Rheological Behaviour for Polymer Melts and Concentrated Solutions Part Ⅰ:A New Multiple Reptation Model to Predict the Nonlinear Visco-elasticity with Nagai Chain Constraints in Entangled Polymer Melts

An approach of stochastically statistical mechanics and a unified molecular theory of nonlinear viscoelasticity with constraints of Nagai chain entanglement for polymer melts have been proposed. A multimode model structure for a single polymer chain with n tail segments and N reversible entanglement sites on the test polymer chain is developed. Based on the above model structure and the mechanism of molecular flow by the dynamical reorganization of entanglement sites, the probability distribution function of the end-to-end vectr for a single polymer chain at entangled state and the viscoelastic free energy of deformation for polymer melts are calculated by using the method of the stochastically statistical mechanics. The four types of stress-strain relation and the memory function are derived from this thery. The above theoretical relations are verified by the experimentaf data for various polymer melts. These relations are found to be in good agreement with the experimental results

HEMORRHEOLOGY, VISCO-ELASTICITY AND THIXOTROPY IN CEREBRAL THROMBOSIS

In this study, we used blood rheometer type HT-I to determine blood viscosity, plasma viscosity, hematocrit, blood red cell visco-elasticity and thixotropy in 70 cases with cerebral thrombosis, compared with normal control group in order to study the relationship between their alteration and cerebral thrombosis blood and plasma viscosity were higher in the patients than in normal control. Hysteresis loop analysis showed that the red blood cell’s visco-elasticity, thixotropy and deformity decrease.

THEORY OF VISCO-ELASTICITY FOR SATURATED POROUS BODY

The analogy method (introduced by E.H. Lee in 1955) between elastic and visco-elastic solid bodies has been extended to the saturated porous body. With the extended method, the 1-dimensional consolidation problems of variable and constant loadings have been solved. Starting from simple conditions, complicated problems of visco-elastic porous bodies are solved, such as the problem of visco-elastic beam and plate on a visco-elastic foundation. Therefore, the visco-elastic theory of saturated porous bodies has been substantiated with the extended analogy method.

谐和与有界噪声联合参激作用下的Visco-Elastic系统

研究了带visco＿elastic项的非线性系统,在谐和与有界噪声联合参激作用下的响应和稳定性问题· 用多尺度法分离了系统的快变项,并求出了系统的最大Liapunov指数和稳态概率密度函数,根据最大Liapunov指数可得系统解稳定的充分必要条件· 讨论了系统的visco＿elastic项对系统阻尼项和刚度项的贡献。

Rayleigh-type wave propagation in incompressible visco-elastic media under initial stress

Propagation of Rayleigh-type surface waves in an incompressible visco-elastic material over incompressible visco-elastic semi-infinite media under the effect of initial stresses is discussed. The dispersion equation is determined to study the effect of differ- ent types of parameters such as inhomogeneity, initial stress, wave number, phase velocity, damping factor, visco-elasticity, and incompressibility on the Rayleigh-type wave prop- agation. It is found that the affecting parameters have a significant effect on the wave propagation. Cardano＇s and Ferrari＇s methods are deployed to estimate the roots of dif- ferential equations associated with layer and semi-infinite media. The MATHEMATICA software is applied to explicate the effect of these parameters graphically.

The Equilibrium of Fractional Derivative and Second Derivative: The Mechanics of a Power-Law Visco-Elastic Solid

This paper investigates the equilibrium of fractional derivative and 2nd derivative, which occurs if the original function is damped (damping of a power-law viscoelastic solid with viscosities η of 0 ≤ η ≤ 1), where the fractional derivative corresponds to a force applied to the solid (e.g. an impact force), and the second derivative corresponds to acceleration of the solid’s centre of mass, and therefore to the inertial force. Consequently, the equilibrium satisfies the principle of the force equilibrium. Further-more, the paper provides a new definition of under- and overdamping that is not exclusively disjunctive, i.e. not either under- or over-damped as in a linear Voigt model, but rather exhibits damping phases co-existing consecutively as time progresses, separated not by critical damping, but rather by a transition phase. The three damping phases of a power-law viscoelastic solid—underdamping, transition and overdamping—are characterized by: underdamping—centre of mass oscillation about zero line;transition—centre of mass reciprocation without crossing the zero line;overdamping—power decay. The innovation of this new definition is critical for designing non-linear visco-elastic power-law dampers and fine-tuning the ratio of under- and overdamping, considering that three phases—underdamping, transition, and overdamping—co-exist consecutively if 0 < η < 0.401;two phases—transition and overdamping—co-exist consecutively if 0.401 < η < 0.578;and one phase— overdamping—exists exclusively if 0.578 < η < 1.

Heat and Mass Transfer in MHD Visco-Elastic Fluid Flow through a Porous Medium over a Stretching Sheet with Chemical Reaction

This paper presents the study of convective heat and mass transfer characteristics of an incompressible MHD visco-elastic fluid flow immersed in a porous medium over a stretching sheet with chemical reaction and thermal stratification effects. The resultant governing boundary layer equations are highly non-linear and coupled form of partial differential equations, and they have been solved by using fourth order Runge-Kutta integration scheme with Newton Raphson shooting method. Numerical computations are carried out for the non-dimensional physical parameters. Here a numerical has been carried out to study the effect of different physical parameters such as visco-elasticity, permeability of the porous medium, magnetic field, Grashof number, Schmidt number, heat source parameter and chemical reaction parameter on the flow, heat and mass transfer characteristics.

Vibration of Visco-Elastic Parallelogram Plate with Parabolic Thickness Variation

The main objective of the present investigation is to study the vibration of visco-elastic parallelogram plate whose thickness varies parabolically. It is assumed that the plate is clamped on all the four edges and that the thickness varies parabolically in one direction i.e. along length of the plate. Rayleigh-Ritz technique has been used to determine the frequency equation. A two terms deflection function has been used as a solution. For visco-elastic, the basic elastic and viscous elements are combined. We have taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here the elastic element means the spring and the viscous element means the dashpot. The assumption of small deflection and linear visco-elastic properties of “Kelvin” type are taken. We have calculated time period and deflection at various points for different values of skew angles, aspect ratio and taper constant, for the first two modes of vibration. Results are supported by tables. Alloy “Duralumin” is considered for all the material constants used in numerical

Effect of Non-Homogeneity on Thermally Induced Vibration of Orthotropic Visco-Elastic Rectangular Plate of Linearly Varying Thickness

The analysis presented here is to study the effect of non-homogeneity on thermally induced vibration of orthotropic visco-elastic rectangular plate of linearly varying thickness. Thermal vibrational behavior of non-homogeneous rectangular plates of variable thickness having clamped boundary conditions on all the four edges is studied. For non–homogeneity of the plate material, density is assumed to vary linearly in one direction. Using the method of separation of variables, the governing differential equation is solved. An approximate but quite convenient frequency equation is derived by using Rayleigh-Ritz technique with a two-term deflection function. Time period and deflection at different points for the first two modes of vibration are calculated for various values of temperature gradients, non- homogeneity constant, taper constant and aspect ratio. Comparison studies have been carried out with non-homogeneous visco-elastic rectangular plate to establish the accuracy and versatility.

ONE-DIMENSIONAL CONSOLIDATION OF LAYERED AND VISCO-ELASTIC SOILS UNDER ARBITRARY LOADING

Based on the layered visco-elastic soil model, according to the Terzaghi's one dimensional consolidation theory, by the method of Laplace transform and matrix transfer technique, the problems about the consolidation of layered and saturated visco-elastic soils under arbitrary loading were solved. Through deductions, the general solution, in the terms of layer thickness, the modulus and the coefficients of permeability and Laplacian transform's parameters was obtained. The strain and deformation of the layered and saturated visco-elastic soils under arbitrary loading can be calculated by Laplace inversion. According to the results of several numerical examples, the consolidation of visco-elastic soils logs behind that of elastic soils. The development of effective stress and the displacement is vibrant process under cyclic loading. Finally, an engineering case is studied and the results prove that the methods are very effective.

Visco-elastic fluid flow past an infinite vertical porous plate in the presence of first-order chemical reaction

An analysis has been developed to study the unsteady free convection flow of an incompressible visco-elastic fluid on a continuously moving vertical porous plate in the presence of a first-order chemical reaction. The governing equations are solved numerically using an implicit finite difference technique. The obtained numerical solutions are compared with the analytical solutions. The velocity profiles are presented. A parametric analysis is performed to illustrate the influences of the visco-elastic parameter, the dimensionless chemical reaction parameter, and the plate moving velocity on the steady state velocity profiles, the time dependent friction coefficient, the Nusselt number, and the Sherwood number.

Thermal Effect on Free Vibration of Non-Homogeneous Orthotropic Visco-Elastic Rectangular Plate of Parabolically Varying Thickness

A simple model presented here is to study the thermal effect on vibration of non-homogeneous orthotropic visco-elastic rectangular plate of parabolically varying thickness having clamped boundary conditions on all the four edges. For non-homogeneity of the plate material, density is assumed to vary linearly in one direction. Using the separation of variables method, the governing differential equation has been solved for vibration of non-homogeneous orthotropic viscoelastic rectangular plate. An approximate frequency equation is derived by using Rayleigh-Ritz technique with a two-term deflection function. Results are calculated for time period and deflection at different points, for the first two modes of vibration, for various values of temperature gradients, non-homogeneity constant, taper constant and aspect ratio and shown by graphs.

A HYBRID FEM ALGORTHM FOR FLUID FLOW IN A VISCO-ELASTIC PIPE

A variational principle of hybrid FEM is proposed to solve the flow in a visco-elaslic pipe. As an example, the influence of an axisymmetrical stenosis on an artery vibrating flow with a single frequency is calculated.

Heat and Mass Transfer in Visco-Elastic Fluid through Rotating Porous Channel with Hall Effect

This paper examined the hydromagnetic boundary layer flow of viscoelastic fluid with heat and mass transfer in a vertical channel with rotation and Hall current. A constant suction and injection is applied to the plates. A strong magnetic field is applied in the direction normal to the plates. The entire system rotates with uniform angular velocity (Ω), about the axis perpendicular to the plates. The governing equations are solved by perturbation technique to obtain an analytical result for velocity, temperature, concentration distributions and results are presented graphically for various values of viscoelastic parameter (K2), Prandtl number (Pr), Schmidt number (Sc), radiation parameter (R), heat generation parameter (Qh) and Hall parameter (m).

NONLINEAR DYNAMICAL CHARACTERISTICS OF PILES UNDER HORIZONTAL VIBRATION

The pile-soil system is regarded as a visco-elastic half-space embedded pile. Based on the method of continuum mechanics, a nonlinear mathematical model of pile-soil interaction was established-a coupling nonlinear boundary value problem. Under the case of horizontal vibration, the nonlinearly dynamical characteristics of pile applying the axis force were studied in horizontal direction in frequency domain. The effects of parameters, especially the axis force on the stiffness were studied in detail. The numerical results suggest that it is possible that the pile applying an axis force will lose its stability. So,the effect of the axis force on the pile is considered.

COMPUTER SIMULATION OF CREEP DAMAGE AT CRACK TIP IN SHORT FIBRE COMPOSITES

Creep damage at crack tip in short fibre composites has been sim- ulated by using the finite element method(FEM).The well-known Schapery non- linear viscoelastic constitutive relationship was used to characterize time-dependent behaviour of the material.A modified recurrence equation was adopted to accelerate the iteration.Kachanov-Rabotnov's damage evolution law was employed.The growth of the damage zone with time around the crack tip was calculated and the results were shown with the so-called 'digit photo',which was produced by the printer.

Viscoelastic properties of wood from Chinese-fir and poplar plantations

Elastic and strength properties （proportional-limit stress （O＇prop）, Young＇s modulus （E）, breaking stress （O＇max） in static bending parallel to grain in a longitudinal direction）, as well as stress relaxation in air-dried condition and water-saturated conditions at seven different constant temperatures and increasing and decreasing temperatures were investigated for wood from Chinese-fir and poplar plantations. The results show that hygrothermal conditions considerably affect these mechanical properties. The higher the moisture content （MC） or temperature, the lower the strength of wood. Further investigation of the effects of constant temperature on stress relaxation indicates that high temperature specimens have low relaxation moduli and high fluidity. In the case of increasing temperature the range of the modulus of relaxation is larger than in the case of a reduction in temperature, while the residual moduli do not show large differences. This is because the modulus at high temperatures decreases more than that at low temperatures. The fluidity of specimens in a state of water desorption increases slowly at the beginning, increases quickly until the MC reaches an equilibrium moisture content （EMC） and then becomes stable, which is quite different from that in a water-saturated state. Fluidity in a desorption state is much higher than in a water-saturated state. This is probably due to the fact that the former is in an unstable state which can be interpreted as a state with internal strain and has therefore a greater potential to release strain.

An explicit finite element－finite difference method for analyzing the effect of visco－elastic local topography on the earthquake motion

An explicit finite element-finite difference method for analyzing the effects of two-dimensional visco-elastic localtopography on earthquake ground motion is prOPosed in this paper. In the method, at first, the finite elementdiscrete model is formed by using the artificial boundary and finite element method, and the dynamic equationsof local nodes in the discrete model are obtained according to the theory of the special finite element method similar to the finite difference method, and then the explicit step-by-step integration formulas are presented by usingthe explicit difference method for solving the visco-elastic dynamic equation and Generalized Multi-transmittingBoundary. The method has the advantages of saving computing time and computer memory space, and it is suitable for any case of topography and has high computing accuracy and good computing stability.

A METHOD FOR THE ANALYSIS OF DYNAMIC RESPONSE OF STRUCTURE CONTAINING NON-SMOOTH CONTACTABLE INTERFACES

A novel single-step method is proposed for the analysis of dynamic response of visco-elastic structures containing non-smooth contactable interfaces. In the method, a two-level algorithm is employed for dealing with a nonlinear boundary condition caused by the dynamic contact of interfaces. At the first level, an explicit method is adopted to calculate nodal displacements of global viscoelastic system without considering the effect of dynamic contact of interfaces and at the second level, by introducing contact conditions of interfaces, a group of equations of lower order is derived to calculate dynamic contact normal and shear forces on the interfaces. The method is convenient and efficient for the analysis of problems of dynamic contact. The accuracy of the method is of the second order and the numerical stability condition is wider than that of other explicit methods.

Dynamic earth pressure on rigid retaining walls induced by a neighboring machine foundation,by the meshless local Petrov-Galerkin method

Dynamic earth pressure induced by machine foundations on a neighboring retaining wall is analyzed with emphasis on factors which control the intensity and location of the design forces. The meshless local Petrov-Galerkin (MLPG) method is used to analyze the problem for a variety of retaining wall and machine foundation geometries. The soil medium is assumed to be homogeneous and visco-elastic. The machine foundation is idealized as a harmonic sinusoidal dynamic force often encountered in practice. A number of analyses have been made to reveal the effect of the loading frequency, the location and size of the foundation and the soil shear wave velocity on the distribution and magnitude of the dynamic earth pressure. Results indicate that there is a critical frequency and a critical location for which the passive pressure takes the maxima in the entire duration of the dynamic load.