Capillarity driven instability of a soft solid

We report the observation of a Plateau instability in a thin filament of solid gel with a very small elastic modulus. A longitudinal undulation of the surface of the cylinder reduces its area thereby triggering capillary instability, but is counterbalanced by elastic forces following the deformation. This competition leads to a nontrivial instability threshold for a solid cylinder. The ratio of surface tension to elastic modulus defines a characteristic length scale. The onset of linear instability is when the radius of the cylinder is one-sixth of this length scale, in agreement with theory presented here.     

Differential growth and instability in elastic shells

Differential growth in elastic materials can produce stress either through incompatibility of growth or by interaction with the surrounding medium. In many situations, this stress can be sufficient to induce shape instability in the growing medium. To gain better insight in growth-induced instabilities, the growth of an elastic shell loaded with hydrostatic pressure or embedded in an elastic medium is studied. The residual stress arising from the incompatibility of growth and the contact stress arising from the interaction with the surrounding medium are computed with respect to growth and geometric parameters and critical values for instability are obtained. Depending on these parameters, different modes of instability can be obtained.     

Anomalous elasticity and anelasticity of GdCu at low temperatures

The temperature dependence of the single crystal and polycrystalline elastic constants of GdCu compound have been determined between the ambient and 77 K, the interval in which the structural instability occurs. From the shear constants, C' and C₄₄ the magnitude of the elastic anisotropy was calculated, and found to be close to unity over the whole temperature range. This is in contrast with the expected behavior of the elastic anisotropy in the vicinity of martensitic transformations, where the anisotropy attains appreciable values. The large changes of the shear elastic constants, relative to the compressional constant suggests that the structural instability in GdCu is induced by a mechanism of isotropic shear. The peak in the ultrasonic attenuation is symmetric, typical of a relaxational process. The behavior of the elastic properties and ultrasonic attenuation in the temperature interval of the structural instability of GdCu is discussed.     

Confinement-induced instability and adhesive failure between dissimilar thin elastic films

When two thin soft elastomeric films are separated from each other, an elastic instability develops at the interface. Although similar instability develops for the case of a soft film separating from a rigid adherent, there are important differences in the two cases. For the single-film case, the wavelength of instability is independent of any material properties of the system, and it scales only with thickness of the film. For the two-film case, a co-operative instability mode develops, which is a non-linear function of the thicknesses and the elastic moduli of both films. We investigate the development of such instability by energy minimization procedures. Understanding the nature of this instability is important, as it affects the adhesive compliance of the system and thus the energy release rate in the debonding of soft interfaces.     

黏性流体中超细长弹性杆的动力学不稳定性

基于坐标基矢摄动的方法研究了黏性流体中超细长弹性杆动力学稳定性判据与失稳后的模态选择,推导出了黏性介质中超细长弹性杆Kirchoff动力学方程的一阶摄动表示,即线性的二阶偏微分方程组.以平面扭转DNA环为例,说明了以上结果的应用,得到了平面扭转DNA环的稳定性判据及其稳定的临界区域,讨论了其失稳后的模态选择及黏性阻力对其的影响.     

Instability of the origami of a ferrofluid drop in a magnetic field

Capillary origami is the wrapping of a usual fluid drop by a planar elastic membrane due to the interplay between capillary and elastic forces. Here, we use a drop of magnetic fluid whose shape is known to strongly depend on an applied magnetic field. We study the quasistatic and dynamical behaviors of such a magnetic capillary origami. We report the observation of an overturning instability that the origami undergoes at a critical magnetic field. This instability is triggered by an interplay between magnetic and gravitational energies in agreement with the theory presented here. Additional effects of elasticity and capillarity on this instability are also discussed.     

Dynamic stability of Timoshenko beams resting on an elastic foundation

A finite element model is developed for the stability analysis of a Timoshenko beam resting on an elastic foundation and subjected to periodic axial loads. The effect of an elastic foundation on the natural frequencies and static buckling loads of hinged-hinged and fixed-free Timoshenko beams is investigated. The results obtained for a Bernoulli-Euler beam which is a special case of the present analysis show excellent agreement with the available results obtained by other analytical methods. The regions of dynamic instability are determined for different values of the elastic foundation constant. As the elastic foundation constant increases the regions of dynamic instability are shifted away from the vertical axis and the width of these regions is decreased, thus making the beam less sensitive to periodic forces.     

Qualitative Aspects of Melting Transition on Fractals

The melting instability on fractals is discussed qualitatively under the Lindemann's hypothesis. The density of elastic vibrational states originating from phonon and elastic fraction modes is used to calculate the mean square displacement of lattice constitutents, and the transition temperature is estimated for fractal aggregates with different dimensionalities of elastic fractons.     

Elastic modes frequencies in the mirrors with “ears” for parametric oscillatory instability in advanced LIGO interferometer

We discuss the importance of accurate numerical calculation of elastic modes in the mirrors with suspension “ears” in advanced LIGO interferometer to enable precise predictions of parametric oscillatory instability problem. We show that “ears” of test masses produce additional shift of elastic modes frequencies which is larger than relaxation rate of optical modes. These shifts may increase the possibility of parametric oscillatory instability.     

Growth induced buckling of morphoelastic rod in viscous medium

Biological growth is a common phenomenon in nature, and some organisms such as DNA molecules and bacterial filaments grow in viscous media. The growth induced instability of morphoelastic rod in a viscous medium is studied in this paper. Based on the Kirchhoff kinetic analogy method, the mechanical model for growing elastic thin rod in the viscous medium is established. A perturbation analysis is used to analyze the stability of the growing elastic rod in the viscous medium. We apply the results into planar growing ring and get its criterion of instability. Take the criterion into DNA ring to discuss the influence of viscous resistance on its instability.     

On diffusion-elastic instabilities in a solid half-space

A model of the diffusion-elastic instability that appears in an ensemble of non-equilibrium atomic defects in unbounded condensed media as well as on the free surface of a half-space is introduced and studied. The dynamical model developed here is based on coupled evolution equations for the elastic displacement of the medium and atomic defect density fields. The idea of an instability model is related to a drift of atomic defects under the influence of elastic fields. It is shown that the development of this instability creates ordered structures of coupled strain and defect-concentration fields. Dispersion relationships for the growth increment of these structures are derived and their characteristic scales are obtained.     

Elastic connection disk subjected to periodically fluctuating transmitted torque and rotational speed

Involving the intrinsic power transmission torque/speed coupling characteristics of prime-movers, a rotating elastic connection disk subjected to periodically fluctuating transmitted torque and rotational speed generated by the fluctuation of external loads is investigated. Using Galerkin's method, the rotating elastic connection disk is modeled as a parametrically excited gyroscopic system. The effects of the torque/speed coupling, transmitted torque fluctuation amplitude and frequency, and constant parts of the transmitted torque and the rotational speed on the system dynamic stability are explored for the disk modes possessing different nodal diameters. The rotational speed, transmitted torque and their fluctuations can all result in system instability of the elastic connection disk. The instability can be suppressed or avoided by operating at small amplitude and low frequency of the transmitted torque fluctuation, and by operating in the weakly coupled torque/speed regime of the prime-movers. Low rotational speed avoids the instability in the case of a small transmitted torque, but medium rotational speed operation is valuable to suppress the instability induced by a large transmitted torque and its fluctuation. Instability parameter regions for the positive and negative torque/speed coupling coefficient are roughly similar in shape, but there are some differences in the value of the instability coefficient.     

Does roughening of rock-fluid-rock interfaces emerge from a stress-induced instability?

Non-planar solid-fluid-solid interfaces under stress are very common in many industrial and natural materials. For example, in the Earth’s crust, many rough and wavy interfaces can be observed in rocks in a wide range of spatial scales, from undulate grain boundaries at the micrometer scale, to stylolite dissolution planes at the meter scale. It is proposed here that these initially flat solid-fluid-solid interfaces become rough by a morphological instability triggered by elastic stress. A model for the formation of these unstable patterns at all scales is thus presented. It is shown that such instability is inherently present due to the uniaxial stress that promotes them, owing to the gain in the total elastic energy: the intrinsic elastic energy plus the work of the external forces. This is shown explicitly by solving the elastic problem in a linear stability analysis, and proved more generally without having resort to the computation of the elastic field.     

Granular elasticity without the Coulomb condition

A self-contained elastic theory is derived which accounts both for mechanical yield and shear-induced volume dilatancy. Its two essential ingredients are thermodynamic instability and the dependence of the elastic moduli on compression.     

Resonant interaction of elastic oscillations of a thin plate with a hydrodynamic flow

It is demonstrated that the wind instability in a nonuniform flow with a velocity profile can give rise to elastic oscillations of a thin plate with a characteristic wavelength. The dispersion relations and the instability increment with a maximum in the long-wavelength range are obtained. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 77–80, July, 2007.     

Magnetorotational-type instability in Couette-Taylor flow of a viscoelastic polymer liquid

We describe an instability of viscoelastic Couette-Taylor flow that is directly analogous to the magnetorotational instability (MRI) in astrophysical magnetohydrodynamics, with polymer molecules playing the role of magnetic field lines. By determining the conditions required for the onset of instability and the properties of the preferred modes, we distinguish it from the centrifugal and elastic instabilities studied previously. Experimental demonstration and investigation should be much easier for the viscoelastic instability than for the MRI in a liquid metal. The analogy holds with the case of a predominantly toroidal magnetic field such as is expected in an accretion disk, and it may be possible to access a turbulent regime in which many modes are unstable.     

Kinetic step bunching instability during surface growth

We study the step bunching kinetic instability in a growing crystal surface characterized by anisotropic diffusion. The instability is due to the interplay between the elastic interactions and the alternation of step parameters. This instability is predicted to occur on a vicinal semiconductor surface Si(001) or Ge(001) during epitaxial growth. The maximal growth rate of the step bunching increases like F4, where F is the deposition flux. Our results are complemented with numerical simulations which reveal a coarsening behavior in the long time evolution for the nonlinear step dynamics.     

Parametric oscillatory instability on axially-symmetrical test mass elastic modes in Advanced LIGO interferometer

We discuss the importance of accurate calculation of axially-symmetrical elastic modes frequencies and forms in test masses (mirrors) of Advanced LIGO interferometer using the method of superposition to analyse the effect of parametric oscillatory instability. This method consists in possibility to construct analytical expressions for partial solutions of media motion equation in the cylindrical coordinates which allow to satisfy all zero boundary conditions. Obtained results allow to predict more exactly (in comparison with numerical calculations) the number of combinations of optical and elastic modes that can create undesirable effect of parametric oscillatory instability.     

Numerical calculations of elastic modes frequencies for parametric oscillatory instability in Advanced LIGO interferometer

We discuss the importance of accurate numerical calculation of elastic modes in the mirrors of Advanced LIGO to enable precise predictions of the problem of parametric oscillatory instability. We propose accuracy estimations through use of analytical solutions based on Chree-Lamb modes. Small deviations from cylindrical test mass shape may produce splitting of non-axial symmetric elastic modes into doublets. This splitting may increase the possibility of parametric oscillatory instability.     

Resonant Interaction of an Air Flow with Bending Vibrations of a Finite Elastic Plate

Russian Physics Journal - Resonant interaction of an elastic plate with an air bypassing it and leading to the development of a wind instability is studied. The dispersive equation of bending...