Membrane Theory Research Articles

The bubble effect on the thermal expansion coefficient of few-layer MoS2

The thermal expansion coefficient of van der Waals layered structures plays an important role in governing the thermal stability of high-performance electronic devices. Meanwhile, bubbles are frequently observed in the van der Waals layered structures due to the weak inter-layer interaction and the extremely small bending stiffness of the layered structure, but the effect of bubbles on the thermal expansion coefficient for layered structures remains unclear. We derive an analytic formula for the bubble effect on the length variation of the MoS2 layer. In the analytic derivation, the MoS2 layer is described by three mechanics models, including the elastic membrane theory, the nonlinear plate theory, and the linear plate theory. The gas inside the bubble is described by two types of state equations, including the ideal gas law and the generalized van der Waals equation. It is found that the nonlinear plate theory with the generalized van der Waals equation gives the most accurate description for the bubble effect, since MoS2 has a moderate bending stiffness. The analytic formula shows that the bubble can cause strong thermal contraction for few-layer MoS2 with increasing temperature. The analytic predictions are verified by comprehensive molecular dynamic simulations for few-layer MoS2 with different layer numbers and different gas molecule numbers. These results shall be valuable for understanding the thermal stability of functional devices based on the van der Waals layered structure.

The Mechanics Difference Between the Outer Torus and Inner Torus

AbstractThe formulation used by the most of studies on elastic torus are either Reissner’s mixed formulation or Novozhilov’s complex-form one; however, for vibration and some displacement boundary-related problem of torus, those formulations face a great challenge. It is highly demanded to have a displacement-type formulation for torus. In this article, we will carry on the first author’s previous work (Sun, 2010, “Closed-Form Solution of Axisymmetric Slender Elastic Toroidal Shells,” J. Eng. Mech., 136, pp. 1281–1288.), and with the help of our own maple codes, we are able to simulate some typical problems of torus. The numerical results are verified by both finite element analysis and H. Reissner’s formulation. Our investigations show that both deformation and stress response of an elastic torus are sensitive to the radius ratio. The analysis of a torus must be done by using the bending theory of a shell instead of membrane theory of shells, and also reveal that the inner torus is stronger than outer torus due to their Gaussian curvature. One of the most interesting discovery is that the crowns of a torus, the turning point of the Gaussian curvature at ϕ = 0, π, are the line where the mechanics response of inner and outer torus is almost separated.

Fluctuations of active membranes with nonlinear curvature elasticity

Biological membranes and vesicles play a vital role in critical physiological processes like endocytosis, cell division, and cell motility. Over decades, statistical and continuum mechanics studies have provided phenomenal insights into the mechanics of these membranes and their biophysical implications. However, most studies, until recently, have focused entirely on passive (or “dead”) membranes that exhibit only equilibrium thermal fluctuations. In this work, we acknowledge the growing consensus that the active nature of membranes is vital to their biophysical functioning. Active membranes contain proteins that are fueled by energy from external sources such as adinosine triphosphate hydrolysis or light. These proteins exert forces on the membrane during their activity causing the membrane to exhibit fluctuations that are non-thermal in origin, thus driving them away from equilibrium. In short, active membranes are “alive” with their own energy source capable of circumventing equilibrium considerations. In this paper, we present a theory for active membranes based on principles of continuum mechanics and a variational formulation that (we hope) provides a unifying framework to understand seemingly disparate but insightful prior works in this field. Using our developed continuum model, we study the statistical mechanics of active closed membranes or vesicles. A specific highlight of our work is that we incorporate nonlinear curvature elasticity in our continuum theory and obtain closed-form results for the fluctuation spectra for active vesicles. Our numerical results reveal a rather unanticipated interplay of active forces, surface tension as well as nonlinear elasticity for small vesicles. To gain insights into the biophysical implications of activity in vesicles, we revisit the problem of determining the vesicle size distribution by assuming that the active vesicles are close to thermal equilibrium. Our numerical calculations show that active forces may significantly impact vesicle size distribution. A tantalizing implication of this finding is that by tuning active forces, active vesicles may attain vesicle size distributions that are improbable for passive vesicles governed only by thermal fluctuations.

Effects of reinforcing steel tanks with intermediate ring stiffeners on wind buckling during construction

Many tank structures may not be stable during the construction phase, and this may lead to their becoming vulnerable to buckling under environmental loading conditions such as wind. Installing intermediate ring stiffeners of the proper size at the mid-height of the cylindrical shell may be the most effective way to stabilize these structures, especially under the effects of wind action. In the study, analytical and numerical studies were conducted to identify the required strength and stiffness for the intermediate ring stiffener. First, a new cylindrical shell-to- intermediate ring stiffness ratio was derived by considering curved beam and shell membrane theories. For strength criteria, the tributary height and the effect of shell- ring interaction on the internal forces and moments were examined by making use of Linear Analysis (LA) and Geometrically Nonlinear Analysis (GNA). The stress resultants developed in the intermediate ring stiffener were identified so that they could be used as strength criteria. For stiffness criteria, by considering the changes in the buckling resistance based on the developed stiffness ratio, an expression to compute the minumum intermediate ring stiffness was determined. In addition, Geometrically Nonlinear Analysis including Imperfections (GNIA) was also performed to examine the effect of the geometric imperfections on buckling strength of the steel tank with an intermediate ring stiffener, taking different imperfection amplitudes into account. The developed design equations in simple algebraic form can be utilized for the structural stability of cylindrical steel tanks during erection.

Nanobubble-induced significant reduction of the interfacial thermal conductance for few-layer graphene.

The heat transport properties of van der Waals layered structures are crucial for ensuring the reliability and longevity of high-performance optoelectronic equipment. Owing to the two-dimensional nature of atomic layers, the presence of bubbles is commonly observed within these structures. Nevertheless, the effect of bubbles on the interfacial thermal conductance remains unclear. Based on the elastic membrane theory and the improved van der Waals gas state equation, we develop an analytical formula to describe the influence of bubble shape on the interfacial thermal conductance. It shows that the presence of bubbles has a considerable impact on reducing the interfacial thermal conductance across graphene/graphene interfaces. More specifically, the presence of nanobubbles can result in a reduction of up to 53% in the interfacial thermal conductance. The validity of the analytical predictions is confirmed through molecular dynamic simulations. These results offer valuable insights into the thermal management of van der Waals layered structures in the application of next-generation electronic nanodevices.

The membrane potential arising from the adsorption of ions at the biological interface.

Membrane theory makes it possible to compute the membrane potential of living cells accurately. The principle is that the plasma membrane is selectively permeable to ions and that its permeability to mobile ions determines the characteristics of the membrane potential. However, an artificial experimental cell system with an impermeable membrane can exhibit a nonzero membrane potential, and its characteristics are consistent with the prediction of the Goldman-Hodgkin-Katz eq., which is a noteworthy concept of membrane theory, despite the membrane's impermeability to mobile ions. We noticed this troublesome facet of the membrane theory. We measured the potentials through permeable and impermeable membranes where we used the broad varieties of membranes. Then we concluded that the membrane potential must be primarily, although not wholly, governed by the ion adsorption-desorption process rather than by the passage of ions across the cell membrane. A theory based on the Association-Induction Hypothesis seems to be a more plausible mechanism for the generation of the membrane potential and to explain this unexpected physiological fact. The Association-Induction Hypothesis states that selective ion permeability of the membrane is not a condition for the generation of the membrane potential in living cells, which contradicts the prediction of the membrane theory. Therefore, the Association-Induction Hypothesis is the actual cause of membrane potential. We continued the theoretical analysis by taking into account the Association-Induction Hypothesis and saw that its universality as a cause of potential generation mechanism. We then concluded that the interfacial charge distribution is one of the fundamental causes of the membrane potential.

Differential geometric formulation of hanging membranes: Shell membrane theory and variational principle

In this paper, we present differential geometric formulation of hanging membrane forms based on the equilibrium equations in the shell membrane theory and the geometric variational problems. We also present the equations of hanging membranes in isothermic coordinates which will be an effective representation for numerical analysis in our forthcoming paper.

Effect of Outstanding Flanges on Stress Concentration in Box Beam

Background of the research: A conventional box-type structure is generally used in constructing the core/shear wall, internal frame, and steel box girders. Tube-in-Tube with single and multiple tubes reduces the shear lag effect and lateral deformation in a tall tubular structure. Purpose: However, the present study focuses on the behavior of a modified form of the conventional box beam, i.e., a box beam with outstanding flanges. Thus, this study analyzes a box beam with outstanding flanges and compares the shear lag effect (Stress concentration) and lateral deformation with a conventional box beam. Methodologies: The minimum potential energy principle is applied to analyze the models and validated with the finite element results. Principal results: The transformation is observed to be reducing the shear lag effect at the web-flange junction and lateral deformations of the beam. In addition, the transformation also controls stress reversal. The modification demonstrated in the present study is stiffer than the conventional box-type structure as a core/shear wall or internal frame. Major conclusions and contributions to the field: This modification may be an integral part of tall tubular buildings producing significantly lowered stress concentration and lateral deformation. The present study is also applicable to strengthening steel box girders. It is possible to extend the bottom plate with the outstanding flange to increase the load-bearing capacity or strengthen the existing steel box girder. Therefore, the transformed box beam can be utilized as an economical alternative in constructing tall tubular buildings and retrofitting the steel box girder bridge. It is convenient and straightforward as there is no need to stiffen any part of the core/shear wall or internal frame. Additionally, there is no need to remove elements from the existing girder or alter its dimensions. Add the remaining flange by welding or bolting it onto the bottom flange to extend it. Limitation of the study and future research: A different assumption of stress function can be used in the flange and web when an orthotropic membrane theory is adapted to analyze the frame tube structure.

A uniformly-valid asymptotic plate theory of growth with numerical implementation

In this paper, we aim to develop a simplified and uniformly-valid finite-strain plate theory of growth. First, starting from a consistent finite-strain plate theory of growth proposed in our previous work, we specify the magnitudes of growth functions in five different cases and conduct systematic asymptotic analyses, from which the original plate theory can be reduced to some classical plate and membrane theories. Based on the asymptotic analyses, it is found that some terms in the original plate equations (which contain the high-order stress tensor S(2)) always have higher asymptotic orders. By dropping these terms, the plate equations can be simplified significantly. Then, a reduced finite-strain plate theory of growth is established, which is valid in a wide range of growth and mechanical loading conditions. The associated weak form of this uniformly-valid plate theory has also been derived for numerical implementation. To demonstrate the efficiency of this plate theory, it is implemented into a finite element software and applied to study four typical examples. To verify the accuracy of the 2D plate models, the corresponding 3D volume models have also been constructed for these examples. Through some comparisons, it is found that the numerical results obtained from the 2D and 3D models can fit each other quite well. Furthermore, the numerical calculations based on the plate models show obvious advantages in the aspects of computational efficiency, convergence rate and stability. In our opinion, the uniformly-valid asymptotic plate theory of growth proposed in the current work is adequate for studying the complex growth behaviors of thin hyperelastic plates.

Indentation of pore-spanning lipid membranes: Spring-stiffening or -softening responses and apparent stiffness prediction

Atomic force microscopy (AFM)-based nanoindentation has emerged as a key nanomechanical mapping method to probe mechanical properties of two-dimensional engineering and biological materials. In comparison with extensive analytical studies on the indentation of freestanding solid thin films, surprisingly little attention has been drawn on analytical predictions of mechanical responses of freestanding lipid membranes to indentation in the framework of Helfrich membrane theory. Here we perform systematic theoretical studies with formulated analysis on indentation of nanopore-spanning lipid membranes. Two types of lipid membranes are considered. One is the membrane subject to uniform area stretching and the membrane is found to exhibit a spring-stiffening behavior during indentation, while the other is the membrane of constant tension and a spring-softening behavior at intermediate indentation is exhibited. The smaller the membrane tension is, the clearer the spring-softening feature is. For both types of membranes, analytical solutions of load–depth relationship at small indentation and apparent membrane stiffnesses are obtained at small and large tension. For the stretched lipid membranes, a cubic nonlinearity arising from membrane stretching is specified. Roles of membrane bending rigidity, (pre-)tension, or area compression modulus, and indenter size in membrane indentation are elucidated. Moreover, pressure of contact between the membrane and indenter and a line load of contact acting along the contact edge are obtained based on the shell theory. Our results provide fundamental insights on nonlinear mechanical behaviors of the lipid membrane indentation.

Mechanical properties and optimal configurations of variable-curvature pressure hulls based on the equal-strength shell theory

Cylindrical pressure hulls are widely used in deep-sea submersibles, but they are affected by limitations imposed by their mechanical characteristics. To improve the bearing capacity of pressure hulls, in this work, variable-curvature shells were proposed. Based on the membrane theory and the non-momental theory, expressions for calculating the stress and buckling load of variable-curvature shells were derived. The generalized equal-strength shell theory was taken as an important index to evaluate the bearing capacity of pressure hulls. Pressure hulls with different geometric configurations were analyzed through numerical simulations. Finally, cylindrical and circular variable-curvature shells were fabricated via additive manufacturing. Furthermore, a comparative experiment was carried out on the two types of shells. The results reveal that variable-curvature shells have better mechanical properties than cylindrical shells, which results in a lower stress in the two main directions and a higher buckling load. Additionally, variable-curvature shells are in better agreement with the equal-strength shell theory and ensure a high material utilization. The expressions for calculating the stress and buckling load in this study are found to be highly accurate.

Upscaling the Poisson–Nernst–Planck equations for ion transport in weakly heterogeneous charged porous media

The Poisson–Nernst–Planck (PNP) equations govern the continuum level description of ions in electrolytes and especially the impact of charged surfaces. In numerous applications such surfaces are complex, varying on a small lengthscale compared to the overall scale of the system, often prohibiting the direct prediction of the osmotic swelling pressures induced by ion behaviours in Debye layers near surfaces. With periodicity, upscaling techniques can be readily used to determine the behaviour of the swelling pressure on large lengthscales without solving the PNP equations on the complex domain, though generalising to cases where the periodicity is only approximate is more challenging. Here, we generalise a method by Bruna and Chapman (2015) for upscaling a non-periodic diffusion equation to the PNP equations. After upscaling, we find a rational derivation of the swelling pressure closely resembling the classical, though phenomenological, use of Donnan membrane theory predictions for the swelling pressure in cartilage, together with a novel contribution driven by heterogeneous fixed (surface) charges. The resulting macroscale model is also shown to be thermodynamically consistent, though its comparison with a recent upscaled models for swelling pressure in cartilage mechanics emphasises the need to understand how macroscale models depend on differing upscaling techniques, especially in the absence of perfect periodicity.

ASSESSMENT OF STRESS-STRAIN STATE FOR DOME-SHELL OF LUNAR MODULE

Problem statement. Today, the world's leading researchers are engaged in investigating the possibilities of building bases and settlements on the surface of the Moon. To ensure the protection of the crew for long-duration missions, the development of residential modules is required. An effective solution for construction on the Moon is the use of local soil (regolith) for the production of concrete and reinforcement. For today, there are already data on the physical and mechanical properties of such materials, but the studies of the performance for monolithic load-bearing structures made of them are limited. The purpose of the article is to assess the stress-strain state for dome-shells of living modules located on the surface of the Moon, taking into account the physical and mechanical characteristics of building materials from local raw materials (regolith) and environmental conditions. Conclusions. Using the membrane theory’ methods of shells and finite element modeling, data on the stress-strain state of thin-walled shell domes for the construction of lunar living modules for 8, 10, and 12 crew members were obtained. On the basis of the data obtained on internal forces, the required thickness and reinforcement area for the module’ shell were determined. A comparative analysis of the results of determining the internal forces and the structural parameters for the dome-shells considered was carried out. It was established that the deviation of the internal forces values near the support ring in the meridional direction, the internal forces in the area of the dome’ top, as well as the cross-sectional reinforcement area and the shell thickness for all considered options do not exceed 10 %. Exceptions are the data on the internal forces near the support in the ring direction caused by the internal pressure for the 8-crew shell dome, and caused by all types of loads for the 10- and 12-crew variant, which is due to differences in the chosen analysis methods.

Ballistic graphene arrays for ultra-high pressure sensing

Atomically thin two-dimensional materials, such as graphene, exhibit extreme high-pressure sensitivity compared to the commercially used pressure sensors due to their high surface-to-volume ratio and excellent mechanical properties. The smaller piezoresistance of graphene across different transport regimes limits its pressure sensitivity compared to other two-dimensional materials. Using membrane theory and the thin-film adhesivity model, we show miniaturization as a means to enhance the overall performance of graphene pressure sensors. Our findings reveal that ballistic graphene can be configured to measure ultra-high pressure (≈109 Pa) with many-fold high-pressure sensitivity than other contemporary two-dimensional materials. Based on these findings, we propose an array of ballistic graphene sensors with extreme high-pressure sensitivity and ultra-high-pressure range that will find applications in next-generation nano-electro-mechanical system pressure sensors. The performance parameters of the array sensors can be further enhanced by reducing the size of graphene membranes and increasing the number of sensors in the array. The methodology developed in this paper can be used to explore similar applications using other two-dimensional materials.

Wrapping of a vesicle nanoparticle with variable bending stiffness by membrane

Cellular uptake of nanoparticle (NP) is an important biological process involving mechanically and structurally heterogeneous environments, such as biophysical heterogeneity of single extracellular vesicles and biomechanical heterogeneity of small viral capsids. Despite of these heterogeneous environments, poor understanding of membrane interacting with vesicle NP of non-uniform mechanical properties still exists. To address this issue, combining the continuum Canham–Helfrich theory of membrane and the stochastic Markov method on state transition, we establish a theoretical model of the wrapping of a NP with any variable bending stiffness. As NPs are hypothesized with two typical types of non-uniform bending stiffness distributions (Gaussian-like and piecewise), through both minimum energy and stochastic dynamic approaches, it is identified that the membrane tends to encapsulate the NP with a sealing near soft region of NP. Because complete wrapping of NP with a sealing near its stiff region requires large elastic deformation of membrane. In addition, during cellular uptake, rotation phenomenon of the NP with variable bending stiffness is found, which is reminiscent of previous observations on homogeneous NP as reported in literature. These predictions are verified by relevant Monte Carlo simulations. Our findings are of interest to not only the fundamental understanding of cellular uptake but also the applications in the design of nanocarriers for drug delivery.

Analytical Modeling of a Soft Pneu-Net Actuator Subjected to Planar Tip Contact

Soft actuators are compliant structures that are generally made of elastomers and generates large deformation. The behavior of these structures cannot be estimated accurately using infinitesimal strain theories. The objective of soft robotics applications is the controlled large deformation of these structures. In this article, we propose an analytical model for a pneu-net soft actuator. The model is based on the Euler–Bernoulli finite strain hyperelastic thin cantilever beam theory. The deformation of the air chambers is modeled using finite strain membrane theory. The analytical model is developed for two different states of the actuator: 1) free space; and 2) when the actuator was subjected to tip contact. The proposed theoretical model predicts the deformation and force characteristics of the actuator for the grasping state. The theoretical formulation of the developed model is different from previously developed infinitesimal strain models for the actuator, as it considers the axial stretch and forces applied to the actuator. In addition, it can be theoretically implemented on similar structured actuators for various applications. The theoretically calculated deformation and force characteristics of different actuators are compared with the finite element (FE) model and experimental characteristics. The results suggest that the proposed model can predict the actuator deformation and force characteristics as accurately as the FE model, but the computation time of the proposed model is less than 1% that of the FE model. The proposed model is further implemented on a three-finger gripper to predict the air pressure required for a stable grasp of different objects and is validated experimentally.

Analytical Modeling of a Membrane-Based Pneumatic Soft Gripper

Finite deformation is the principal actuation basis of elastomer-based pneumatic soft actuators. Desired deformation behavior is the key design requirement for such actuators. The objective of current study is to optimize the design of a flat shell gripper and to investigate its interaction with a cylindrical object. Herein, we propose an analytical model for a membrane-based flat shell gripper. The model is based on finite strain membrane theory and neo-Hookean material. The proposed model considers the contact interaction of the actuator with flat and cylindrical rigid substrates. The model is developed for three different states of the actuator: 1) free-space; 2) contact with a flat substrate; and 3) contact with a cylindrical substrate. In application, the model was used to predict the relative position and air pressure required to grasp a cylindrical object by a parallel two-fingered shell gripper. Additionally, the frictional behavior of the actuator in contact with a cylindrical substrate is investigated. The model involves only solving nonlinear algebraic equations and is computationally efficient. The theoretically predicted deformation behavior of the actuator is experimentally validated via free-space deformation, force measurement, and grasping tests.

Fundamental membranes and the string dilaton

We study the quantization of the bosonic sector of supermembrane theory in double dimensional reduction, in order to extract the dependence of the resulting world-sheet action on the string dilaton (which cannot be obtained from a purely kinematic reduction). Our construction relies on a Polyakov-type approach with all six metric components on the world-volume as independent quantum fields, and shows that the correct and unique answer is only obtained if the target-space dimension of the theory is restricted to the critical value (D = 11 for the supermembrane). As a corollary, our analysis implies that there are no analogs of the non-critical string for (super-)membrane theory.

A simplified method for assessing the serviceability performance of geosynthetic reinforced and pile-supported embankment

A simplified method for assessing the serviceability performance of geosynthetic reinforced and pile-supported embankment is presented, where the subsoil consolidation is introduced remaining compatible with the development of soil arching and the reinforcement sag. A piecewise function of the ground reaction curve is developed and used to quantify the arching efficiency. The link between the arching evolution and the subsoil consolidation is then established through the load-carrying equilibrium in the area between piles together with the tensile membrane theory. The reaction of the subsoil is described using the 1-D consolidation theory where the stress history is considered. A parametric study is performed to demonstrate the serviceability performance of a geosynthetic reinforced and pile-supported embankment. The serviceability design of the geosynthetic reinforced and pile-supported embankment is achieved with the proposed method which offers an approach to estimate the time consumed and the subsoil settlement required to achieve a service state.

A pressure vessel with a special barrelled shape

The paper is devoted to a pressure vessel with a special barrelled shape. The analytical model of this vessel composed of shells of revolution is developed. Based on the membrane theory the state of stress in the vessel is determined analytically. Moreover, a numerical FEM model (ANSYS – system) of the vessel is formulated. The distribution of the stresses in the exemplary vessels with the use of two methods are calculated and compared. The proposed shape, for selected geometrical properties, assures that the stress distribution is relatively smooth as for the multi-shell tank. The stability analysis of selected shells showed that the post-buckling behaviour of the presented structure is unstable and the imperfection sensitivity is high.