Instability of Streaming Viscoelastic Fluids in the Presence of ��Effective Interfacial Tension�� Through Porous Medium

The ??effective interfacial tension?? effect on the instability of the plane interface between two uniform, superposed, and streaming Rivlin?CEricksen viscoelastic fluids through a porous medium is considered. The case of two uniform streaming Rivlin?CEricksen viscoelastic fluids separated by a horizontal boundary is studied. In the absence of ??effective interfacial tension??, stability/instability of the system as well as perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming if the perturbations in the direction of streaming are ignored, whereas for perturbations in all other directions, there exists instability for a certain wave number range. ??Effective interfacial tension?? is able to suppress this Kelvin?CHelmholtz instability for small wavelength perturbations, the medium porosity reduces the stability range given in terms of a difference in streaming velocities.     

Aerodynamic characteristics of solid particles�� acceleration by shock waves

In this study, the interaction of a planar shock wave with a group of particles has been investigated using high-speed photography and dynamic pressure measurements. Experiments were carried out in a horizontal circular shock tube. The influence of the particle loading ratio, particle diameter, driving gas and shock wave Mach number on the acceleration was studied. It was found that the higher the particle loading ratio, the greater was the particle velocity. This is due to the higher driving pressure. Helium and nitrogen gases play quite different roles in acceleration. Pressure multiplication during shock wave interaction with particles also appears. Based on the experimental results, the discussion regarding partial quantitative velocities and accelerations of particle groups, as well as the attenuation factors when shock waves pass through the particles, is given.     

Analytic derivation of the Cox�CMerz rule using the MLD ��toy�� model for polydisperse linear polymers

A general constitutive formalism, the ??na?ve?? polydisperse MLD model, has been developed by Mead et al. (Macromolecules 31:7895?C7914, 1998) and Mead (Rheol Acta 46:369?C395, 2007) at both the tube coordinate level and the mathematically simplified ??toy?? level independent of the tube coordinate. The model includes constraint release generated by convection-driven chain retraction (which is equivalent to ??convective constraint release?? (CCR)), reptation, and tube contour length fluctuations. The properties of the mathematically simplified na?ve polydisperse ??toy?? MLD model are explored in linear and nonlinear steady shear flows where we analytically derive the Cox?CMerz rule relating the steady shear viscosity to the modulus of the linear viscoelastic dynamic viscosity. The Cox?CMerz rule relating the linear viscoelastic material properties and the nonlinear material properties is shown to be a direct consequence of convective constraint release. The specific feature of CCR that leads to this result is that the relaxation rate due to convective constraint release is proportional to the shear rate, $\dot{{\gamma }}$ , independent of molecular weight. The viability of this well-known empirical relationship is a direct consequence of a coincidence in the mathematical structure of the linear viscoelastic material properties and convective constraint release. There is no physical analogy or relationship between the molecular relaxation mechanisms operative in linear (diffusive relaxation) and nonlinear (convective relaxation) flow regimes. The polydisperse MLD model predictions of the individual molecular weight component contributions to the flow curve, and interpretations thereof, are effectively identical to those first postulated by Bersted (J Appl Polym Sci 19:2167?C2177, 1975, J Appl Polym Sci 20:2705?C2714, 1976). Following the theoretical developments, a limited experimental study is executed with a commercial polydisperse polystyrene melt. Nearly quantitative agreement between the polydisperse MLD theory and experimental measurements of steady-shear viscosity and dynamic moduli is achieved over a wide range of shear rates.     

The monotonicity and critical periods of periodic waves?of?the �� 6 field model

In this paper, we study the relationship between period and energy of periodic traveling wave solutions for the ?? ⁶ field model. The various topological phase portraits with periodic annulus are given by using standard phase portrait analytical technique. Some analytic behaviors (convexity, monotonicity and number of critical periods) of the period functions associated with periodic waves are investigated. We prove that the period function has exactly one critical period under certain conditions. Moreover, the numerical simulation is made. The results show that our theoretical analysis agrees with the numerical simulation.     

Fiber Remodeling During Torsion of a Fiber Reinforced Hyperelastic Cylinder��Unloading Behavior

Previous studies introduced a constitutive theory for fiber reinforced hyperelastic materials that allows the fibers to undergo microstructural changes. In this theory, increasing deformation of the matrix leads to increasing stretch of the fibers that causes their gradual dissolution. The dissolving fibers reassemble in the direction of maximum principal stretch of the matrix. The implications of the constitutive theory were first studied for two homogeneous deformations: uniaxial extension along the fibers and simple shear in the direction normal to the fibers. The constitutive theory was then used in treatment of the non-homogeneous deformation of combined axial stretch and twisting. The emphasis was on the determination of the influence of increasing axial stretch and twist on the spatial distribution of fiber dissolution and reassembly within the cylinder and also on the axial force and torque applied to the end faces of the cylinder. The present work is concerned with another aspect of combined axial stretch and twisting of the cylinder, namely unloading following dissolution and reassembly of some of the fibers. In this case, the cylinder is given an initial twist until there is an inner core of original fiber/matrix material and an outer sheath of remodeled fiber/matrix material. A condition is established that determines the combinations of axial stretch and twist that cause no additional dissolution and reassembly of fibers during unloading. It is also shown that there is a residual axial stretch and twist if the axial force and torque become zero. A numerical example illustrates this for a particular choice of matrix and fiber properties.     

Plane-Strain Problems for a Class of Gradient Elasticity Models��A Stress Function Approach

The plane strain problem is analyzed in detail for a class of isotropic, compressible, linearly elastic materials with a strain energy density function that depends on both the strain tensor ?? and its spatial gradient ???. The appropriate Airy stress-functions and double-stress-functions are identified and the corresponding boundary value problem is formulated. The problem of an annulus loaded by an internal and an external pressure is solved.     

Modified Young��s moduli of nano-materials taking into account the scale effects and vacancies

In this paper, the modified Young??s moduli in both directions are obtained for the two-dimensional single crystal body with a square lattice by using the continuum approach of continuum mechanics and taking into account only the interaction of neighboring atoms. Separately, an expression is obtained taking into account the linear defects such as vacancies. The values of effective Young??s moduli compared with the same values for an infinite crystal lattice. Analyses show that the influences of scale effects and vacancies on the Young??s moduli are considerable. In addition, it is shown that the effective Young??s moduli have three components: the macroscopic value; factors determining the scale effect; factors determining the vacancy. The last component is analogous to the parameter of the damage of the theory of fracture.     

Normal stress differences in large-amplitude oscillatory shear flow for the corotational ��ANSR�� model

Using the integral form of a nonlinear corotational model, we derive explicit analytical expressions for the zeroth, second, and fourth harmonics of the second normal stress difference in large-amplitude oscillatory shear (LAOS). This model yields an arbitrary normal stress ratio (ANSR) in any simple shearing deformation, including LAOS. This corotational ANSR model adds one parameter to the corotational Maxwell model, a time constant ?? ₀ controlling the ratio ??₂/??₁ for both the real and imaginary parts of each harmonic of the normal stress difference. The explicit analytical expressions for all harmonics of the alternating shear stress and first normal stress difference responses in LAOS match those obtained previously for the corotational Maxwell model. We evaluate the corotational ANSR model for the case of a single Maxwell relaxation time fluid.     

Optimum Young��s Modulus of a Homogeneous Cylinder Energetically Equivalent to a Functionally Graded Cylinder

For a functionally graded (FG) circular cylinder loaded by uniform pressures on the inner and the outer surfaces and Young??s modulus varying in the radial direction, we find lower and upper bounds for Young??s modulus of the energetically equivalent homogeneous cylinder. That is, the strain energies of the FG and the homogeneous cylinders are equal to each other. For a typical power law variation of Young??s modulus in the FG cylinder, it is shown that taking only two series terms, yields good values for bounds of the equivalent modulus. We also study two inverse problems. First, an investigation is made to find the radial variation of Young??s modulus in the FG cylinder, having a constant Poisson??s ratio, that gives the maximum value of the equivalent modulus. Second, the complementary problem of finding the radial variation of Poisson??s ratio in the FG cylinder, having a constant stiffness, that gives the maximum value of the equivalent modulus, is considered. It is found that the spatial variation of the elastic properties, that maximizes the equivalent modulus, depends strongly upon the external loading on the cylinder.     

The effect of rider��s passive steering impedance on?motorcycle stability: identification and analysis

Many scientific papers deal with motorcycle stability (weave and wobble modes) but very seldom they take into account the passive response of rider??s body. This paper aims at studying the interaction of the rider??s arms and torso with the handlebar and the frame. First the rider??s steering impedance is identified from experimental tests on a motorcycle riding simulator, then this information is used on a motorcycle model and the effect on straight-motion stability is investigated by eigenvalues calculation.     

Modeling and motion simulation of a three-wheeled mobile robot with front wheel driven and steered taking into account wheels�� slip

The problem of modeling of dynamics of a three-wheeled mobile robot with front wheel driven and steered is analyzed in this paper. Kinematical structure and kinematics of the robot are described. A universal methodology of analytical modeling of robot??s dynamics is applied. This methodology takes into account wheel-ground contact conditions and wheels?? slip. Its essence is the use of a contact model of deformable tire with rigid ground and division of the robot??s dynamics model into parts connected with wheels, including tire model, and with the mobile platform. The tire model used in this paper results from empirical dependencies determined during investigations of car tires. Ground geometry and type are specified in the environment model. Tire-ground interface is characterized by coefficients of friction and rolling resistance. The robot model takes into account the presence of friction in kinematical pairs. The model of servomotors is included as well. The important part of this work is simulation research performed using Matlab/Simulink package. Simulation research includes solving of the forward and inverse dynamics problems as well as the tracking control task. During simulations, the robot was moving on concrete and on a piece of ice. The simulation research enabled verification of the elaborated solutions.     

Effect of Conduction in Bottom Wall on B��nard Convection in a Porous Enclosure with Localized Heating and Lateral Cooling

Darcy-Bénard convection in a square porous enclosure with a localized heating from below and lateral cooling is studied numerically in the present paper. A finite-thickness bottom wall is locally heated, the top wall is kept at a lower temperature than the bottom wall temperature, and the lateral walls are cooled. The finite difference method has been used to solve the dimensionless governing equations. The analysis in the undergoing numerical investigation is performed in the following ranges of the associated dimensionless groups: the heat source length?? ${0.2\leq H \leq 0.9}$ , the wall thickness?? ${0.05\leq D \leq 0.4}$ , the thermal conductivity ratio?? ${0.8\leq K_{\rm r} \leq 9.8}$ , and the Biot number?? ${0.1\leq Bi \leq 1.1}$ . It is observed that the heat transfer rate could increase with increasing heat source lengths, thermal conductivity ratio, and cooling intensity. There exists a critical wall thickness for a high wall conductivity below which the increasing wall thickness increases the heat transfer rate and above which the increasing wall thickness decreases the heat transfer rate.     

Mullins�� effect in semicrystalline polymers: experiments and?modeling

Experimental data are reported on isotactic polypropylene in uniaxial cyclic tensile tests with various maximum strains at room temperature. It is demonstrated that polypropylene reveals all characteristic features (hysteresis of energy, damage accumulation, and strain-hardening) of the Mullins effect. Constitutive equations are derived for the viscoplastic behavior of semicrystalline polymers at three-dimensional deformations with small strains. Adjustable parameters in the stress?Cstrain relations are found by fitting the observations. Numerical simulation shows that the model adequately predicts the viscoplastic response of polypropylene in uniaxial and biaxial cyclic tests.     

From non-linear elasticity to linear elasticity with initial stress via ��-convergence

We consider a initially stressed hyperelastic body in equilibrium in its undeformed configuration under a system of dead loads. We give sufficient conditions on the stored energy which guarantee that when the loads undergo a small perturbation, the energy functional Γ converges, after some re-scaling, to the energy functional of linear elasticity with initial stress. We also show, under stronger conditions, that quasi-minimizers of the non-linear problem converge to a minimizer of the incremental problem.     

Neural network based robust hybrid control for robotic system: an H �� approach

A novel robust hybrid tracking control for robotic system is proposed. This hybrid control scheme combines computed torque control (CTC) with neural network, variable structure control (VSC) and nonlinear H _?? control methods. It is assumed that the nominal system of robotic system is completely known, which is controlled by using CTC method. Neural network is designed to approximate parameter uncertainties, VSC is used to eliminate the effect of approximation error, and H _?? control is employed to achieve a desired robust tracking performance. Based on Lyapunov stability theorem, it can be guaranteed that all signals in closed loop are bounded and a specified H _?? tracking performance is achieved by employing the proposed robust hybrid control. The validity of the control scheme is shown by computer simulation of a two-link robotic manipulator.     

Supercritical CO2-Brine Relative Permeability Experiments in Reservoir Rocks��Literature Review and Recommendations

The relative permeability of carbon dioxide (CO₂) to brine influences the injectivity and plume migration when CO₂ is injected in a reservoir for CO₂ storage or enhanced oil recovery (EOR) purposes. It is common practice to determine the relative permeability of a fluid by means of laboratory measurements. Two principal approaches are used to obtain a relative permeability data: steady state and unsteady state. Although CO₂ has been employed in enhanced oil recovery, not much data can be found in the open literature. The few studies available report wide ranges for CO₂ relative permeability in typical sedimentary rocks such as Berea sandstone, dolomite, and others. The experimental setups vary for each study, employing steady and unsteady state approaches, different experimental parameters such as temperature, pressure, rock type, etc. and various interpretation methods. Hence, it is inherently difficult to compare the data and determine the origin of differences. It is evident that more experiments are needed to close this knowledge gap on relative permeability. This article concludes that standards for lab measurements need to be defined a. to establish a reliable CO₂-brine relative permeability measurement method that can be repeated under the same conditions in any lab and b. to enable comparison of the data to accurately predict the well injection and fluid migration behavior in the reservoir.     

Investigation of the Stability Problems of Elastic Bodies Using the Method of Mathematical Theory of Elasticity

In this paper,using the equilibrium equations and boundary conditionsof elastic stability problem of Новожилов and the method of mathematicaltheory of elasticity,we solve some elastic stability problems,which werestudied byищлинскииandвоицеховская,and obtained more reason-able results than theirs.     

Homogenization of the nonlinear Kelvin–Voigt model of viscoelasticity and of the Prager model of plasticity

Denoting by the stress tensor, by the linearized strain tensor, by A the elasticity tensor, and assuming that is a convex potential, the inclusion accounts for nonlinear viscoelasticity, and encompasses both the linear Kelvin–Voigt model of solid-type viscoelasticity and the Prager model of rigid plasticity with linear kinematic strain-hardening. This relation is assumed to represent the constitutive behavior of a space-distributed system, and is here coupled with the dynamical equation. An initial- and boundary-value problem is formulated, and the existence and uniqueness of the solution are proved via classical techniques based on compactness and monotonicity. A composite material is then considered, in which the function and the tensor A rapidly oscillate in space. A two-scale model is derived via Nguetseng’s notion of two-scale convergence. This provides a detailed account of the mesoscopic state of the system. Any dependence on the fine-scale variable is then eliminated, and the existence of a solution of a new single-scale macroscopic model is proved. The final outcome is at variance with the nonlinear extension of the generalized Kelvin–Voigt model, which is based on an apparently unjustified mean-field-type hypothesis.     

Model of Self‐Organization of an Ensemble of Cracks Radiating Sound

A model of selforganization of cracks arising in a rock specimen (granite) compressed by a press is proposed. The model is based on the assumption of acoustic wave interaction between the cracks. To construct the model of selforganization of cracks, solutions of the Fokker–Planck equation are used. The experimentally observed spontaneous increase in the activity of acoustic emission, spatial and temporal clusterization, and formation of a fractal structure in rock specimens under constant and slowly varying loads are explained.