Soft Elastic Shells Research Articles

Grapho-analytical studies of deformation in deformed thin-walled contours

Increasing the levels of operational reliability of technical means of modern production involves, in particular, the optimization of the deformation parameters of individual components of these tools. The main deformation-operational feature of such structures as elastic shells of the pneumatic periphery of mobile vehicles, and individual links of long-link cargo chains is a stochastic change of their shape in contact with the deformed environment. The basis for the optimization of the operational reliability of deformed thin-walled circuits of such structures under power load is to determine the ratios of their geometric parameters, in which the process of deformation under load does not transform their initial shape from “folded” (out-of-bounds) state to “foldless” state toroidal surfaces, which should be described using the Cassini family of ovals. Based on the established regularities of changing the configuration of the meridian of soft elastic shell and flat closed structures, which are deformed by external loads, three main conditions of using model typical contours of Cassini ovals as graph-analytical models of elastic shells of pneumatic mobile periphery chains. These conditions of graph-analytical modelling include: closedness and continuity of the curvature of the toroidal surface; generalization of the initial shape of the surfaces of toroidal contours; reduction of variable geometric shapes of contours to a single generalized equation. The results of the given grapho-analytical researches allow to define design structural and geometrical parameters of tires of engines of mobile means and separate links of cargo chains with the increased operational indicators of reliability of their work.

Elastohydrodynamic Scaling Law for Heart Rates.

Animal hearts are soft shells that actively pump blood to oxygenate tissues. Here, we propose an allometric scaling law for the heart rate based on the idea of elastohydrodynamic resonance of a fluid-loaded soft active elastic shell that buckles and contracts axially when twisted periodically. We show that this picture is consistent with numerical simulations of soft cylindrical shells that twist-buckle while pumping a viscous fluid, yielding optimum ejection fractions of 35%-40% when driven resonantly. Our scaling law is consistent with experimental measurements of heart rates over 2 orders of magnitude, and provides a mechanistic basis for how metabolism scales with organism size. In addition to providing a physical rationale for the heart rate and metabolism of an organism, our results suggest a simple design principle for soft fluidic pumps.

Driven self-assembly of hard nanoplates on soft elastic shells**Project supported by the National Natural Science Foundation of China (Grant No. 21174131).

The driven self-assembly behaviors of hard nanoplates on soft elastic shells are investigated by using molecular dynamics (MD) simulation method, and the driven self-assembly structures of adsorbed hard nanoplates depend on the shape of hard nanoplates and the bending energy of soft elastic shells. Three main structures for adsorbed hard nanoplates, including the ordered aggregation structures of hard nanoplates for elastic shells with a moderate bending energy, the collapsed structures for elastic shells with a low bending energy, and the disordered aggregation structures for hard shells, are observed. The self-assembly process of adsorbed hard nanoplates is driven by the surface tension of the elastic shell, and the shape of driven self-assembly structures is determined on the basis of the minimization of the second moment of mass distribution. Meanwhile, the deformations of elastic shells can be controlled by the number of adsorbed rods as well as the length of adsorbed rods. This investigation can help us understand the complexity of the driven self-assembly of hard nanoplates on elastic shells.

Self-assembly of binary nanoparticles on soft elastic shells

The self-assembly behaviors and phase transitions of binary nanoparticles (NPs) adsorbed on a soft elastic shell are investigated through molecular dynamics simulation. The conformations of adsorbed binary NPs depend on the bending energy K(b) of elastic shell and the binding energy D0 between the NPs and the elastic shell. The ordered structures of binary NPs are observed at the moderate adhesive strength and bending energy, in which the small NPs are located near the vertices of regular pentagons as well as the large NPs are distributed along the sides of the regular pentagons. The shape of soft elastic shell can be adjusted by adding the adsorbed binary NPs, and this investigation can provide an effective way to regulate and reshape surfaces or membranes with the sizes in the micrometer range or smaller.

Ordered regular pentagons for semiflexible polymers on soft elastic shells

Statistical properties and phase transitions of semiflexible polymers on a soft elastic shell are investigated by using a molecular dynamics (MD) simulation method. The phase diagram of adsorbed semiflexible polymers depends on the bending energy of the elastic shell and the binding energy between polymers and the elastic shell. The ordered regular pentagons of polymers are observed at a moderate adhesive strength and bending energy. At the same time, the shape of the soft elastic shell can be controlled easily by adjusting the chain length of adsorbed polymers, which is helpful for the regulation and reshaping of membranes in the micrometre range or smaller sizes.

Self-assembly of nanorods on soft elastic shells

The self-assembly behavior of nanorods (NRs) on soft elastic shells is investigated using the molecular dynamics (MD) simulation method. The self-assembly structures of the adsorbed nanorods depend on the length of the nanorods as well as the bending energy of the soft elastic shells. For short nanorods, the aggregates consist of regular pentagons around the gibbosity at low bending energies, and the ordered structures are gradually broken when the bending energy increases. In the meantime, the adsorption ability of the nanorods on the elastic shells decreases when the binding energy increases. For long nanorods, the binding energy can induce the nanorods to aggregate in clusters on shells with low or moderate bending energy, and each cluster is formed by several parallel long nanorods. However, the self-assembly structures of long nanorods disappear for shells with high bending energy because the adsorption becomes isotropic for nanorods on a rigid shell. Meanwhile, the adsorption of nanorods on the shell can also affect the shape of the soft elastic shell, especially for long nanorods. This investigation can help us understand the complexity of the self-assembly of nanorods on an elastic shell.

Theoretical basis for estimating the elastic characteristics of individual living human eyes

AbstractPurpose To develop a method for estimating the effective elastic parameters of an individual eye from the data obtainable in various clinical tests with a static load applied.Methods Our mathematical model that represents the fibrous coat as a system consisting of a soft elastic shell (cornea) and an elastic element characterized by a single elastic constant (sclera and tissues surrounding it) is used for calculating the mechanical behavior of the eyeball during different loading procedures. The calculations were performed for two types of external mechanical loading corresponding to applanation and impression tonometry, as well as for inflating the eye by liquid. The presence in the model of only two important mechanical constants makes it possible to identify them by comparing the data of different tests and then to find the effective elastic characteristics important in diagnostics.Results A technique of determining the elastic constants of the model from the standard diagnostic tests is developed. This technique is applied to estimating the average elastic characteristics of the human eyeball in vivo basing on the data available from the literature.Conclusion Our results form a basis for obtaining in standard clinical tests representative individual mechanical characteristics of the living eye. This makes it possible to calculate effective (integral) elastic parameters needed in processing a specific test from the data obtained from other tests, for example, to estimate the volume rigidity from elastometry data. We can now correctly interpret the term “rigidity”: in different tests it is commonly used for characteristics that may differ substantially.

Particle self-assembly on soft elastic shells

We use numerical simulations to show how noninteracting hard particles binding to a deformable elastic shell may self-assemble into a variety of linear patterns. This is a result of the nontrivial elastic response to deformations of shells. The morphology of the patterns can be controlled by the mechanical properties of the surface, and can be fine-tuned by varying the binding energy of the particles. We also repeat our calculations for a fully flexible chain and find that the chain conformations follow patterns similar to those formed by the nanoparticles under analogous conditions. We propose a simple way of understanding and sorting the different structures and relate it to the underlying shape transition of the shell. Finally, we discuss the implications of our results.

Biomechanical analysis of the pressure‐volume relationship in a statically loaded human eye

Abstract Purpose To develop an approach for estimating the mechanical characteristics of the individual eye in the ophthalmologic procedures based on static load application (tonometry, et al.). Methods The fibrous coat is mathematically modeled as a soft elastic shell (cornea) connected with an elastic system that mainly consists of the sclera and is characterized by a single elastic constant describing its response to the intraocular pressure. A function representing the intraocular volume as a function of two variables, the intraocular pressure and the load applied, called the volume function is introduced. This function is then specified on the basis of a simple model characterized by two elastic constants in the case of an applanating load. Results A general method of estimating the integral elastic behavior of the individual eye is developed and specific relationships between elastic constants important in different loading processes are obtained. Conclusion The method developed makes it possible to reliably estimate the integral elastic behavior of the fibrous coat and, as a result, to obtain more correct data on the intraocular pressure and other mechanical characteristics. Although in different loading processes (for example, in tonometry and inflating the eye by a liquid volume) different integral elastic contacts are involved, the model proposed provides a means for obtaining efficient approximate relationships between these constants.

Soft lubrication.

We consider some basic principles of fluid-induced lubrication at soft interfaces. In particular, we quantify how a soft substrate changes the geometry of and the forces between surfaces sliding past each other. By considering the model problem of a symmetric nonconforming contact moving tangentially to a thin elastic layer, we determine the normal force in the small and large deflection limit, and show that there is an optimal combination of material and geometric properties which maximizes the normal force. Our results can be generalized to a variety of other geometries which show the same qualitative behavior. Thus, they are relevant in the elastohydrodynamic lubrication of soft elastic and poroelastic gels and shells, and in the context of biolubrication in cartilaginous joints.

Effect of a mudcake on the propagation of stoneley waves in a borehole

The problem of detecting a permeable stratum blocked by a mudcake with the help of acoustic measurements inside a borehole is considered. Different physical models of the mudcake are compared: in the form of a highly viscous liquid layer, in the form of a soft elastic shell, and in the form of an elastic shell fixed in an arbitrary way to the borehole walls. Numerical calculations are presented for the wave field in a borehole.

Soft elastic shells undergoing large deformations

Soft shells made of elastomers and undergoing large deformations under load are studied. The inverse design problem, non-linear under large deformations, is solved. The results obtained are illustrated on a two-parameter shell of revolution fabricated from a two-constant material. The problems of coupling the biaxial and uniaxial zones of the shell and of designing the composite shell are clarified. Amongst the papers dealing with the theory of soft shells and, generally, under small deformations, /1–7/ merit attention.

A comparison of acoustical scattering from fluid-loaded elastic shells and sound soft objects

Comparisons are presented for acoustical scattering from fluid-loaded prolate spheroidal sound soft scatterers and elastic shells of the same shape, ranging in thickness from 0.1% to 2.5% of the semi-major axis. The Ka region being studied varies from 3 to 12, where K is the wavenumber of the incident wave and a is one-half the length of the major axis. Exact theoretical calculations are performed using a modified T-matrix approach which for the first time allows one to perform calculations on very thin nonspherical elastic shells. The calculations show that, with the exception of the very thin shell, one does not observe a sound soft background. Furthermore, resonances for these objects are very broad and tend to dominate the form function plots. Of particular interest is the fact that by the time the thickness reaches 2.5%, the background begins to appear rigid for suitably high Ka with a shift in resonance nulls, which is related to the fact that rigid scattering is out of phase by 180° with sound soft scattering

A comparison of acoustical scattering from fluid loaded elastic shells and sound soft objects

Comparisons are presented for acoustical scattering from fluid loaded prolate spheroidal sound soft scatterers and elastic shells of the same shape ranging in thickness from 0.1% to 2.5% of the semi‐major axis. The Ka region being studied varies from 3–12 where K is the wavenumber of the incident wave and a is one‐half the length of the major axis. Exact theoretical calculations are performed using a modified T‐matrix approach which allows one for the first time, to perform calculations on very thin nonspherical elastical shells. The calculations show that with the exception of the very thin shell, one does not observe a sound soft background. Furthermore, resonances for these objects are very broad and tend to dominate the form function plots. Of particular interest is the fact that by the time one reaches a thickness of 2.5% the background begins to appear rigid with a shift in resonance nulls which is related to the fact that rigid scattering is out of phase with sound soft scattering by 180°.