Inelastic Membrane Research Articles

Surface wave interaction with a vertical viscoelastic barrier

In this study, the surface wave interaction with a thin vertical submerged viscoelastic sheet as a wave barrier is investigated analytically without pre-assumption of the sheet dynamic behavior. The viscoelastic sheet spans over the entire water depth, and is tensioned and hinged on both ends. The Voigt model is employed for the viscoelastic representation. Analytical solutions are obtained using the eigenfunction expansion method with the hydroelastic and viscoelastic parameters of α and β, respectively. Five hydro-viscoelastic regimes with varying tension from elastic plate to inelastic membrane are identified based on the analysis. As the regime changes from plate-like to membrane-like, the wave transmission diminishes and the sheet boundary displacement together with the flexural strain and shear force reduce, while the corresponding resonating wavenumber increases instead. The sheet response with tension-resistance dominance is more dependent on α than that with bending-resistance dominance. Furthermore, as the sheet transits from tension- to bending-resistance dominance, the reduction of wave transmission with β near the resonating wavenumber becomes significant due to the internal energy dissipation.

Dura Mater: Anatomy and Clinical Implication

The dura mater is of similar embryological origin to the fascial organ. It contains several fibroblasts which make the dura mater a flexible structure. Dura mater is the outermost of the three layers of meninges, a thick and rigid inelastic membrane that covers the brain and spinal cord and that is impermeable to the cerebrospinal fluid. The cranial dura mater in certain respects differs anatomically from the dura material in the spinal cord, and it is important to classify them separately. This article reviews the anatomical structure of spinal and cranial dura mater and its anatomy with muscle, fascia, bone structure and ligaments. Dura mater is a structure in the body that is connected with systemic functions.

Mechanics of surface area regulation in cells examined with confined lipid membranes.

Cells are wrapped in inelastic membranes, yet they can sustain large mechanical strains by regulating their area. The area regulation in cells is achieved either by membrane folding or by membrane exo- and endocytosis. These processes involve complex morphological transformations of the cell membrane, i.e., invagination, vesicle fusion, and fission, whose precise mechanisms are still under debate. Here we provide mechanistic insights into the area regulation of cell membranes, based on the previously neglected role of membrane confinement, as well as on the strain-induced membrane tension. Commonly, the membranes of mammalian and plant cells are not isolated, but rather they are adhered to an extracellular matrix, the cytoskeleton, and to other cell membranes. Using a lipid bilayer, coupled to an elastic sheet, we are able to demonstrate that, upon straining, the confined membrane is able to regulate passively its area. In particular, by stretching the elastic support, the bilayer laterally expands without rupture by fusing adhered lipid vesicles; upon compression, lipid tubes grow out of the membrane plane, thus reducing its area. These transformations are reversible, as we show using cycles of expansion and compression, and closely reproduce membrane processes found in cells during area regulation. Moreover, we demonstrate a new mechanism for the formation of lipid tubes in cells, which is driven by the membrane lateral compression and may therefore explain the various membrane tubules observed in shrinking cells.

Equations for the filled inelastic membrane: a more general derivation

An earlier paper discussed the case of a flexible but inextensible membrane filled to capacity with incompressible fluid. It was found that the resulting shape satisfies a set of three simultaneous partial differential equations. This article gives a more general derivation of these equations and shows their form in an interesting special case.

A variational formulation for finite deformation wrinkling analysis of inelastic membranes

This paper is concerned with a novel, fully variational formulation for finite deformation analysis of inelastic membranes with wrinkling. In contrast to conventional approaches, every aspect of the physical problem derives from minimization of suitable energy functionals. A variational formulation of finite strain plasticity theory, which leads to a minimization problem for the constitutive updates, serves as the starting point for the derivations. In order to take into account the kinematics induced by wrinkles and slacks, a relaxed version of the finite strain functional is postulated. In effect, the local incremental stress–strain relations are established via differentiation of the relaxed energy functional with respect to the strains. Hence, the presented formulation is fully analogous to that of hyperelasticity with the sole exception that the aforementioned functional depends on history variables and, accordingly, it is path dependent. The advantages associated with the developed variational method are manifold. From a practical point of view, the possibility of applying standard optimization algorithms to solve the minimization problem describing inelastic membranes is remunerative. From a mathematical point of view, on the other hand, the energy of the system induces some sort of natural metric representing an essential requirement for error estimation and thus, for adaptive finite element methods. The presented derivation of the model allows to consider possible material symmetries in the elastic as well as plastic response of the material. As a prototype, a von Mises-type model is implemented. The efficiency and performance of the resulting algorithm are demonstrated by means of numerical examples.

A fully variational algorithmic formulation for wrinkling at finite strains

AbstractThis contribution is concerned with an efficient novel algorithmic formulation for wrinkling at finite strains. In contrast to previously published numerical implementations, the advocated method is fully variational. More precisely, the parameters describing wrinkles or slacks, together with the unknown deformation mapping, are computed jointly by minimizing the potential energy of the considered mechanical system. Furthermore, the wrinkling criteria are naturally included within the presented variational framework. The presented approach allows to employ three–dimensional constitutive models directly, i.e., plane stress conditions characterizing membranes are variationally enforced by minimizing the potential energy with respect to the transversal strains. Since the proposed formulation for wrinkling in membranes is fully variational, it can be conveniently combined with other variational methods (based on energy minimization). As an example, a variationally consistent framework for finite strain plasticity theory is considered. More precisely, the minimization principle characterizing wrinkling in elastic membranes and that describing plasticity in inelastic solids are coupled leading to a novel variational approach for inelastic membranes. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Linear Heave Dynamics of an Air-Cushion Vehicle Bag-and-Finger Skirt.

Results from a linear analysis of the heave dynamics of an air-cushion vehicle equipped with a bag-and-finger skirt are described. A two-dimensional section of the cushion is subject to pure heave or long-wave surface motion inputs. The skirt mass is lumped in the fingers, with the bag being modelled as a combination of massless inelastic membranes and links. The airflows from bag to cushion and from cushion to atmosphere are assumed quasisteady, and the bag and cushion volumes are modelled as lumped pneumatic capacitances. For a configuration representative of a 37t vehicle, frequency response characteristics show the effect of skirt geometry and mass changes, and cushion capacitance. The results suggest that changes in skirt geometry cannot be used to radically modify an undesirable heave response, but reducing the skirt mass may be effective. The air compressibility also affects heave response at high frequencies, with the effect becoming more prominent at the low cushion-flow rates now used in practice.

Nonlinear Heave Dynamics of an Air Cushion Vehicle Bag-and-Finger Skirt*

The flexible skirt system used almost exclusively on large amphibious air cushion vehicles such as the U.S. Navy's 150 tonne landing craft is the bag-and-finger skirt, but little information on its dynamical properties is available in the journal literature. The present paper describes results of an analysis of the nonlinear heave dynamics of a simplified configuration chosen specifically to allow formulation from first principles The skirt mass is lumped in the fingers, with the bag being modeled as a combination of massless inelastic membranes and links. Airflow processes are assumed quasi-steady, and the bag-and-cushion volumes are modeled as lumped pneumatic capacitances. The modulation of cushion air escape by skirt-surface contact is also included. The numerical results show that nonlinear effects occur at wave input amplitudes expected to be encountered in practice. At a given frequency, input amplitude increase causes jumps in heave response, period doubling, and chaos. Furthermore, results for two typical configurations show resonance at frequencies at which humans are most sensitive. One solution to this problem may be to reduce skirt mass The paper concludes with a discussion of issues requiring further investigation.

Multifaceted ultrasound transducer probe system and methods for its use

A High Intensity Focused Ultrasound system is provided for treatment of focal disease. The preferred embodiment includes an intracavity probe having two active ultrasound radiating surfaces with different focal geometries. Selectively energizing the first surface focuses therapeutic energy a first distance from the housing, energizing the second surface focuses therapeutic energy nearer the housing. Preferably, the probe includes a thin, flexible, inelastic membrane which is rigidized with pressure to allow blunt manipulation of tissue. Methods of use of the probe are also provided, particularly for treatment of diseases of the prostate.

Heave Stiffness of an Air Cushion Vehicle Bag-and-Finger Skirt

The heave stiffness of a bag-and-finger flexible skirt air cushion is investigated analytically and experimentally. The investigations use a two-dimensional section of the skirt confined between end-plates and moving in heave. This simplified geometry facilitates analysis involving a minimum of empiricism. Experiments show that the airflows, including leaks between fingers and at the end-plates, can be modeled as orifice-like. The analysis assumes that the fingers can be modeled as rigid massless bodies. Three models of the bag, based on combinations of massless inelastic membranes and rigid links, are investigated. The predictions and experiments are in good agreement and show that modest geometry changes can have large effects on heave stiffness. It is suggested that these simple skirt models can provide useful insights into the dynamics.

General Solutions for the Inelastic Behavior of Pressurized Membranes

The small-deflection behavior of inelastic membranes supported along arbitrary contours and subjected to lateral pressure is considered. Hill and Stora˚kers’ (1980) solution for isotropic power-law hardening membranes is extended to a wide class of anisotropic material response. Applications to circular membranes are given for anisotropic materials characterized by Budiansky’s (1984) general transversely isotropic yield function. Specific results corresponding to the yield functions proposed by Hill (1979) and Bassani (1977) are also presented.

Analysis of continuous steel plates subjected to uniform transverse loads

The economic design of steel caissons for drilling and production platforms in the Arctic Ocean, formed from steel plates and supported by a rectangular grid of stiffeners, beams, and girders, requires that the full strength of the plates be mobilized to withstand extreme ice forces. A comprehensive method of analysis is needed to describe the behaviour of continuous steel plates into the inelastic range when they are acted upon by transverse loads. From this analysis, design procedures could then be developed.An extensive literature search has not revealed that satisfactory solutions exist for the load–deflection response of transversely loaded flat plates beyond the elastic limit when both flexural and membrane action are taken into account. Experimental data available in the inelastic range of behaviour are also limited.By considering various limiting simplified behavioural modes for the load–deflection response of uniformly loaded flat plates of zero aspect ratio, possible load–deflection domains are established. The limiting responses investigated are: elastic–inelastic flexural action, elastic membrane action, inelastic membrane action with increased stiffness resulting from increased Poisson's ratio in the inelastic range, elastic flexural membrane action, and action of a fully yielded cross section in flexure that gradually gives away to a fully yielded cross section in tension. Within the domain so established, a load–deflection behaviour is proposed that is in reasonable agreement with the results of the limited test data available. The results of a finite element analysis using the ADINA computer program are also in reasonable agreement with the proposed analysis. Design applications are discussed. Key words: deflection, elastic, elastoplastic, flexural resistance, membrane force, membrane resistance, plates, steel, strains, stresses, transverse load.

Static roll stiffness characteristics of two multicell type air cushion systems

Although there is growing interest in the use of flexible skirted air cushions for various off-road and other over-land transportation tasks, relatively little data on their suspension properties are available in the open literature. This paper presents the results of some experimental studies of the static roll stiffness of two resistance orifice-fed multicellular cushion designs. The conditions for scaling the tests to full-size behaviour are discussed. A simple theory, based on the assumptions that the skirt material is an inelastic membrane and that the cushion air flow can be described by one-dimensional orifice flow laws, is developed for one of the cushion systems. Good agreement between theory and experiment is obtained under certain restricted conditions, but in general the experimental results show that the skirt material properties can play an important role. This manifests itself in two ways: as a potential scaling problem, and the appearance of hysteresis in the rolling moment produced by the cushion. The latter can, under certain circumstances, be so large as to completely destroy its stiffness when rolled. At least two hysteresis mechanisms are indicated, and one has been observed. This is a buckling failure of the cells leading to large-scale venting and consequent loss of pressure. A detailed explanation of the other mechanism has not been obtained, but it is noted that skirt-ground friction does not appear to be important. It is concluded that a careful study of the structural properties of air-inflated cones is required. In particular, buckling phenomena need clarification.

An osmometer model for changes in the buoyant density of chromaffin granules

We present a model for the structure of isolated bovine adrenal medulla chromaffin granules derived from the dependence of granule density on the osmotic pressure of the suspension medium at 2 degrees C. The granule consists of a flexible, inelastic membrane bounding an osmotically active core. The core consists of a solution space and a separate, nonosmotic phase. Since the granule behaves like a "perfect" osmometer over a wide range of osmolarities, we conclude that (a) within these limits, the core consists of a constant amount of condensed material and a constant number of particles in solution, (b) from the constraints of the osmometer model, the osmolality inside the granule must equal the osmolality outside. Therefore the high concentrations of catecholamines (greater than 0.7 M) and ATP (greater than 0.18 M) measured biochemically cannot be dissolved in the core solution as separate molecules, but must be condensed into larger aggregates. These results are supported by electron micrographic examination of the effect of osmotic pressure changes on granule morphology.

The aerodynamic theory of sails. I. Two-dimensional sails

This paper deals with the preliminaries essential for any theoretical investigation of three-dimensional sails—namely, with the two-dimensional flow of inviscid incompressible fluid past an infinitely-long flexible inelastic membrane. If the distance between the luff and the leach of the two-dimensional sail is c , and if the length of the material of the sail between luff and leach is ( c + l ), then the problem is to determine the flow when the angle of incidence α between the chord of the sail and the wind, and the ratio l / c are both prescribed; especially, we need to know the shape of, the loading on, and the tension in, the sail. The aerodynamic theory follows the lines of the conventional linearized theory of rigid aerofoils; but in the case of a sail, there is an additional equation to be satisfied which ex­presses the static equilibrium of each element of the sail. The resulting fundamental integral equation—the sail equation—is consequently quite different from those of aerofoil theory, and it is not susceptible to established methods of solution. The most striking result is the theoretical possibility of more than one shape of sail for given values of α and l / c ; but there appears to be no difficulty in choosing the shape which occurs in reality. The simplest result for these realistic shapes is that the lift coefficient of a sail exceeds that of a rigid flat plate (for which l / c = 0) by an amount approximately equal to 0.636 ( l / c ) ½ . It seems very doubtful whether analytical solutions of the sail equation will be found, but a method is developed in this paper which comes to the next best thing; namely, an explicit expression, as a matrix quotient, which gives numerical values to a high degree of accuracy at so many chord-wise points. The method should have wide application to other types of linear equations.