Deflections of a rubber membrane

This paper deals with the problem of the transverse deflection of a natural rubber membrane that is fixed along a circular boundary. Uniaxial experiments were performed in order to characterize the constitutive behaviour of the rubber material in terms of several constitutive models available in the literature. These constitutive models were used to develop computational estimates for the quasi-static load-displacement response of a rigid spherical indentor that deflects the rubber membrane in a controlled fashion and to determine the deflected shape of the membrane at specified load levels. Both axisymmetric and asymmetric deflections of the rubber membrane were investigated. The paper provides a comparison of the experimental results for the membrane deflections with results derived from computational simulations.     

An atomistic-based finite deformation membrane for single layer crystalline films

A general methodology to develop hyper-elastic membrane models applicable to crystalline films one-atom thick is presented. In this method, an extension of the Born rule based on the exponential map is proposed. The exponential map accounts for the fact that the lattice vectors of the crystal lie along the chords of the curved membrane, and consequently a tangent map like the standard Born rule is inadequate. In order to obtain practical methods, the exponential map is locally approximated. The effectiveness of our approach is demonstrated by numerical studies of carbon nanotubes. Deformed configurations as well as equilibrium energies of atomistic simulations are compared with those provided by the continuum membrane resulting from this method discretized by finite elements.     

Biofouling in water systems

The paper describes the mechanisms in the development of biofouling layers (initial surface conditioning, microbial transport and attachment, mass transfer of nutrients to the biofilm surface and through the microbial layer, cell metabolism, and detachment of cells and of larger parts of the biofilm) and summarizes the effects of several factors on the buildup and stability of biofilms (nutrient availability, fluid velocity and turbulence, temperature, surface condition, and nonliving particles). Mass transfer within biofilms is treated in more detail. A biofouling model applied to the development of biofilms in heat exchangers is presented. Finally, references are made to biofouling control methods (biocide and the proper design and operation of heat exchangers) and to future research needs in this area.     

Wrinkling of anisotropic soft membranes

We study the mechanical response of a fiber-reinforced non-linearly elastic thin-walled circular tube subject to torsional twist. If as a result of the applied deformation compressive stresses arise, wrinkling is taken into account. We investigate this phenomenon using the general tension-field theory, extended to account for the presence of oriented reinforcing fibers. The material under consideration is neo-Hookean with an additional term that accounts for the existence of the directional reinforcements. We first consider membranes characterized by uniaxial reinforcement and then extend our investigation to anisotropic materials characterized by two families of fibers in two preferred directions.     

反向Qm6非协调元

为通过强式分片试验,Qm6单元对Q6单元非协调部分的[G]矩阵进行了特殊的计算处理,但抗畸变性能下降,本文提出对有关处理反向进行,以恢复甚至提高抗畸变性能。分析了Qm6单元的原理,指出其实质是修改雅可比矩阵[J]的伴随矩阵[J*],在非协调部分[G]矩阵的计算时,把[J*]看成可变量,由Qm6的对应点向Q6方向进行反向搜索,查找有利的计算点。进行了典型和苛刻的算例测试,结果表明反向调整是有效的,调整系数取镜像值-1以及扩展到-2时,新单元的抗畸变性能优于原Q6和Qm6,其中取-2对消除剪切闭锁是最优点;除弱式分片试验外,总体性能和精度接近各类4节点四边形单元的最好水平。由于方法和原理简便,实现以及推广到三维问题都有显著优势。     

Reverse plasticity in single crystal silicon nanospheres

Nanoparticles in the range of 20 to 100 nm in size can be deposited, isolated, and individually probed for their mechanical properties. With a hypersonic plasma particle deposition technique, this has been successfully accomplished for silicon and titanium. We have already shown that silicon nanoparticles are superhard in the 30 to 50 GPa range after work hardening (Gerberich, W.W., Mook, W.M., Perrey, C.R., Carter, C.B., Baskes, M.I., Mukherjee, R., Gidwani, A., Heberlein, J., McMurry, P.H., Girshick, S.L., 2003a. Superhard silicon nanospheres. J. Mech. Phys. Solids 51, 979). At the same time when small nanospheres are compressed, a fraction of the plastic strain is reversed after unloading. Initially, the amount of reverse dislocation motion was small but appeared to accelerate once a threshold strain was reached. The cumulative reverse plastic strain from repeated loading of the same nanosphere appeared to increase from less than 0.04 to approximately 0.4 as cumulative strain increased from 0.2 to 0.6. For large strains then, it appears that a greater amount of plastic strain is recovered after unloading. This can at least partially be understood in terms of the enormous back stress developed at the small scale when dislocations are only a few nm apart. As the ramifications to nanoscopic features on MEMS, micromachines and magnetic recording devices is considerable, it is desirable to understand if a length scale can be developed for such phenomena. In terms of classic dislocation theory an attempt is made. Problems and prospects are discussed with regards to predictive models for hardness and reverse plasticity.     

On the Wrinkling of Anisotropic Elastic Membranes

The existence and uniqueness of a relaxed energy function for anisotropic elastic membranes is established. It is shown that the extra strains during wrinkling abide by a normality rule akin to that of metal plasticity, and that throughout such wrinkling processes both the strain energy and the Piola-Kirchhoff stresses remain constant. This revised version was published online in August 2006 with corrections to the Cover Date.     

Dynamics of liquid membranes. I: Non-adaptive finite difference methods

A non-adaptive method and a Lagrangian-Eulerian finite difference technique are used to analyse the dynamic response of liquid membrancs to imposed pressure variations. The non-adaptive method employs a fixed grid and upwind differences for the convection terms, whereas the Lagrangian-Eulerian technique uses operator splitting and decomposes the mixed convection-diffusion system of equations into a sequence of convection and diffusion operators. The convection operator is solved exactly by means of the method of characteristics, and its results are interpolated onto the fixed (Eulerian) grid used to solve the diffusion operator. It is shown that although the method of characteristics eliminates the numerical diffusion associated with upwinding the convection terms in a fixed Eulerian grid, the Lagrangian-Eulerian method may yield overshoots and undershoots near steep flow gradients or when rapid pressure gradients are imposed, owing to the interpolation of the results of the convection operator onto the fixed grid used to solve the diffusion operator. This interpolation should be monotonic and positivity-preserving and should satisfy conservation of mass and linear momentum. It is also shown that both the non-adaptive and Lagrangian-Eulerian finite difference methods produce almost identical (within 1%) results when liquid membranes are subjected to positive and negative step and ramp changes in the pressure coefficient. However, because of their non-adaptive character, these techniques require an estimate of the (unknown) length of the membrane and do not use all the grid points in the calculations. The liquid membrane dynamic response is also analysed as a function of the Froude number, convergence parameter and nozzle exit angle for positive and negative step and ramp changes in the pressure coefficient.     

复合Logistic映射中的逆分岔与分形

利用分岔图，揭示出复合Logistic映射可按倍周期分岔走向混沌，且混沌区中存在混沌危机及逆分岔现象．同时，分析了复合Logistic映射临界点的轨道，给出了复合Logistic映射Mandelbrot-Julia集(简称M-J集)的定义，推广了Welstead和Cromer所提出的周期点查找技术，并利用该技术，构造出一系列复合Logistic映射的M-J集．在此基础上，研究了M-J集的对称性；探索了M集周期区域分布的拓扑不变性；通过定性地建立M集上J集的整体刻画，发现M集包含了J集构造的大量信息．     

Boundary-value problems in the theory of lipid membranes

General contact conditions are developed for lipid membranes interacting with curved substrates along their edges. These include the anchoring conditions familiar from liquid-crystal theory and accommodate non-uniform membranes and non-uniform adhesion between a bulk fluid or membrane and a rigid substrate. The theory is illustrated through explicit solutions and numerical simulations.      

RATE DEPENDENT STRESS-STRETCH RELATION OF DIELECTRIC ELASTOMERS SUBJECTED TO PURE SHEAR LIKE LOADING AND ELECTRIC FIELD

The performance of dielectric elastomer(DE) transducers is significantly affected by viscoelastic relaxation-induced electromechanical dissipations.This paper presents an experimental study to obtain the rate dependent stress-stretch relation of DE membranes(VHB TM 9473) subjected to pure shear like loading and electric loading simultaneously.Stretching rate dependent behavior is observed.The results also show that the tensile force decreases as the voltage increases.The observations are compared with predictions by a viscoelastic model of DE.This experiment may be used for further studies of dynamic electromechanical coupling properties of DEs.     

Network Model of Flow,Transport and Biofilm Effects in Porous Media

In this paper, we develop a network model to determine porosity and permeability changes in a porous medium as a result of changes in the amount of biomass. The biomass is in the form of biofilms. Biofilms form when certain types of bacteria reproduce, bond to surfaces, and produce extracellular polymer (EPS) filaments that link together the bacteria. The pore spaces are modeled as a system of interconnected pipes in two and three dimensions. The radii of the pipes are given by a lognormal probability distribution. Volumetric flow rates through each of the pipes, and through the medium, are determined by solving a linear system of equations, with a symmetric and positive definite matrix. Transport through the medium is modeled by upwind, explicit finite difference approximations in the individual pipes. Methods for handling the boundary conditions between pipes and for visualizing the results of numerical simulations are developed. Increases in biomass, as a result of transport and reaction, decrease the pipe radii, which decreases the permeability of the medium. Relationships between biomass accumulation and permeability and porosity reduction are presented.     

Experimental study of the osmotic behaviour of reverse osmosis membranes for different NaCl solutions and hydrostatic pressure differences

The osmotic behaviour of five different present-day reverse osmosis membranes was studied, using different NaCl solutions (<6 wt.%) and applying different hydrostatic pressure differences (<5.2 bar) between the high and low concentration sides. The osmotic water flux through the membranes was found to increase non-linearly with respect to the increasing concentration difference over the membrane, leading to non-constant values for apparent water permeability. The polyamide composite membranes studied resulted only in very weak osmosis for even relatively small hydrostatic pressure differences and for strong NaCl solutions. Asymmetric cellulose acetate membranes showed somewhat better osmotic behaviour. However, all the osmotic water fluxes measured were still far too small for practical application in the production of energy.     

Analysis of Annular Liquid Membranes and Their Singularities

The singularities of the equations governing the fluid dynamics of steady, axisymmetric, annular liquid membranes subject to gravity are analyzed by means of two techniques based on the membranes's slope and curvature, and the membrane's mean radius, mass per unit length, and axial and radial velocity components, respectively. It is shown that no singularity is possible at or downstream from the nozzle exit for Weber numbers greater than unity because of the gravitational pull. For a Weber number equal to one, a singularity at the nozzle exit appears and the flow slope there is undetermined; however, the slope acquires a finite value if the liquid is assumed to leave the nozzle at angle different from that of the annular orifice. It is also shown that, for Weber numbers smaller than one, a singularity may occur downstream from the nozzle exit which may also be removed, and that the shapes of annular liquid membranes for Weber numbers equal to or less than one take a rounded form which is in agreement with experimental observations. An asymptotic analysis shows that, to leading order, the shapes of capillary, annular liquid membranes are arcs of circumferences, and this result is again in accord with available experimental findings.     

监控陀螺正反转周期确定方法研究

附加监控陀螺的陀螺监控方法是减小陀螺漂移的有效途径之一，基于漂移补偿实时性和有效性的双重要求，需要针对监控陀螺选择最佳的正反转周期。基于时间序列和马尔科夫分析方法，提出了一种确定监控陀螺正反转周期的行之有效的方法。     

A NOVEL METHOD FOR FABRICATING COMPOSITE MOSAIC MEMBRANE WITH UNIQUE NF SELECTIVITY

A novel method of fabricating composite mosaic membranes was studied on the basis of interracial polymerization （IP） by coating a thin selective layer onto the surface of a micro-porous hollow-fiber membrane, in which, 2,5-diaminobenzene sulfonic acid was used as one monomer of the IP reaction, and a mixture of trimesoyl chloride （TMCI） and 4-（chloromethyl） benzoyl chloride as the other monomer. Through the IP reaction a thin selective layer with negatively charged groups could be first formed on the polyethersulfone （PES） support membrane. Then trimethylamine solution was introduced to modify the IP layer through a quaternization reaction. Thus the selective layer of this composite membrane contained both negatively charged and positively charged groups to perform the mosaic functionality. Characterization of the composite mosaic membranes was carried out through permeation experiments using different inorganic salts and dyes. The experimental results showed that the membranes could permeate both mono- and bi-valent inorganic salts, but reject larger organic molecules. Such a mosaic membrane is potentially useful for the separation of salts from water-soluble organics, especially in dye and textile industries.     

Mechanics of fish skin: A computational approach for bio-inspired flexible composites

Natural materials and structures are increasingly becoming a source of inspiration for the design novel of engineering systems. In this context, the structure of fish skin, made of an intricate arrangement of flexible plates growing out of the dermis of a majority of fish, can be of particular interest for materials such as protective layers or flexible electronics. To better understand the mechanics of these composite shells, we introduce here a general computational framework that aims at establishing a relationship between their structure and their overall mechanical response. Taking advantage of the periodicity of the scale arrangement, it is shown that a representative periodic cell can be introduced as the basic element to carry out a homogenization procedure based on the Hill-Mendel condition. The proposed procedure is applied to the specific case of the fish skin structure of the Morone saxatilis, using a computational finite element approach. Our numerical study shows that fish skin possesses a highly anisotropic response, with a softer bending stiffness in the longitudinal direction of the fish. This softer response arises from significant scale rotations during bending, which induce a stiffening of the response under large bending curvature. Interestingly, this mechanism can be suppressed or magnified by tuning the rotational stiffness of the scale-dermis attachment but is not activated in the lateral direction. These results are not only valuable to the engineering design of flexible and protective shells, but also have implications on the mechanics of fish swimming.     

Dynamics of liquid membranes. II: Adaptive finite difference methods

Two domain-adaptive finite difference methods are presented and applied to study the dynamic response of incompressible, inviscid, axisymmetric liquid membranes subject to imposed sinusoidal pressure oscillations. Both finite difference methods map the time-dependent physical domain whose downstream boundary is unknown onto a fixed computational domain. The location of the unknown time-dependent downstream boundary of the physical domain is determined from the continuity equation and results in an integrodifferential equation which is non-linearly coupled with the partial differential equations which govern the conservation of mass and linear momentum and the radius of the liquid membrane. One of the finite difference methods solves the non-conservative form of the governing equations by means of a block implicit iterative method. This method possesses the property that the Jacobian matrix of the convection fluxes has an eigenvalue of algebraic multiplicity equal to four and of geometric multiplicity equal to one. The second finite difference procedure also uses a block implicit iterative method, but the governing equations are written in conservation law form and contain an axial velocity which is the difference between the physical axial velocity and the grid speed. It is shown that these methods yield almost identical results and are more accurate than the non-adaptive techniques presented in Part I. It is also shown that the actual value of the pressure coefficient determined from linear analyses can be exceeded without affecting the stability and convergence of liquid membranes if the liquid membranes are subjected to sinusoidal pressure variations of sufficiently high frequencies.