Elastic response and wrinkling onset of curved elastic membranes subjected to indentation test

Starting from a polymeric-fluid droplet, by vulcanization of the fluid free surface, curved elastic membranes, several nanometers thick and a few millimeters in diameter, which enclose a constant fluid volume, are produced. In an indentation-type test, carried out by pushing the membrane along its normal by means of a micro-needle, under some conditions, wrinkles are likely to appear around the contact region. Interestingly, we observe that the instability does not significantly alter the force-displacement relation: the relation between the force and the displacement remains linear and the associated stiffness is simply proportional to the tension of the membrane. In addition, we determine that the wrinkles develop when the stretching modulus of the membrane compares with its tension, which provides a useful method to estimate the elastic constant.     

Force distributions and force chains in random stiff fiber networks

We study the elasticity of random stiff fiber networks. The elastic response of the fibers is characterized by a central force stretching stiffness as well as a bending stiffness that acts transverse to the fiber contour. Previous studies have shown that this model displays an anomalous elastic regime where the stretching mode is fully frozen out and the elastic energy is completely dominated by the bending mode. We demonstrate by simulations and scaling arguments that, in contrast to the bending dominated elastic energy, the equally important elastic forces are to a large extent stretching dominated. By characterizing these forces on microscopic, mesoscopic and macroscopic scales we find two mechanisms of how forces are transmitted in the network. While forces smaller than a threshold F_c are effectively balanced by a homogeneous background medium, forces larger than F_c are found to be heterogeneously distributed throughout the sample, giving rise to highly localized force chains known from granular media.     

Effect of the configuration of a wrinklon on the distributions of the energy and elastic strain in a graphene nanoribbon

The formation of wrinkles in thin membranes is a widespread phenomenon. In particular, wrinkles can appear in graphene, which is the thinnest natural membrane, and affect its properties. A region where wrinkles with different wavelengths are linked is called wrinklon. Conditions of the fixing of an elastically deformed graphene sheet dictate a certain wavelength of wrinkles near the fixed edge. Wrinkles with a longer wavelength become more energetically favorable with an increase in the distance from the edge. As a result, wrinklons appear and reduce the potential energy of the system by uniting wrinkles into larger wrinkles with an increase in the distance from the edge. The possibility of implementing various equilibrium configurations of wrinklons at given plane strains in graphene has been demonstrated by the molecular quasistatic method. The distributions of the energy and elastic strain components in wrinklons with various configurations for nanoribbons with different widths have been calculated.     

Simulation of triaxial response of granular materials by modified DEM

A modified discrete element method(DEM)with rolling effect taken into consideration is developed to examine macroscopic behavior of granular materials in this study.Dimensional analysis is firstly performed to establish the relationship between macroscopic mechanical behavior,mesoscale contact parameters at particle level and external loading rate.It is found that only four dimensionless parameters may govern the macroscopic mechanical behavior in bulk.The numerical triaxial apparatus was used to study their influence on the mechanical behavior of granular materials.The parametric study indicates that Poisson’s ratio only varies with stiffness ratio,while Young’s modulus is proportional to contact modulus and grows with stiffness ratio,both of which agree with the micromechanical model.The peak friction angle is dependent on both inter-particle friction angle and rolling resistance.The dilatancy angle relies on inter-particle friction angle if rolling stiffness coefficient is sufficiently large.Finally,we have recommended a calibration procedure for cohesionless soil,which was at once applied to the simulation of Chende sand using a series of triaxial compression tests.The responses of DEM model are shown in quantitative agreement with experiments.In addition,stress-strain response of triaxial extension was also obtained by numerical triaxial extension tests.     

Wrinkling of vesicles during transient dynamics in elongational flow

Recent experiments by Kantsler et al. [Phys. Rev. Lett. 99, 178102 (2007)10.1103/PhysRevLett.99.178102] have shown that the relaxational dynamics of a vesicle in external elongation flow is accompanied by the formation of wrinkles on a membrane. Motivated by these experiments we present a theory describing the dynamics of a wrinkled membrane. The formation of wrinkles is related to the dynamical instability induced by negative surface tension of the membrane. For quasispherical vesicles we perform analytical study of the wrinkle structure dynamics. We derive the expression for the instability threshold and identify three stages of the dynamics. The scaling laws for the temporal evolution of wrinkling wavelength and surface tension are established, confirmed numerically, and compared to experimental results.     

Wrinkle formations in axi-symmetrically stretched membranes

We study experimentally the main features of wrinkles that form in an initially stretched and flat elastic membrane when subjected to an axi-symmetric traction force at the center. The wavelength and amplitude of the wrinkle pattern are accurately characterized as the membrane tension and the traction forced are varied. We show that wrinkles are the result of a supercritical instability and appear for a well-defined critical traction force that is a function of the membrane tension. Wrinkle length and amplitude increase as the traction force is increased further. By contrast, both quantities decrease as the membrane tension is increased. Calculations based on symmetry arguments and elastic-energy minimization are in good agreement with experiments and provide a simple way to investigate configurations that are difficult to access experimentally. Such problems include wrinkles in elastic nano-films on finite-thickness viscous substrates used in semiconductor technology or in cellular forces detection.Received: 10 August 2004, Published online: 19 October 2004PACS: 46.32. + x Static buckling and instability - 87.19.St Movement and locomotion - 85.40.Ls Metallization, contacts, interconnects; device isolationJ.-C. Géminard: Permanent address: Laboratoire de Physique, Ecole Normale Supérieure de Lyon, 64, Allée dItalie, 69364 Lyon cedex 07, France     

Vesicle dynamics in time-dependent elongation flow: wrinkling instability

We present experimental results on the relaxation dynamics of vesicles subjected to a time-dependent elongation flow. We observed and characterized a new instability, which results in the formation of higher-order modes of the vesicle shape (wrinkles), after a switch in the direction of the velocity gradient. This surprising generation of membrane wrinkles can be explained by the appearance of a negative surface tension during the vesicle deflation, which tunes itself to alternating stress. Moreover, the formation of buds in the vesicle membrane was observed in the vicinity of the dynamical transition point.     

Nonlocal constitutive relation for steady granular flow

Extending recent modeling efforts for emulsions, we propose a nonlocal fluidity relation for flowing granular materials, capturing several known finite-size effects observed in steady flow. We express the local Bagnold-type granular flow law in terms of a fluidity ratio and then extend it with a particular Laplacian term that is scaled by the grain size. The resulting model is calibrated against a sequence of existing discrete element method data sets for two-dimensional annular shear, where it is shown that the model correctly describes the divergence from a local rheology due to the grain size as well as the rate-independence phenomenon commonly observed in slowly flowing zones. The same law is then applied in two additional inhomogeneous flow geometries, and the predicted velocity profiles are compared against corresponding discrete element method simulations utilizing the same grain composition as before, yielding favorable agreement in each case.     

Velocity autocorrelations and viscosity renormalization in sheared granular flows

The decay of the velocity autocorrelation function in a sheared granular flow is analyzed in the limit where the wavelength of fluctuations is larger than the "conduction length," so that energy is a nonconserved variable. The decay of the velocity autocorrelation function is much faster than that in a fluid at equilibrium for which energy is a conserved variable. Specifically, the autocorrelation function in a sheared granular flow decays proportional to t-3 in 2D and t-9/2 in 3D, in contrast with the decay proportional to t-1 in 2D and t-3/2 in 3D for a fluid at equilibrium. The renormalization of the viscosity due to mode coupling is evaluated using this form of the decay of the autocorrelation function. It is found that the logarithmic divergence in the viscosity in 2D, and the divergence of the Burnett coefficients in 3D, which is characteristic of a fluid of elastic particles at equilibrium, is absent in a sheared granular flow.     

Geometry and physics of wrinkling

The wrinkling of thin elastic sheets occurs over a range of length scales, from the fine scale patterns in substrates on which cells crawl to the coarse wrinkles seen in clothes. Motivated by the wrinkling of a stretched elastic sheet, we deduce a general theory of wrinkling, valid far from the onset of the instability, using elementary geometry and the physics of bending and stretching. Our main result is a set of simple scaling laws; the wavelength of the wrinkles lambda approximately K(-1/4), where K is the stiffness due to an "elastic substrate" effect with a multitude of origins, and the amplitude of the wrinkle A approximately lambda. These could form the basis of a highly sensitive quantitative wrinkling assay for the mechanical characterization of thin solid membranes.     

Dressed Josephson junction network models and low-field magnetic response of high-Tc granular superconductors

A bare three-dimensional model, in which grains are reduced to points, cannot fully account for the magnetic properties of granular superconductors. A dressed version of these network models is proposed to discuss the quantitative link between the low-field magnetic response of high-T_c superconducting granular samples and the characteristic properties of Josephson junction network models. By means of dressed models, the temperature dependence of the d.c. field-cooled susceptibility of a simple three-dimensional granular system, consisting of eight grains in a cubic arrangement, is studied.     

Shear and compressional wave speeds in Hertzian granular media

It is shown that the shear wave speed in a granular medium is less than that in an elastic solid of the same shear modulus-to-density ratio. Shear and compressional wave speeds are derived for granular media using a conservation of energy approach. The grains are assumed to be spherical with elastic Hertzian contacts of constant stiffness. The affine approximation is used to determine the relative displacements of grain centers, and it is also assumed that the grains are small compared to a wavelength, consistent with the effective medium approximation. Potential and kinetic energies associated with linear motion are the same as those in an elastic solid, but it is found that shear wave propagation in a granular medium involves additional energies associated with grain rotation. The partition of energies results in a reduction in the shear wave speed, relative to an elastic solid of the same shear modulus-to-density ratio. It is shown that the reduction is an inherent property of granular media, independent of any departure from the affine approximation or fluctuations in coordination number or contact stiffness. The predicted wave speed ratios are consistent with published measurements.     

二维成分无序颗粒体系中法向力的分布

运用离散元法研究成分无序体系中法向力的几率分布,该体系由两种不同刚度系数的颗粒规则堆积而成, 体系的无序程度由缺陷率控制.模拟发现,无缺陷时体系的力网几乎是均匀的,而有缺陷时力网变得不均匀. 提出了主法向力与次法向力的概念,并对它们分别进行统计;随着缺陷率的增加,主法向力的分布经历了比较复杂的变化过程,而次法向力总是指数型分布.模拟结果表明,缺陷率较小时成分无序体系中的法向力分布与随机堆积体系很不相同,而缺陷率较大时得到了与随机堆积类似的结果.这些结果有助于理解力网的不均匀性与体系无序性的关系.     

Experimental validation and applications of a modified gap stiffness model for granular marine sediments

The author has proposed a modified gap stiffness model, which is incorporated into the Biot model; the resultant model is called the BIMGS model. By using this model, it is theoretically demonstrated that the frame bulk modulus is dependent on frequency [M. Kimura, "Frame bulk modulus of porous granular marine sediments," J. Acoust. Soc. Am. 120, 699-710 (2006)]. In this study, the modified gap stiffness model is reinvestigated and approximated expressions are derived for low- and high-frequency ranges. In particular, experimental validation of the BIMGS model is carried out. First, for glass beads and beach sands, the modified gap stiffness at a high frequency is experimentally obtained as a function of the grain size. Second, by using the measured values of the longitudinal wave velocities in the glass beads with two types of alcohol-water-mixed liquids, it is validated that the frame bulk modulus is a linear function of the fluid bulk modulus and that the frame bulk modulus is dependent on frequency, which can be derived from the BIMGS model. Finally, for applying the BIMGS model, it is shown that the reported velocity dispersion and the frequency dependence of attenuation, which cannot be explained by using the Biot-Stoll model with a constant frame bulk modulus, can be explained.     

Switching mechanics with chemistry: a model for the bending stiffness of amphiphilic bilayers with interacting headgroups in crystalline order

Bilayer structures in catanionic systems experimentally showed peculiar mechanical behavior. The observed increase in the bending stiffness is supposedly connected to additional hydrogen bonds forming between anionic headgroups. With a simple model, we can explain the extreme sensitivity of the bending stiffness of the membrane on the molar ratio of the charged molecules. This effect is further amplified by the sandwichlike structure of the membrane, where the apolar core separating the headgroups acts via a kind of lever-arm principle. As a consequence of these combined effects, the model membrane changes from a soft behavior with bending rigidities on the order of 10k(B)T to an extremely stiff membrane with a bending stiffness more than 2 orders of magnitude larger where most of this change occurs within a molar ratio interval smaller than 0.1.     

Information-Corrected Estimation: A Generalization Error Reducing Parameter Estimation Method

Modern computational models in supervised machine learning are often highly parameterized universal approximators. As such, the value of the parameters is unimportant, and only the out of sample performance is considered. On the other hand much of the literature on model estimation assumes that the parameters themselves have intrinsic value, and thus is concerned with bias and variance of parameter estimates, which may not have any simple relationship to out of sample model performance. Therefore, within supervised machine learning, heavy use is made of ridge regression (i.e., L2 regularization), which requires the the estimation of hyperparameters and can be rendered ineffective by certain model parameterizations. We introduce an objective function which we refer to as Information-Corrected Estimation (ICE) that reduces KL divergence based generalization error for supervised machine learning. ICE attempts to directly maximize a corrected likelihood function as an estimator of the KL divergence. Such an approach is proven, theoretically, to be effective for a wide class of models, with only mild regularity restrictions. Under finite sample sizes, this corrected estimation procedure is shown experimentally to lead to significant reduction in generalization error compared to maximum likelihood estimation and L2 regularization.     

Fragmentation of grains in a two-dimensional packing

A numerical model of fragmentation of a two-dimensional granular medium under pressure is investigated. The fragmentation process is found to be strongly dependent on the type of force used as the criterion for breaking the grains. The fragmentation mode affects the process less dramatically. There is a power-law divergence in the pressure when the medium approaches the full packing limit, . Both log-normal and power-law fragment-size distributions are found. Gravity is demonstrated to be an important factor. Received: 14 December 1997 / Accepted: 17 March 1998     

Morphological phases of crumpled wire

We find that in two dimensions wires can crumple into different morphologies and present the associated morphological phase diagram. Our results are based on experiments with different metallic wires and confirmed by numerical simulations using a discrete element model. We show that during crumpling, the number of loops increases according to a power law with different exponents in each morphology. Furthermore, we observe a power law divergence of the structure's bulk stiffness similar to what is observed in forced crumpling of membranes.     

Theoretical and experimental comparison of the Soret coefficient for water-methanol and water-ethanol binary mixtures

The role played by the history of packing in the behaviour of a granular material confined in a column is studied experimentally. The mean pressure applied by the granular assembly to the base is measured as a function of the height of material poured in the column. We obtain reproducible mean vertical normal stress measurements without using a particular procedure to mobilise the wall friction. We focus on the influence of the filling method on the mean vertical normal stress. Filling the column via the edges induces a higher apparent mass of grain than filling it via the centre. Particular attention is devoted to the measurement of the effect of the force sensor stiffness. We show that the lower the base stiffness, the lower the mean pressure on the base. We also vary the packing fraction. We obtain an increasing relation between the apparent mass and the mean packing fraction, and show that this relation depends on the filling method.Received: 4 April 2004, Published online: 20 July 2004PACS: 45.70.Cc Static sandpiles; granular compaction - 81.05.Rm Porous materials; granular materials - 83.80.Fg Granular solidsM. Tixier: Mireille.Tixier@meca.uvsq.fr     

Three-dimensional nonlinear vibration of gear pairs

This work investigates the three-dimensional nonlinear vibration of gear pairs where the nonlinearity is due to portions of gear teeth contact lines losing contact (partial contact loss). The gear contact model tracks partial contact loss using a discretized stiffness network. The nonlinear dynamic response is obtained using the discretized stiffness network, but it is interpreted and discussed with reference to a lumped-parameter gear mesh model named the equivalent stiffness representation. It consists of a translational stiffness acting at a changing center of stiffness location (two parameters) and a twist stiffness. These four parameters, calculated from the dynamic response, change as the gears vibrate, and tracking their behavior as a post-processing tool illuminates the nonlinear gear response. There is a gear mesh twist mode where the twist stiffness is active in addition to the well-known mesh deflection mode where the translational stiffness is active. The twist mode is excited by periodic back and forth axial movement of the center of stiffness in helical gears. The same effect can occur in wide facewidth spur gears if tooth lead modifications or other factors such as shaft and bearing deflections disrupt symmetry about the axial centers of the mating teeth. Resonances of both modes are shown to be nonlinear due to partial and total contact loss. Comparing the numerical results with gear vibration experiments from the literature verifies the model and confirms partial contact loss nonlinearity in experiments.