis in continuum mechanics, finite element analysis, and experimental validations. Imitation of buckling-induced shape transformation and its applications are also discussed for the innovations of sophisticated materials and devices in future.

Buckling of thermally fluctuating spherical shells: Parameter renormalization and thermally activated barrier crossing

We study the influence of thermal fluctuations on the buckling behavior of thin elastic capsules with spherical rest shape. Above a critical uniform pressure, an elastic capsule becomes mechanically unstable and spontaneously buckles into a shape with an axisymmetric dimple. Thermal fluctuations affect the buckling instability by two mechanisms. On the one hand, thermal fluctuations can renormalize the capsule's elastic properties and its pressure because of anharmonic couplings between normal displacement modes of different wavelengths. This effectively lowers its critical buckling pressure [Košmrlj and Nelson, Phys. Rev. X 7, 011002 (2017)2160-330810.1103/PhysRevX.7.011002]. On the other hand, buckled shapes are energetically favorable already at pressures below the classical buckling pressure. At these pressures, however, buckling requires to overcome an energy barrier, which only vanishes at the critical buckling pressure. In the presence of thermal fluctuations, the capsule can spontaneously overcome an energy barrier of the order of the thermal energy by thermal activation already at pressures below the critical buckling pressure. We revisit parameter renormalization by thermal fluctuations and formulate a buckling criterion based on scale-dependent renormalized parameters to obtain a temperature-dependent critical buckling pressure. Then we quantify the pressure-dependent energy barrier for buckling below the critical buckling pressure using numerical energy minimization and analytical arguments. This allows us to obtain the temperature-dependent critical pressure for buckling by thermal activation over this energy barrier. Remarkably, both parameter renormalization and thermal activation lead to the same parameter dependence of the critical buckling pressure on temperature, capsule radius and thickness, and Young's modulus. Finally, we study the combined effect of parameter renormalization and thermal activation by using renormalized parameters for the energy barrier in thermal activation to obtain our final result for the temperature-dependent critical pressure, which is significantly below the results if only parameter renormalization or only thermal activation is considered.

Finite indentation of highly curved elastic shells

Experimentally measuring the elastic properties of thin biological surfaces is non-trivial, particularly when they are curved. One technique that may be used is the indentation of a thin sheet of material by a rigid indenter, while measuring the applied force and displacement. This gives immediate information on the fracture strength of the material (from the force required to puncture), but it is also theoretically possible to determine the elastic properties by comparing the resulting force–displacement curves with a mathematical model. Existing mathematical studies generally assume that the elastic surface is initially flat, which is often not the case for biological membranes. We previously outlined a theory for the indentation of curved isotropic, incompressible, hyperelastic membranes (with no bending stiffness) which breaks down for highly curved surfaces, as the entire membrane becomes wrinkled. Here, we introduce the effect of bending stiffness, ensuring that energy is required to change the shell shape without stretching, and find that commonly neglected terms in the shell equilibrium equation must be included. The theory presented here allows for the estimation of shape- and size-independent elastic properties of highly curved surfaces via indentation experiments, and is particularly relevant for biological surfaces.

Synthesizing Sodium Tungstate and Sodium Molybdate Microcapsules via Bacterial Mineral Excretion

We present a method, the bacterial mineral excretion (BME), for synthesizing two kinds of microcapsules, sodium tungstate and sodium molybdate, and the two metal oxides' corresponding nanoparticles-the former being as small as 22 nm and the latter 15 nm. We fed two strains of bacteria, Shewanella algae and Pandoraea sp., with various concentrations of tungstate or molybdate ions. The concentrations of tungstate and molybdate were adjusted to make microcapsules of different length-to-diameter ratios. We found that the higher the concentration the smaller the nanoparticles were. The nanoparticles came in with three length-to-diameter ratios: 10:1, 3:1 and 1:1, which were achieved by feeding the bacteria respectively with a low concentration, a medium concentration, and a high concentration. The images of the hollow microcapsules were taken via the scanning electron microsphere (SEM). Their crystal structures were verified by X-ray diffraction (XRD)-the crystal structure of molybdate microcapsules is Na2MoO4 and that of tungstate microcapsules is Na2WO4 with Na2W2O7. These syntheses all were accomplished under a near ambient condition.

Mechanics and Buckling of Biopolymeric Shells and Cell Nuclei

We study a Brownian dynamics simulation model of a biopolymeric shell deformed by axial forces exerted at opposing poles. The model exhibits two distinct, linear force-extension regimes, with the response to small tensions governed by linear elasticity and the response to large tensions governed by an effective spring constant that scales with radius as R^-0.25. When extended beyond the initial linear elastic regime, the shell undergoes a hysteretic, temperature-dependent buckling transition. We experimentally observe this buckling transition by stretching and imaging the lamina of isolated cell nuclei. Furthermore, the interior contents of the shell can alter mechanical response and buckling, which we show by simulating a model for the nucleus that quantitatively agrees with our micromanipulation experiments stretching individual nuclei.

The avian egg exhibits general allometric invariances in mechanical design

The avian egg exhibits extraordinary diversity in size, shape and color, and has a key role in avian adaptive radiations. Despite extensive work, our understanding of the underlying principles that guide the "design" of the egg as a load-bearing structure remains incomplete, especially over broad taxonomic scales. Here we define a dimensionless number C, a function of egg weight, stiffness and dimensions, to quantify how stiff an egg is with respect to its weight after removing geometry-induced rigidity. We analyze eggs of 463 bird species in 36 orders across five orders of magnitude in body mass, and find that C number is nearly invariant for most species, including tiny hummingbirds and giant elephant birds. This invariance or "design guideline" dictates that evolutionary changes in shell thickness and Young's modulus, both contributing to shell stiffness, are constrained by changes in egg weight. Our analysis illuminates unique reproductive strategies of brood parasites, kiwis, and megapodes, and quantifies the loss of safety margin for contact incubation due to artificial selection and environmental toxins. Our approach provides a mechanistic framework for a better understanding of the mechanical design of the avian egg, and may provide clues to the evolutionary origin of contact incubation of amniote eggs.

Geometric localization of thermal fluctuations in red blood cells

Cell shapes are related to their biological function. More generally, membrane morphology plays a role in the segregation and activity of transmembrane proteins. Here we show geometric implications regarding how cellular mechanics plays a role in localizing thermal fluctuations on the membrane. We show theoretically that certain geometric features of curved shells control the spatial distribution of membrane undulations. We experimentally verify this theory using discocyte red blood cells and find that geometry alone is sufficient to account for the observed spatial distribution of fluctuations. Our results, based on statistical physics and membrane elasticity, have general implications for the use of membrane shape to control thermal undulations in a variety of nanostructured materials ranging from cell membranes to graphene sheets.

The thermal fluctuations of membranes and nanoscale shells affect their mechanical characteristics. Whereas these fluctuations are well understood for flat membranes, curved shells show anomalous behavior due to the geometric coupling between in-plane elasticity and out-of-plane bending. Using conventional shallow shell theory in combination with equilibrium statistical physics we theoretically demonstrate that thermalized shells containing regions of negative Gaussian curvature naturally develop anomalously large fluctuations. Moreover, the existence of special curves, “singular lines,” leads to a breakdown of linear membrane theory. As a result, these geometric curves effectively partition the cell into regions whose fluctuations are only weakly coupled. We validate these predictions using high-resolution microscopy of human red blood cells (RBCs) as a case study. Our observations show geometry-dependent localization of thermal fluctuations consistent with our theoretical modeling, demonstrating the efficacy in combining shell theory with equilibrium statistical physics for describing the thermalized morphology of cellular membranes.

Programming temporal shapeshifting

Shapeshifting enables a wide range of engineering and biomedical applications, but until now transformations have required external triggers. This prerequisite limits viability in closed or inert systems and puts forward the challenge of developing materials with intrinsically encoded shape evolution. Herein we demonstrate programmable shape-memory materials that perform a sequence of encoded actuations under constant environment conditions without using an external trigger. We employ dual network hydrogels: in the first network, covalent crosslinks are introduced for elastic energy storage, and in the second one, temporary hydrogen-bonds regulate the energy release rate. Through strain-induced and time-dependent reorganization of the reversible hydrogen-bonds, this dual network allows for encoding both the rate and pathway of shape transformations on timescales from seconds to hours. This generic mechanism for programming trigger-free shapeshifting opens new ways to design autonomous actuators, drug-release systems and active implants.

Actuation of shape-shifting materials has typically required an external trigger. Here, the authors design a shape-memory hydrogel, regulated by a dual network of covalent and temporary hydrogen bonds, whose actuations are encoded by an intrinsic temporal mechanism.

Magnetic domain wall tweezers: a new tool for mechanobiology studies on individual target cells

In vitro tests are of fundamental importance for investigating cell mechanisms in response to mechanical stimuli or the impact of the genotype on cell mechanical properties. In particular, the application of controlled forces to activate specific bio-pathways and investigate their effects, mimicking the role of the cellular environment, is becoming a prominent approach in the emerging field of mechanobiology. Here, we present an on-chip device based on magnetic domain wall manipulators, which allows the application of finely controlled and localized forces on target living cells. In particular, we demonstrate the application of a magnetic force in the order of hundreds of pN on the membrane of HeLa cells cultured on-chip, via manipulation of 1 μm superparamagnetic beads. Such a mechanical stimulus produces a sizable local indentation of the cellular membrane of about 2 μm. Upon evaluation of the beads' position within the magnetic field originated by the domain wall, the force applied during the experiments is accurately quantified via micromagnetic simulations. The obtained value is in good agreement with that calculated by the application of an elastic model to the cellular membrane.

Endosperm turgor pressure decreases during early Arabidopsis seed development

In Arabidopsis, rapid expansion of the coenocytic endosperm after fertilisation has been proposed to drive early seed growth, which is in turn constrained by the seed coat. This hypothesis implies physical heterogeneity between the endosperm and seed coat compartments during early seed development, which to date has not been demonstrated. Here, we combine tissue indentation with modelling to show that the physical properties of the developing seed are consistent with the hypothesis that elevated endosperm-derived turgor pressure drives early seed expansion. We provide evidence that whole-seed turgor is generated by the endosperm at early developmental stages. Furthermore, we show that endosperm cellularisation and seed growth arrest are associated with a drop in endosperm turgor pressure. Finally, we demonstrate that this decrease is perturbed when the function of POLYCOMB REPRESSIVE COMPLEX 2 is lost, suggesting that turgor pressure changes could be a target of genomic imprinting. Our results indicate a developmental role for changes in endosperm turgor pressure in the Arabidopsis seed.

A Mechanical Model to Interpret Cell-Scale Indentation Experiments on Plant Tissues in Terms of Cell Wall Elasticity and Turgor Pressure

Morphogenesis in plants is directly linked to the mechanical elements of growing tissues, namely cell wall and inner cell pressure. Studies of these structural elements are now often performed using indentation methods such as atomic force microscopy. In these methods, a probe applies a force to the tissue surface at a subcellular scale and its displacement is monitored, yielding force-displacement curves that reflect tissue mechanics. However, the interpretation of these curves is challenging as they may depend not only on the cell probed, but also on neighboring cells, or even on the whole tissue. Here, we build a realistic three-dimensional model of the indentation of a flower bud using SOFA (Simulation Open Framework Architecture), in order to provide a framework for the analysis of force-displacement curves obtained experimentally. We find that the shape of indentation curves mostly depends on the ratio between cell pressure and wall modulus. Hysteresis in force-displacement curves can be accounted for by a viscoelastic behavior of the cell wall. We consider differences in elastic modulus between cell layers and we show that, according to the location of indentation and to the size of the probe, force-displacement curves are sensitive with different weights to the mechanical components of the two most external cell layers. Our results confirm most of the interpretations of previous experiments and provide a guide to future experimental work.

Mechanics and morphogenesis of fission yeast cells

The integration of biochemical and biomechanical elements is at the heart of morphogenesis. While animal cells are relatively soft objects which shape and mechanics is mostly regulated by cytoskeletal networks, walled cells including those of plants, fungi and bacteria are encased in a rigid cell wall which resist high internal turgor pressure. How these particular mechanical properties may influence basic cellular processes, such as growth, shape and division remains poorly understood. Recent work using the model fungal cell fission yeast, Schizosaccharomyces pombe, highlights important contribution of cell mechanics to various morphogenesis processes. We envision this genetically tractable system to serve as a novel standard for the mechanobiology of walled cell.

Geometrically controlled snapping transitions in shells with curved creases

Curvature and mechanics are intimately connected for thin materials, and this coupling between geometry and physical properties is readily seen in folded structures from intestinal villi and pollen grains to wrinkled membranes and programmable metamaterials. While the well-known rules and mechanisms behind folding a flat surface have been used to create deployable structures and shape transformable materials, folding of curved shells is still not fundamentally understood. Shells naturally deform by simultaneously bending and stretching, and while this coupling gives them great stability for engineering applications, it makes folding a surface of arbitrary curvature a nontrivial task. Here we discuss the geometry of folding a creased shell, and demonstrate theoretically the conditions under which it may fold smoothly. When these conditions are violated we show, using experiments and simulations, that shells undergo rapid snapping motion to fold from one stable configuration to another. Although material asymmetry is a proven mechanism for creating this bifurcation of stability, for the case of a creased shell, the inherent geometry itself serves as a barrier to folding. We discuss here how two fundamental geometric concepts, creases and curvature, combine to allow rapid transitions from one stable state to another. Independent of material system and length scale, the design rule that we introduce here explains how to generate snapping transitions in arbitrary surfaces, thus facilitating the creation of programmable multistable materials with fast actuation capabilities.

Does joint architecture influence the nature of intra-articular fractures?

INTRODUCTION

The architecture of joints has potentially the greatest influence on the nature of intra-articular fractures. We analysed a large number of intra-articular fractures with two aims: (1) to determine if the pattern of injuries observed supports our conjecture that the local skeletal architecture is an important factor and (2) to investigate whether associated dislocations further affect the fracture pattern.

METHODS

A retrospective study of intra-articular fractures over a 3.5-year period; 1003 joints met inclusion criteria and were analysed. Three independent investigators determined if fractures affected the convex dome, the concave socket, or if both joint surfaces were involved. Further review determined if a joint dislocation occurred with the initial injury. Statistical analysis was performed using a one-way frequency table, and the χ(2) test was used to compare the frequencies of concave and convex surface fractures. The odds ratios (ORs) were calculated to establish the association between the frequencies of concave and convex surface fractures, as well as between dislocation and either fracture surface involvement.

RESULTS

Of the 1003 fractures analysed, 956 (95.3%) involved only the concavity of the joint; in 21 fractures (2.1%) both joint surfaces were involved; and in 26 fractures (2.6%) only the convexity was involved (χ(2)=1654.9, df=2, p<0.0001). As expected, the concavity was 20.8 times more likely to fail than the convexity (11.2-36.6, 95% CI). However, the risk of fracturing the convex surface was 18.6 times higher (9.8-35.2, 95% CI) in association with a simultaneous joint dislocation, compared to those cases without a joint dislocation.

CONCLUSIONS

These results very strongly support the study hypotheses: the skeletal architecture of joints clearly plays a highly significant role in determining the nature of intra-articular fractures. Intra-articular fractures involving the convexity are much more likely to be associated with a concurrent joint dislocation.

Quantifying hydrostatic pressure in plant cells by using indentation with an atomic force microscope

Plant cell growth depends on a delicate balance between an inner drive-the hydrostatic pressure known as turgor-and an outer restraint-the polymeric wall that surrounds a cell. The classical technique to measure turgor in a single cell, the pressure probe, is intrusive and cannot be applied to small cells. In order to overcome these limitations, we developed a method that combines quantification of topography, nanoindentation force measurements, and an interpretation using a published mechanical model for the pointlike loading of thin elastic shells. We used atomic force microscopy to estimate the elastic properties of the cell wall and turgor pressure from a single force-depth curve. We applied this method to onion epidermal peels and quantified the response to changes in osmolality of the bathing solution. Overall our approach is accessible and enables a straightforward estimation of the hydrostatic pressure inside a walled cell.

Mechanically, the Shoot Apical Meristem of Arabidopsis Behaves like a Shell Inflated by a Pressure of About 1 MPa

In plants, the shoot apical meristem contains the stem cells and is responsible for the generation of all aerial organs. Mechanistically, organogenesis is associated with an auxin-dependent local softening of the epidermis. This has been proposed to be sufficient to trigger outgrowth, because the epidermis is thought to be under tension and stiffer than internal tissues in all the aerial part of the plant. However, this has not been directly demonstrated in the shoot apical meristem. Here we tested this hypothesis in Arabidopsis using indentation methods and modeling. We considered two possible scenarios: either the epidermis does not have unique properties and the meristem behaves as a homogeneous linearly-elastic tissue, or the epidermis is under tension and the meristem exhibits the response of a shell under pressure. Large indentation depths measurements with a large tip (~size of the meristem) were consistent with a shell-like behavior. This also allowed us to deduce a value of turgor pressure, estimated at 0.82±0.16 MPa. Indentation with atomic force microscopy provided local measurements of pressure in the epidermis, further confirming the range of values obtained from large deformations. Altogether, our data demonstrate that the Arabidopsis shoot apical meristem behaves like a shell under a MPa range pressure and support a key role for the epidermis in shaping the shoot apex.

How a curved elastic strip opens

An elastic strip is transversely clamped in a curved frame. The induced curvature decreases as the strip opens and connects to its flat natural shape. Various ribbon profiles are measured and the scaling law for the opening length validates a description where the in-plane stretching gradually relaxes the bending stress. An analytical model of the strip profile is proposed and a quantitative agreement is found with both experiments and simulations of the plates equations. This result provides a unique illustration of smooth nondevelopable solutions in thin sheets.

Flowers under pressure: ins and outs of turgor regulation in development

BACKGROUND

Turgor pressure is an essential feature of plants; however, whereas its physiological importance is unequivocally recognized, its relevance to development is often reduced to a role in cell elongation.

SCOPE

This review surveys the roles of turgor in development, the molecular mechanisms of turgor regulation and the methods used to measure turgor and related quantities, while also covering the basic concepts associated with water potential and water flow in plants. Three key processes in flower development are then considered more specifically: flower opening, anther dehiscence and pollen tube growth.

CONCLUSIONS

Many molecular determinants of turgor and its regulation have been characterized, while a number of methods are now available to quantify water potential, turgor and hydraulic conductivity. Data on flower opening, anther dehiscence and lateral root emergence suggest that turgor needs to be finely tuned during development, both spatially and temporally. It is anticipated that a combination of biological experiments and physical measurements will reinforce the existing data and reveal unexpected roles of turgor in development.

DNA nanoparticles with core-shell morphology

Mannobiose-modified polyethylenimines (PEI) are used in gene therapy to generate nanoparticles of DNA that can be targeted to the antigen-presenting cells of the immune system. We report that the sugar modification alters the DNA organization within the nanoparticles from homogenous to shell-like packing. The depth-dependent packing of DNA within the nanoparticles was probed using AFM nano-indentation. Unmodified PEI-DNA nanoparticles display linear elastic properties and depth-independent mechanics, characteristic of homogenous materials. Mannobiose-modified nanoparticles, however, showed distinct force regimes that were dependent on indentation depth, with 'buckling'-like response that is reproducible and not due to particle failure. By comparison with theoretical studies of spherical shell mechanics, the structure of mannobiosylated particles was deduced to be a thin shell with wall thickness in the order of few nanometers, and a fluid-filled core. The shell-core structure is also consistent with observations of nanoparticle denting in altered solution conditions, with measurements of nanoparticle water content from AFM images, and with images of DNA distribution in Transmission Electron Microscopy.

Microcapsule mechanics: from stability to function

Microcapsules are reviewed with special emphasis on the relevance of controlled mechanical properties for functional aspects. At first, assembly strategies are presented that allow control over the decisive geometrical parameters, diameter and wall thickness, which both influence the capsule's mechanical performance. As one of the most powerful approaches the layer-by-layer technique is identified. Subsequently, ensemble and, in particular, single-capsule deformation techniques are discussed. The latter generally provide more in-depth information and cover the complete range of applicable forces from smaller than pN to N. In a theory chapter, we illustrate the physics of capsule deformation. The main focus is on thin shell theory, which provides a useful approximation for many deformation scenarios. Finally, we give an overview of applications and future perspectives where the specific design of mechanical properties turns microcapsules into (multi-)functional devices, enriching especially life sciences and material sciences.

Anisotropic blistering instability of highly ellipsoidal shells

The formation of localized periodic structures in the deformation of elastic shells is well documented and is a familiar first stage in the crushing of a spherical shell such as a ping-pong ball. While spherical shells manifest such periodic structures as polygons, we present a new instability that is observed in the indentation of a highly ellipsoidal shell by a horizontal plate. Above a critical indentation depth, the plate loses contact with the shell in a series of well-defined "blisters" along the long axis of the ellipsoid. We characterize the onset of this instability and explain it using scaling arguments, numerical simulations, and experiments. We also characterize the properties of the blistering pattern by showing how the number of blisters and their size depend on both the geometrical properties of the shell and the indentation but not on the shell's elastic modulus. This blistering instability may be used to determine the thickness of highly ellipsoidal shells simply by squashing them between two plates.