Development of a Procedure for the Determination of the Buckling Resistance of Steel Spherical Shells according to EC 1993-1-6

This paper presents the process of developing a new procedure for estimating the buckling capacity of spherical shells. This procedure is based entirely on the assumptions included in the standard mentioned, EN-1993-1-6 and also becomes a complement of EDR5th by unifying provisions included in them. This procedure is characterized by clarity and its algorithm is characterized by a low degree of complexity. While developing the procedure, no attempt was made to change the main postulates accompanying the dimensions of the spherical shells. The result is a simple engineering approach to the difficult problem of determining the buckling capacity of a spherical shell. In spite of the simple calculation algorithm for estimating the buckling capacity of spherical shells, the results obtained reflect extremely accurately the behavior of real spherical shells, regardless of their geometry and the material used to manufacture them.     

Interactions between the termini of lumen enzymes and shell proteins mediate enzyme encapsulation into bacterial microcompartments

Bacterial microcompartments (MCPs) are a widespread family of proteinaceous organelles that consist of metabolic enzymes encapsulated within a protein shell. For MCPs to function specific enzymes must be encapsulated. We recently reported that a short N-terminal targeting sequence of propionaldehyde dehydrogenase (PduP) is necessary and sufficient for the packaging of enzymes into a MCP that functions in 1,2-propanediol (1,2-PD) utilization (Pdu) by Salmonella enterica. Here we show that encapsulation is mediated by binding of the PduP targeting sequence to a short C-terminal helix of the PduA shell protein. In vitro studies indicated binding between PduP and PduA (and PduJ) but not other MCP shell proteins. Alanine scanning mutagenesis determined that the key residues involved in binding are E7, I10, and L14 of PduP and H81, V84, and L88 of PduA. In vivo targeting studies indicated that the binding between the N terminus of PduP and the C terminus of PduA is critical for encapsulation of PduP within the Pdu MCP. Structural models suggest that the N terminus of PduP and C terminus of PduA both form helical structures that bind one another via the key residues identified by mutagenesis. Cumulatively, these results show that the N-terminal targeting sequence of PduP promotes its encapsulation by binding to MCP shell proteins. This is a unique report determining the mechanism by which a MCP targeting sequence functions. We propose that specific interactions between the termini of shell proteins and lumen enzymes have general importance for guiding the assembly and the higher level organization of bacterial MCPs.     

Preparation of High Thermo-Stability and Compactness Microencapsulated Phase Change Materials with Polyurea/Polyurethane/Polyamine Three-Composition Shells through Interfacial Polymerization

In the preparation of microencapsulated phase change materials (MicroPCMs) with a three-composition shell through interfacial polymerization, the particle size, phase change behaviors, core contents, encapsulation efficiency morphology, thermal stability and chemical structure were investigated. The compactness of the MicroPCMs was analyzed through high-temperature drying and weighing. The effect of the core/shell ratio and stirring rate of the system was studied. The results indicated that the microcapsules thus-obtained possessed a spherical shape and high thermal stability and the surfaces were intact and compact. Furthermore, in the emulsification stage, the stirring speed had a significant influence on the microcapsules’ particle size, and smaller particles could be obtained under the higher stirring speed, and the distributions were more uniform in these cases. When the core/shell ratio was lower than 4, both the core content and the encapsulation efficiency was high. Additionally, when the core/shell ratio was higher than 4, the encapsulation efficiency was decreased significantly. The three-composition shell greatly increased the compactness of microcapsules, and when the core/shell ratio was adjusted to 3, the mass loss of the MicroPCMs was lower than 6% after drying at 120 °C for 1 h. After the microencapsulation, double exothermic peaks appeared on the crystallization curve of the MicroPCMs, the crystallization mechanism was changed from the heterogeneous nucleation to the homogeneous nucleation and the super cooling degree was enhanced.     

Active multistage coarsening of actin networks driven by myosin motors

In cells, many vital processes involve myosin-driven motility that actively remodels the actin cytoskeleton and changes cell shape. Here we study how the collective action of myosin motors organizes actin filaments into contractile structures in a simplified model system devoid of biochemical regulation. We show that this self-organization occurs through an active multistage coarsening process. First, motors form dense foci by moving along the actin network structure followed by coalescence. Then the foci accumulate actin filaments in a shell around them. These actomyosin condensates eventually cluster due to motor-driven coalescence. We propose that the physical origin of this multistage aggregation is the highly asymmetric load response of actin filaments: they can support large tensions but buckle easily under piconewton compressive loads. Because the motor-generated forces well exceed this threshold, buckling is induced on the connected actin network that resists motor-driven filament sliding. We show how this buckling can give rise to the accumulation of actin shells around myosin foci and subsequent coalescence of foci into superaggregates. This new physical mechanism provides an explanation for the formation and contractile dynamics of disordered condensed actomyosin states observed in vivo.     

Failures of Cu-Cu Joints under Temperature Cycling Tests

In this study, the failure mechanisms of Cu-Cu joints under thermal cycling were investigated. Two structures of dielectrics (PBO/underfill/PBO and SiO₂) were employed to seal the joints. Stress gradients induced in the joints with the different dielectrics were simulated using a finite element method (FEM) and correlated with experimental observations. We found that interfacial voids were forced to move in the direction from high stress regions to low stress ones. The locations of migrated voids varied with the dielectric structures. Under thermal cycling, such voids were likely to move forward to the regions with a small stress change. They relocated and merged with their neighboring voids to lower the interfacial energy.     

Self-assembly of soft-matter quasicrystals and their approximants

The surprising recent discoveries of quasicrystals and their approximants in soft-matter systems poses the intriguing possibility that these structures can be realized in a broad range of nanoscale and microscale assemblies. It has been theorized that soft-matter quasicrystals and approximants are largely entropically stabilized, but the thermodynamic mechanism underlying their formation remains elusive. Here, we use computer simulation and free-energy calculations to demonstrate a simple design heuristic for assembling quasicrystals and approximants in soft-matter systems. Our study builds on previous simulation studies of the self-assembly of dodecagonal quasicrystals and approximants in minimal systems of spherical particles with complex, highly specific interaction potentials. We demonstrate an alternative entropy-based approach for assembling dodecagonal quasicrystals and approximants based solely on particle functionalization and shape, thereby recasting the interaction-potential-based assembly strategy in terms of simpler-to-achieve bonded and excluded-volume interactions. Here, spherical building blocks are functionalized with mobile surface entities to encourage the formation of structures with low surface contact area, including non-close-packed and polytetrahedral structures. The building blocks also possess shape polydispersity, where a subset of the building blocks deviate from the ideal spherical shape, discouraging the formation of close-packed crystals. We show that three different model systems with both of these features-mobile surface entities and shape polydispersity-consistently assemble quasicrystals and/or approximants. We argue that this design strategy can be widely exploited to assemble quasicrystals and approximants on the nanoscale and microscale. In addition, our results further elucidate the formation of soft-matter quasicrystals in experiment.     

Fluctuating shells under pressure

Thermal fluctuations strongly modify the large length-scale elastic behavior of cross-linked membranes, giving rise to scale-dependent elastic moduli. Whereas thermal effects in flat membranes are well understood, many natural and artificial microstructures are modeled as thin elastic shells. Shells are distinguished from flat membranes by their nonzero curvature, which provides a size-dependent coupling between the in-plane stretching modes and the out-of-plane undulations. In addition, a shell can support a pressure difference between its interior and its exterior. Little is known about the effect of thermal fluctuations on the elastic properties of shells. Here, we study the statistical mechanics of shape fluctuations in a pressurized spherical shell, using perturbation theory and Monte Carlo computer simulations, explicitly including the effects of curvature and an inward pressure. We predict novel properties of fluctuating thin shells under point indentations and pressure-induced deformations. The contribution due to thermal fluctuations increases with increasing ratio of shell radius to thickness and dominates the response when the product of this ratio and the thermal energy becomes large compared with the bending rigidity of the shell. Thermal effects are enhanced when a large uniform inward pressure acts on the shell and diverge as this pressure approaches the classical buckling transition of the shell. Our results are relevant for the elasticity and osmotic collapse of microcapsules.The elastic theory of thin plates and shells (1), a subject over a century old, has recently found new applications in understanding the mechanical properties of a wide range of natural and artificial structures at microscopic length scales. The mechanical properties of viral capsids (2–4), red blood cells (5), and hollow polymer and polyelectrolyte capsules (6–10) have been measured and interpreted in terms of elastic constants of the materials making up these thin-walled structures. Theoretically, models that quantify the deformation energy of a 2D membrane have been used to investigate the shapes of viral capsids (11–13) and their expected response to point forces and pressures (14–17), as well as shape transitions of pollen grains (18).Like its counterparts in other areas of science, such as fluid dynamics and the theory of electrical conduction in metals, thin shell theory aims to describe the physics of slowly varying disturbances in terms of a few macroscopic parameters, such as the shear viscosity of incompressible fluids and the electrical conductivity of metals. Despite such venerable underpinnings as the Navier–Stokes equations and Ohm’s law, these hydrodynamic theories can break down, sometimes in spectacular ways. For example, it is known from mode coupling theory (19) and from renormalization group calculations (20) that thermal fluctuations cause the shear viscosity of incompressible fluids to diverge logarithmically with system size in a 2D incompressible fluid. In the theory of electrical conduction, quenched disorder due to impurities coupled with interactions between electrons lead to a dramatic breakdown of Ohm’s law in thin films and one-dimensional wires at low temperatures, with a conductance that depends on the sample dimensions (21).Even more dramatic breakdowns of linear response theory can arise in thin plates and shells. Unlike the macroscopic shell structures of interest to civil engineers, thermal fluctuations can strongly influence structures with size of order microns, because the elastic deformation energies of extremely thin membranes (with nanoscale thicknesses) can be of the order of the thermal energy (where is the Boltzmann constant and T the temperature) for typical deformations. The statistical mechanics of flat solid plates and membranes (i.e., membranes with no curvature in the unstrained state) have been studied previously (see refs. 22 and 23 and references therein). Thermal fluctuations lead to scale-dependent elastic moduli for flat membranes, causing the in-plane elastic moduli to vanish at large length scales while the bending rigidity diverges (24, 25). These anomalies arise from the the nonlinear couplings between out-of-plane deformations (transverse to the plane of the undeformed membrane) and the resultant in-plane strains, which are second order in the out-of-plane displacements.Much less is known about spherical shells subject to thermal fluctuations (Fig. 1A). In fact, the coupling between in-plane and out-of-plane modes is significantly different. Geometry dictates that a closed spherical shell cannot be deformed without stretching; as a result, out-of-plane deformations provide a first-order contribution to the in-plane strain tensor (1). This introduces new nonlinear couplings between in-plane and out-of-plane deformations, which are forbidden by symmetry in flat membranes. We can also consider the buckling of spherical shells under uniform external pressure, which has no simple analog for plates (Fig. 1B). An early exploration with computer simulations combined an analysis of the elastic energy due to the linear strain contributions of a spherical membrane with the nonlinear corrections from flat membranes to suggest new scaling behavior for thermally fluctuating spherical membranes (26). However, an important nonlinear coupling triggered by the curved background metric was not considered, nor was the effect of an external pressure investigated. Here, we study the mechanics of fluctuating spherical shells, using perturbation theory and numerical simulations, taking into account the nonlinear couplings introduced by curvature as well as the effects of a uniform external pressure.Open in a separate windowFig. 1.Simulated thermally fluctuating shells. (A) Triangulated shell with 5,530 points separated by average nearest-neighbor distance with Young’s modulus and bending rigidity at temperature , where ɛ is the energy scale of the Lennard-Jones potential used to generate the disordered mesh. (B) Same as in A with external pressure , where is the classical buckling pressure. The thermally excited shell has already buckled under pressure to a shape with a much smaller enclosed volume than in A.     

Pearling in cells: A clue to understanding cell shape

Gradual disruption of the actin cytoskeleton induces a series of structural shape changes in cells leading to a transformation of cylindrical cell extensions into a periodic chain of "pearls." Quantitative measurements of the pearling instability give a square-root behavior for the wavelength as a function of drug concentration. We present a theory that explains these observations in terms of the interplay between rigidity of the submembranous actin shell and tension that is induced by boundary conditions set by adhesion points. The theory allows estimation of the rigidity and thickness of this supporting shell. The same theoretical considerations explain the shape of nonadherent edges in the general case of untreated cells.     

Elasticity and wrinkled morphology of Bacillus subtilis pellicles

Wrinkled morphology is a distinctive phenotype observed in mature biofilms produced by a great number of bacteria. Here we study the formation of macroscopic structures (wrinkles and folds) observed during the maturation of Bacillus subtilis pellicles in relation to their mechanical response. We show how the mechanical buckling instability can explain their formation. By performing simple tests, we highlight the role of confining geometry and growth in determining the symmetry of wrinkles. We also experimentally demonstrate that the pellicles are soft elastic materials for small deformations induced by a tensile device. The wrinkled structures are then described by using the equations of elastic plates, which include the growth process as a simple parameter representing biomass production. This growth controls buckling instability, which triggers the formation of wrinkles. We also describe how the structure of ripples is modified when capillary effects are dominant. Finally, the experiments performed on a mutant strain indicate that the presence of an extracellular matrix is required to maintain a connective and elastic pellicle.     

Buckling Behavior of Sandwich Cylindrical Shells Covered by Functionally Graded Coatings with Clamped Boundary Conditions under Hydrostatic Pressure

The buckling behavior of sandwich shells with functionally graded (FG) coatings operating under different external pressures was generally investigated under simply supported boundary conditions. Since it is very difficult to determine the approximation functions satisfying clamped boundary conditions and to solve the basic equations analytically within the framework of first order shear deformation theory (FOST), the number of publications on this subject is very limited. An analytical solution to the buckling problem of FG-coated cylindrical shells under clamped boundary conditions subjected to uniform hydrostatic pressure within the FOST framework is presented for the first time. By mathematical modeling of the FG coatings, the constitutive relations and basic equations of sandwich cylindrical shells within the FOST framework are obtained. Analytical solutions of the basic equations in the framework of the Donnell shell theory, obtained using the Galerkin method, is carried out using new approximation functions that satisfy clamped boundary conditions. Finally, the influences of FG models and volume fractions on the hydrostatic buckling pressure within the FOST and classical shell theory (CT) frameworks are investigated in detail.     

Molecular Dynamics Investigation of the Influence of Voids on the Impact Mechanical Behavior of NiTi Shape-Memory Alloy

To date, research on the physical and mechanical behavior of nickel-titanium shape-memory alloy (NiTi SMA) has focused on the macroscopic physical properties, equation of state, strength constitution, phase transition induced by temperature and stress under static load, etc. The behavior of a NiTi SMA under high-strain-rate impact and the influence of voids have not been reported. In this present work, the behavior evolution of (100) single-crystal NiTi SMA and the influencing characteristics of voids under a shock wave of 1.2 km/s are studied by large-scale molecular dynamics calculation. The results show that only a small amount of B2 austenite is transformed into B19’ martensite when the NiTi sample does not pass through the void during impact compression, whereas when the shock wave passes through the hole, a large amount of martensite phase transformation and plastic deformation is induced around the hole; the existence of phase transformation and phase-transformation-induced plastic deformation greatly consumes the energy of the shock wave, thus making the width of the wave front in the subsequent propagation process wider and the peak of the foremost wave peak reduced. In addition, the existence of holes disrupts the orderly propagation of shock waves, changes the shock wave front from a plane to a concave surface, and reduces the propagation speed of shock waves. The calculation results show that the presence of pores in a porous NiTi SMA leads to significant martensitic phase transformation and plastic deformation induced by phase transformation, which has a significant buffering effect on shock waves. The results of this study provide great guidance for expanding the application of NiTi SMA in the field of shock.     

Ordered patterns of liquid crystal toroidal defects by microchannel confinement

In this article we present experimental results demonstrating an approach to controlling the size and spatial patterning of defect domains in a smectic liquid crystal (LC) by geometric confinement in surface-modified microchannels. By confining the LC 4'-octyl-4-cyanobiphenyl in mum-sized rectangular channels with controlled surface polarity, we were able to generate defect domains that are not only nearly uniform in size but also arranged in quasi-2D ordered patterns. Atomic force microscopy measurements revealed that the defects have a toroidal topology, which we argue is dictated by the boundary conditions imposed by the walls of the microchannel. We show that the defects can be considered to be colloidal objects, which interact with each other to form ordered patterns. This method opens the possibility for exploiting the unique optical and rheological properties associated with LC defects to making new materials. For example, the control of the shape, size, and spatial arrangement of the defects at the mesoscale suggests applications in patterning, templating, and when extended to lyotropic LCs, a process leading to uniform-sized spherical particles for chemical encapsulation and delivery.     

Effective Interactions between Multilayered Ionic Microgels

Using a one-component reduction formalism, we calculate the effective interactions and the counterion density profiles for microgels that feature a multilayered shell structure. We follow a strategy that involves second order perturbation theory and obtain analytical expressions for the effective interactions by modeling the layers of the particles as linear superpostion of homogeneously charged spheres. The general method is applied to the important case of core–shell microgels and compared with the well-known results for a microgel that can be approximated by a macroscopic, and homogeneously charged, spherical macroion.     

The Effect of Void Arrangement on the Pattern Transformation of Porous Soft Solids under Biaxial Loading

Structural topology and loading condition have important influences on the mechanical behaviors of porous soft solids. The porous solids are usually set to be under uniaxial tension or compression. Only a few studies have considered the biaxial loads, especially the combined loads of tension and compression. In this study, porous soft solids with oblique and square lattices of circular voids under biaxial loadings were studied through integrated experiments and numerical simulations. For the soft solids with oblique lattices of circular voids, we found a new pattern transformation under biaxial compression, which has alternating elliptic voids with an inclined angle. This kind of pattern transformation is rarely reported under uniaxial compression. Introducing tensile deformation in one direction can hamper this kind of pattern transformation under biaxial loading. For the soft solids with square lattices of voids, the number of voids cannot change their deformation behaviors qualitatively, but quantitatively. In general, our present results demonstrate that void morphology and biaxial loading can be harnessed to tune the pattern transformations of porous soft solids under large deformation. This discovery offers a new avenue for designing the void morphology of soft solids for controlling their deformation patterns under a specific biaxial stress-state.     

High pressure ices

H(2)O will be more resistant to metallization than previously thought. From computational evolutionary structure searches, we find a sequence of new stable and meta-stable structures for the ground state of ice in the 1-5 TPa (10 to 50 Mbar) regime, in the static approximation. The previously proposed Pbcm structure is superseded by a Pmc2(1) phase at p = 930 GPa, followed by a predicted transition to a P2(1) crystal structure at p = 1.3 TPa. This phase, featuring higher coordination at O and H, is stable over a wide pressure range, reaching 4.8 TPa. We analyze carefully the geometrical changes in the calculated structures, especially the buckling at the H in O-H-O motifs. All structures are insulating--chemistry burns a deep and (with pressure increase) lasting hole in the density of states near the highest occupied electronic levels of what might be component metallic lattices. Metallization of ice in our calculations occurs only near 4.8 TPa, where the metallic C2/m phase becomes most stable. In this regime, zero-point energies much larger than typical enthalpy differences suggest possible melting of the H sublattice, or even the entire crystal.     

The molecular mechanism of lipid monolayer collapse

Lipid monolayers at an air–water interface can be compressed laterally and reach high surface density. Beyond a certain threshold, they become unstable and collapse. Lipid monolayer collapse plays an important role in the regulation of surface tension at the air–liquid interface in the lungs. Although the structures of lipid aggregates formed upon collapse can be characterized experimentally, the mechanism leading to these structures is not fully understood. We investigate the molecular mechanism of monolayer collapse using molecular dynamics simulations. Upon lateral compression, the collapse begins with buckling of the monolayer, followed by folding of the buckle into a bilayer in the water phase. Folding leads to an increase in the monolayer surface tension, which reaches the equilibrium spreading value. Immediately after their formation, the bilayer folds have a flat semielliptical shape, in agreement with theoretical predictions. The folds undergo further transformation and form either flat circular bilayers or vesicles. The transformation pathway depends on macroscopic parameters of the system: the bending modulus, the line tension at the monolayer–bilayer connection, and the line tension at the bilayer perimeter. These parameters are determined by the system composition and temperature. Coexistence of the monolayer with lipid aggregates is favorable at lower tensions of the monolayer–bilayer connection. Transformation into a vesicle reduces the energy of the fold perimeter and is facilitated for softer bilayers, e.g., those with a higher content of unsaturated lipids, or at higher temperatures.     

Stress-driven buckling patterns in spheroidal core/shell structures

Many natural fruits and vegetables adopt an approximately spheroidal shape and are characterized by their distinct undulating topologies. We demonstrate that various global pattern features can be reproduced by anisotropic stress-driven buckles on spheroidal core/shell systems, which implies that the relevant mechanical forces might provide a template underpinning the topological conformation in some fruits and plants. Three dimensionless parameters, the ratio of effective size/thickness, the ratio of equatorial/polar radii, and the ratio of core/shell moduli, primarily govern the initiation and formation of the patterns. A distinct morphological feature occurs only when these parameters fall within certain ranges: In a prolate spheroid, reticular buckles take over longitudinal ridged patterns when one or more parameters become large. Our results demonstrate that some universal features of fruit/vegetable patterns (e.g., those observed in Korean melons, silk gourds, ribbed pumpkins, striped cavern tomatoes, and cantaloupes, etc.) may be related to the spontaneous buckling from mechanical perspectives, although the more complex biological or biochemical processes are involved at deep levels.     

Generation of new transforming viruses from SIRC cells "phenotypically transformed" in the medium with low concentrations of serum or calcium ions

The work reported here demonstrates the possibility of rapid generation of highly transforming viruses from rabbit epithelial corneal cells (SIRC) originated from simian sarcoma associated virus (SSAV). The results of the experiments indicate a possible association of the phenomenon of "phenotypic transformation" with the expression of cellular genes with a potential transforming activity. SIRC/SSAV phenotypic transformation was induced by cultivation of these cells in the medium with a low concentration of serum or calcium ions. During subsequent infection of mink lung fibroblasts the authors succeeded in obtaining two new transforming SSAV isolates which induced transformation foci of various morphological types in cellular lines permissive for SSAV replication.     

Material Design for Optimal Postbuckling Behaviour of Composite Shells

Lightweight thin-walled structures are crucial for many engineering applications. Advanced manufacturing methods are enabling the realization of composite materials with spatially varying material properties. Variable angle tow fibre composites are a representative example, but also nanocomposites are opening new interesting possibilities. Taking advantage of these tunable materials requires the development of computational design methods. The failure of such structures is often dominated by buckling and can be very sensitive to material configuration and geometrical imperfections. This work is a review of the recent computational developments concerning the optimisation of the response of composite thin-walled structures prone to buckling, showing how baseline products with unstable behaviour can be transformed in stable ones operating safely in the post-buckling range. Four main aspects are discussed: mechanical and discrete models for composite shells, material parametrization and objective function definition, solution methods for tracing the load-displacement path and assessing the imperfection sensitivity, structural optimisation algorithms. A numerical example of optimal material design for a curved panel is also illustrated.     

On the Solution of Thermal Buckling Problem of Moderately Thick Laminated Conical Shells Containing Carbon Nanotube Originating Layers

This study presents the solution for the thermal buckling problem of moderately thick laminated conical shells consisting of carbon nanotube (CNT) originating layers. It is assumed that the laminated truncated-conical shell is subjected to uniform temperature rise. The Donnell-type shell theory is used to derive the governing equations, and the Galerkin method is used to find the expression for the buckling temperature in the framework of shear deformation theories (STs). Different transverse shear stress functions, such as the parabolic transverse shear stress (Par-TSS), cosine-hyperbolic shear stress (Cos-Hyp-TSS), and uniform shear stress (U-TSS) functions are used in the analysis part. After validation of the formulation with respect to the existing literature, several parametric studies are carried out to investigate the influences of CNT patterns, number and arrangement of the layers on the uniform buckling temperature (UBT) using various transverse shear stress functions, and classical shell theory (CT).