Long-term aging effects on the rheology of neat laponite and laponite–PEO dispersions

We observe aging behavior of neat laponite systems over the course of 1,000 or more days. Under basic conditions, low laponite concentrations (1 wt%) slowly evolve from a viscoelastic liquid to a glass made of clusters acting as constituent elements interacting via long-range repulsion. Higher concentrations of laponite (3 wt%) quickly form a glass of individual particles. Intermediate concentrations of laponite form a glass that is a combination of clusters and individual particles. The aging rheological response and upturn of the loss modulus at low frequencies are well predicted by models of soft glassy systems (Fielding et al., J Rheol, 44(2):323–369, 2000; Sollich, Phys Rev E, 58(1):738–759, 1998). If low amounts of high-molecular-weight (M _n ≥ 163 kg/mol) poly(ethylene oxide) (PEO) are added, the aging behavior follows the dynamical response of the clay. Above a critical ratio, φ, of the free polymer chains in solution to the total laponite surface area, the PEO dynamics dominate at high frequencies. It appears that the dynamics of these complex laponite-PEO systems are governed by the parameter φ.     

New insights on free energies and Saint-Venant’s principle in viscoelasticity

Explicit expressions for the minimum free energy of a linear viscoelastic material and Noll’s definition of state are used here to explore spatial energy decay estimates for viscoelastic bodies, in the full dynamical case and in the quasi-static approximation.In the inertial case, Chirita et al. obtained a certain spatial decay inequality for a space–time integral over a portion of the body and over a finite time interval of the total mechanical energy. This involves the work done on histories, which is not a function of state in general. Here it is shown that for free energies which are functions of state and obey a certain reasonable property, the spatial decay of the corresponding space–time integral is stronger than the one involving the work done on the past history. It turns out that the bound obtained is optimal for the minimal free energy.Two cases are discussed for the quasi-static approximation. The first case deals with general states, so that general histories belonging to the equivalence class of any given state can be considered. The continuity of the stress functional with respect to the norm based on the minimal free energy is proved, and the energy measure based on the minimal free energy turns out to obey the decay inequality derived Chirita et al. for the quasi-static case.The second case explores a crucial point for viscoelastic materials, namely that the response is influenced by the rate of application of loads. Quite surprisingly, the analysis of this phenomenon in the context of Saint-Venant principles has never been carried out explicitly before, even in the linear case. This effect is explored by considering states, the related histories of which are sinusoidal. The spatial decay parameter is shown to be frequency-dependent, i.e. it depends on the rate of load application, and it is proved that of those considered, the most conservative estimate of the frequency-dependent decay is associated with the minimal free energy. A comparison is made of the results for sinusoidal histories at low frequencies and general histories.     

An experimental study of the first normal stress difference — shear stress relationship in simple shear flow for concentrated shear thickening suspensions

For many polymeric solutions in a simple shear flow a plot of the logarithm of the first normal stress difference N ₁ against the logarithm of the shear stress , for a range of temperatures results in a linear relationship. For such polymer solutions these plots yield a straight line of slope very close to 2 when measured at low shear rates. This relationship is tested against a polymer solution (polyacrylamide in a 50/50 mixture of glycerol/water), a polymer melt (polyethylene), and three concentrated suspensions. These are Superclay (supplied by English China Clays, Cornwall, U.K.) in water, polyvinylchloride in dioctylphthalate and polystyrene latex in water, at volume concentrations of 40% 48%, and 60%, respectively. It was found that the log N ₁ — log relationship is applicable to the polymer solution and melt over a significant range of shear rates and temperatures. In the cases of concentrated suspensions the relationship holds to the point of onset of the shear thickening behaviour. Beyond this point a different relationship exists, however, flow instabilities are apparent. A comment on the contribution of N ₁ and N ₂ to the flow instabilities is made.     

New Progress on Fine Particles in China

~~New Progress on Fine Particles in China     

New Green’s function for stress field and a note of its application in quantum-wire structures

The elastic field caused by the lattice mismatch between the quantum wires and the host matrix can be modeled by a corresponding two-dimensional hydrostatic inclusion subjected to plane strain conditions. The stresses in such a hydrostatic inclusion can be effectively calculated by employing the Green’s functions developed by Downes and Faux, which tend to be more efficient than the conventional method based on the Green’s function for the displacement field. In this study, Downes and Faux’s paper is extended to plane inclusions subjected to arbitrarily distributed eigenstrains: an explicit Green’s function solution, which evaluates the stress field due to the excitation of a point eigenstrain source in an infinite plane directly, is obtained in a closed-form. Here it is demonstrated that both the interior and exterior stress fields to an inclusion of any shape and with arbitrarily distributed eigenstrains are represented in a unified area integral form by employing the derived Green’s functions. In the case of uniform eigenstrain, the formulae may be simplified to contour integrals by Green’s theorem. However, special care is required when Green’s theorem is applied for the interior field. The proposed Green’s function is particularly advantageous in dealing numerically or analytically with the exterior stress field and the non-uniform eigenstrain. Two examples concerning circular inclusions are investigated. A linearly distributed eigenstrain is attempted in the first example, resulting in a linear interior stress field. The second example solves a circular thermal inclusion, where both the interior and exterior stress fields are obtained simultaneously.     

Wall material and roughness effects on transmittable shear stresses of magnetorheological fluids in plate–plate magnetorheometry

A direct comparison of plate–plate magnetorheometry results for nonmagnetic (titanium/brass) and ferromagnetic plates is presented, using a modified Anton Paar magnetocell MRD180/1T. Necessary corrections to derive the true flux density in the magnetorheological fluid (MRF) from the online Hall probe reading and to account for the gap opening effect caused by normal forces on shear stress and flux density are addressed. The measured shear stress versus magnetic flux density characteristics agree in the low flux density regime <0.1 T but yield distinctly higher transmittable shear stresses for ferromagnetic plates at elevated flux densities (49% increase at 1 T for 90% by weight carbonyl iron powder (CIP) and 84% for 85% by weight CIP). Remarkably, the normal force, if corrected for its magnetostatic part, remains independent of the type of plates up to about 0.6 T. We address the role of normal forces, of magnetic interactions between CIP and wall, as well as the role of wall roughness in a solid body friction model. A systematic variation of wall properties and materials was achieved by introducing both a modular rotor and stator, which ease the variation of the walls in contact to the MRF. The transmittable shear stress of nonmagnetic plates (e.g., brass) may be increased up to the level of ferromagnetic disks by a higher wall roughness or by grooves. No shear stress increase is obtained for grooves in ferromagnetic plates, which is explained by the different local flux density modulation at the grooves for ferromagnetic compared to nonmagnetic plates. Finally, we address the effect of ferromagnetic and nonmagnetic coatings on brass and steel disks, and show that, e.g., a layer of CIP on brass efficiently increases the transmittable shear stress.     

Average and extremal properties of heat transfer and shear stress on a wall surface in Rayleigh–Bénard convection

In this study surface-averaged and extremal properties of heat transfer and shear stress on the upper wall surface of Rayleigh–Bénard convection are numerically examined. The Prandtl number was raised up to 10³, and the Rayleigh number was changed between 10⁴ and 10⁷. As a result, average Nusselt number Nu and shear rate τ/Pr depends on Pr, Ra, and the entire numerical results are distributed between two correlation equations corresponding to small and large Pr. The small and large Pr equations are closely related to steady and unsteady flow regimes, respectively. Nevertheless, a single relation τ/Pr ~ Nu ^3.0 exists to explain the entire results. Similarly the change of local maximal properties Nu _max and τ _max/Pr depends on Pr, Ra, and these values are also distributed between two correlation equations corresponding to small and large Pr cases. Despite such complicated dependence we can obtain a correlation equation as a form of τ _max/Pr ~ Nu _max^2.6, which has not been obtained theoretically.     

Granular pressure—temperature relation during regime change in a simple shear state

In a recent study, a regime chart was established for sheared granular systems. For a soft particle system under simple shear, the internal stress showed a range of rate dependency. As the particle concentration increased, the system transitioned from a kinetic gas to a plastic solid. This transition was gradual for low stiffness systems but became more abrupt as the stiffness increased. In this study, the relationship between the granular temperature and pressure is investigated for the same system of particles. The granular temperature is defined as the average kinetic energy per unit volume and the pressure is defined as the trace of the stress tensor. It is found that this pressure-temperature (P-T curve depicts a sharp turn when the system moves away from the kinetic gas regime. However, no signature is found in the P-T relationship in other regimes.     

Theoretical research on rotational dispersion coefficient of fiber in turbulent shear flow of fiber suspension

The rotational dispersion coefficient of the fiber in the turbulent shear flow of fiber suspension was studied theoretically. The function of correlation moment between the different fluctuating velocity gradients of the flow was built firstly. Then the expression, dependent on the characteristic length, time, velocity and a dimensionless parameter related to the effect of wall, of rotational dispersion coefficient is derived. The derived expression of rotational dispersion coefficient can be employed to the inhomogeneous and non-isotropic turbulent flows. Furthermore it can be expanded to three-dimensional turbulent flows and serves the theoretical basis for solving the turbulent flow of fiber suspension.     

Comment on “A theorem for a shear stress-free plane boundary in Stokes flow”

The results proved in a recent paper by Akhtar and Sen [Mech. Res. Commun. 38 (2011) 529–531] are not new and are already known in the literature. In fact, the main expressions – presented in the form of a theorem – in the cited article follow as a special case of the more general results for a two-fluid Stokes flow with a planar interface proved earlier by Palaniappan [Acta Mechanica 139 (2000) 1–13]. We briefly demonstrate the reduction of particular cases of the solution given by Palaniappan which also reveals the duplication of another special solution elsewhere.     

Slurry flow in horizontal pipes—experimental and modeling

The hydraulic transport of coarse particles in horizontal tubes has been investigated. A physical model for the prediction of the pressure drop and flow patterns is presented. The proposed model is compared with new experimental data and shows good agreement. Comparison with other proposed correlations is also satisfactory.     

Adiabatic shear banding in high speed machining of Ti–6Al–4V: experiments and modeling

An experimental analysis of orthogonal cutting of a Ti–6Al–4V alloy is proposed. Cutting speeds are explored in a range from 0.01 to 73 m/s by using an universal high-speed testing machine and a ballistic set-up. The evolution of the cutting force in terms of the cutting speed and the development of adiabatic shear banding are analyzed. The shear band width and the distance between bands have been determined by micrographic observations. Their dependence upon the cutting velocity is analyzed. A modeling is proposed which restitutes well this velocity dependence.     

The Relationship between Structural Model Design Competition and Innovation on Mechanics—Structure Course Groups in Applied Civil Engineering

介绍了结构模型设计制作的基本过程, 阐述了开展模型竞赛与土木工程专业应用型人才体系的关系. 在此基础上, 从强化实践力学$\!$-$\!$-$\!$结构课程体系、改革课程内容、设置开放性实践环节等方面阐述了构建创新性、应用型人才培养体系的思路, 并通过教学实例加以分析.     

Weakly R-KKM mappings——intersection theorems and minimax inequalities in topological spaces

In this paper, we introduce the concepts of weakly R-KKM mappings, R-convex and ,R-β-quasiconvex in general topological spaces without any convex structure. Relating to these, we obtain an extension to general topological spaces of Fan's matching theorem, namely that Lemma 1.2 in this paper. On this basis, two intersection theorems are proved in topological spaces. By using intersection theorems, some minimax inequalities of Ky Fan type are also proved in topological spaces. Our results generalize and improve the corresponding results in the literature.     

New ANCF solid-beam element: relationship with Bézier volume and application on leaf spring modeling

Acta Mechanica Sinica - An eight-node solid-beam element based on absolute nodal coordinate formulation (ANCF) which uses cubic interpolation at the longitudinal direction and linear at the...