General Relationship Between Contact Stiffness, Contact Depth, and Mechanical Properties for Indentation in Linear Viscoelastic Solids Using Axisymmetric Indenters of Arbitrary Profiles

We derive a relationship between the initial unloading slope, contact depth, and the instantaneous relaxation modulus for indentation in linear viscoelastic solids by a rigid indenter with an arbitrary axisymmetric smooth profile. Although the same expression is well known for indentation in elastic and in elastic-plastic solids, we show that it is also true for indentation in linear viscoelastic solids, provided that the unloading rate is sufficiently fast. Furthermore, the same expression holds true for both fast loading and unloading. These results should provide a sound basis for using the relationship for determining properties of viscoelastic solids using indentation techniques.

On the non-linear stability theory of spinning solid bodies with liquid-filled cavities and its application to the columbus problem

In this paper, we first present a system of differential-integral equations for the largedisturbance to the general case that any arbitrarily shaped solid body with a cavity contain-ing viscous liquid rotates uniformly around the principal axis of inertia, and then develop aweakly non-linear stability theory by the Lyapunov direct approach. Applying this theoryto the Columbus problem, we have proved the consistency between the theory and Kelvin'sexperiments.

Strengthening carbon deposition of polyolefin using combined catalyst as a general method for improving fire retardancy

Combination of Ni2O3 and solid acid with Bronsted acid sites and Lewis acid sites (such as HZSM-5 and H-beta) could dramatically improve fire retardancy of polyolefin, including polypropylene and linear low-density polyethylene. This is mainly attributed to the formation of a large amount of residual char from degradation products of polyolefin in the intermediate stage of combustion. Thus, the amount of flammable components diffusing into the flame zone was small.

THE GENERAL AN INDEX AND ITS APPLICATION .4. THE APPLICATION OF GENERAL AN INDEX TO HYDROCARBONS

The general a(N) index (GAI) was used to characterize the cis, trans isomers of hydrocarbons. The best one-variable equations were obtained with GAI for several physicochemical properties of seven pairs of olefin cis, trans isomers. The linear correlation coefficients are in the range of 0.975 to 0.997. GAI was also compared with the other five topological indices, Randic connectivity index chi, Wiener number W, Hosoya index Z, the average distance sum connectivity J proposed by Balaban and a(N) index introduced by Yang, in correlating with the octane number (MON) of heptanes and octanes.

Dielectric response of graded composites having general power-law-graded cylindrical inclusions

The dielectric response of graded composites having general power-law-graded cylindrical inclusions under a uniform applied electric field is investigated. The dielectric profile of the cylindrical inclusions is modeled by the equation epsilon(i)(r)=c(b+r)(k) (where r is the radius of the cylindrical inclusions and c, b and k are parameters). Analytical solutions for the local electrical potentials are derived in terms of hypergeometric functions and the effective dielectric response of the graded composites is predicted in the dilute limit. Moreover, for a simple power-law dielectric profile epsilon(i)(r) = cr(k) and a linear dielectric profile epsilon(i)(r) = c(b + r), analytical expressions of the electrical potentials and the effective dielectric response are derived exactly from our results by taking the limits b -> 0 and k -> 1, respectively. For a higher concentration of inclusions, the effective dielectric response is estimated by an effective-medium approximation. In addition, we have discussed the effective response of graded cylindrical composites with a more complex dielectric profile of inclusion, epsilon(i)(r)=c(b+r)(k)e(beta r). (c) 2005 American Institute of Physics.

Effective dielectric responses of graded composites of the particles with a general power-law gradation profile

The effective dielectric response of graded spherical composites having general power-law gradient inclusions is investigated under a uniform applied electric field, where the dielectric gradation profile of the spherical inclusions is modeled by the equation epsilon(i) (r) = c(b+r)(k). Analytical solutions of the local electrical potentials are derived in terms of hyper-geometric function and the effective dielectric response of the graded composites is predicted in the dilute limit. From our result, the local potentials of graded spherical composites having both simple power-law dielectric profile epsilon(i)(r) = cr(k) and linear dielectric profile epsilon(i) (r) = c(b+r) are derived exactly by taking the limits b --> 0 and k --> 1, respectively. In the dilute limit, our exact result is used to test the validity of differential effective dipole approximation (DEDA) for estimating the effective response of graded spherical composites, and it is shown that the DEDA is in excellent agreement with exact result. (C) 2005 Elsevier B.V. All rights reserved.

Effective response of a non-linear composite in external AC electric field

A general effective response is proposed for nonlinear composite media, which obey a current field relation of the form J = sigmaE + chi\E\(2) E when an external alternating current (AC) electrical field is applied. For a sinusoidal applied field with finite frequency omega, the effective constitutive relation between the current density and electric field can be defined as, = sigma(e) + chi(e) <\E(x, omega, t)\(2) E(x, omega, t)> + (. . .), where sigma(e) and chi(e) are the general effective linear and nonlinear conductive responses, respectively. The angled brackets <(. . .)> denotes the ensemble average. As two examples, we have investigated the cylindrical and spherical inclusions embedded in a host and also derived the formulae of the general effective linear and nonlinear conductive responses in dilute limit. For higher volume fraction of inclusions, we have proposed a nonlinear effective medium approximation (EMA) method to estimate the general effective response of nonlinear composites in external AC field. Furthermore, the effective nonlinear responses at harmonics are predicted by using the general effective response. (C) 2002 Elsevier Science B.V. All rights reserved.

Linear solvation energy relationships regarding sorption and retention properties of hydrophobic organic compounds in soil leaching column chromatography

The capacity factors of a series of hydrophobic organic compounds (HOCs) were measured in soil leaching column chromatography (SLCC) on a soil column, and in reversed-phase liquid chromatography on a C-18 column with different volumetric fractions (phi) of methanol in methanol-water mixtures. A general equation of linear solvation energy relationships, log(XYZ) = XYZ(0) + mV(1)/100 + spi* + bbeta(m) + aalpha(m), was applied to analyze capacity factors (k'), soil organic partition coefficients (K-oc) and octanol-water partition coefficients (P). The analyses exhibited high accuracy. The chief solute factors that control log K-oc, log P, and log k' (on soil and on C-18) are the solute size (V-1/100) and hydrogen-bond basicity (beta(m)). Less important solute factors are the dipolarity/polarizability (pi*) and hydrogen-bond acidity (alpha(m)). Log k' on soil and log K-oc have similar signs in four fitting coefficients (m, s, b and a) and similar ratios (m:s:b:a), while log k' on C-18 and log P have similar signs in coefficients (m, s, b and a) and similar ratios (m:s:b:a). Consequently, log k' values on C-18 have good correlations with log P (r > 0.97), while log k' values on soil have good correlations with log K-oc (r > 0.98). Two K-oc estimation methods were developed, one through solute solvatochromic parameters, and the other through correlations with k' on soil. For HOCs, a linear relationship between logarithmic capacity factor and methanol composition in methanol-water mixtures could also be derived in SLCC. (C) 2002 Elsevier Science Ltd. All rights reserved.