Experiment investigation on effects of elastic modulus on cavitation erosion of silicone rubber

Research into cavitation phenomena in various fields shows that the elastic modulus of a boundary has a potential impact on cavitation erosion. To obtain the direct relationship between the elastic modulus of the boundary and cavitiation erosion, single-layer samples with different chemical composition and moduli, and double-layer samples with different elastic moduli and the same surface layer material, were prepared with silicone rubber. The results of cavitation experiments on single-layer samples, show that the coating chemical composition and mechanical properties together affect the cavitation morphology of the coating, and dominant factors vary with erosion stage. Through the cavitation test of double-layer samples, it was found that there is a positive correlation between the elastic modulus of the coating and the degree of cavitation. This study helps us to understand the relationship between coating elastic modulus and cavitation more directly, and provides theoretical and technical guidance for the application of anti-cavitation for elastic coating in engineering.     

Finite amplitude elastic waves due to non-uniform traction at the surface of a cylindrical cavity

This paper is concerned with two spatial dimension, finite amplitude wave propagation emanating from the surface of an initially circular cylindrical cavity in an unbounded isotropic compressible isotropic hyperelastic solid. The solid is initially in the natural reference configuration and the wave propagation is due to an azimuthally non-uniform, sudden application of compressive nominal traction at the surface of the cavity. Governing equations for the problem are obtained in Lagrangian form in terms of cylindrical polar coordinates and two different classes of strain energy functions are considered. Numerical solutions, for a particular application of traction, are obtained from a fully explicit finite difference scheme. It was found that the responses to the particular application of traction differed negligibly for the various strain energy functions considered.     

The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape

The contact of an indenter of arbitrary shape on an elastically anisotropic half space is considered. It is demonstrated in a theorem that the solution of the contact problem is the one that maximizes the load on the indenter for a given indentation depth. The theorem can be used to derive the best approximate solution in the Rayleigh-Ritz sense if the contact area is a priori assumed to have a certain shape. This approach is used to analyze the contact of a sphere and an axisymmetric cone on an anisotropic half space. The contact area is assumed to be elliptical, which is exact for the sphere and an approximation for the cone. It is further shown that the contact area is exactly elliptical even for conical indenters when a limited class of Green's functions is considered. If only the first term of the surface Green's function Fourier expansion is retained in the solution of the axisymmetric contact problem, a simpler solution is obtained, referred to as the equivalent isotropic solution. For most anisotropic materials, the contact stiffness determined using this approach is very close to the value obtained for both conical and spherical indenters by means of the theorem. Therefore, it is suggested that the equivalent isotropic solution provides a quick and efficient estimate for quantities such as the elastic compliance or stiffness of the contact. The “equivalent indentation modulus”, which depends on material and orientation, is computed for sapphire and diamond single crystals.     

电磁轴承低偏置控制方式的实现

介绍了电磁轴承的基本组成，通过对电磁力的力学方程进行分析，提出了低偏置磁通控制的思想，并从功放的角度出发分析了低偏置电流工作的优点。经过仿真及实验，结果表明，这种方法对于减少功耗损失、获得满意的动态响应和高频动态性能方面是行之有效的。     

The effects of shear on delamination in layered materials

The effect of transverse shear on delamination in layered, isotropic, linear-elastic materials has been determined. In contrast to the effects of an axial load or a bending moment on the energy-release rate for delamination, the effects of shear depend on the details of the deformation in the crack-tip region. It therefore does not appear to be possible to deduce rigorous expressions for the shear component of the energy-release rate based on steady-state energy arguments or on any type of modified beam theory. The expressions for the shear component of the energy-release rate presented in this work have been obtained using finite-element approaches. By combining these results with earlier expressions for the bending-moment and axial-force components of the energy-release rates, the framework for analyzing delamination in this type of geometry has been extended to the completely general case of any arbitrary loading. The relationship between the effects of shear and other fracture phenomena such as crack-tip rotations, elastic foundations and cohesive zones are discussed in the final sections of this paper.     

Non-Newtonian effects of second-order fluids on double-layered porous Rayleigh-step bearings

Theoretical study of double-layered porous Rayleigh-step bearings with second-order fluid as lubricant is presented. An approximate method for the solutions of the governing fluid film equations for a porous region is proposed. The expressions for the pressure distribution, load capacity and frictional coefficient are obtained in compact form. Calculations of the dimensionless load capacity, frictional force and frictional coefficients are presented for specific values of the material parameters. It is found that the double porous layer yields an increase in the load capacity and ensures decrease in frictional force at the porous lining as compared with the conventional porous Rayleigh-step bearings. The maximum dimensionless load-carrying capacity is found to occur at a slightly larger step ratio as compared with the conventional porous Rayleigh-step bearings.     

Elastic and Damage Longitudinal Shear Behavior of Highly Concentrated Long Fiber Composites

The elastic and damage longitudinal shear behavior of highly concentrated long fiber composites is analyzed by means of a simplified model where it is supposed that the fibers are rigid and touch each other in a regular hexagonal array. In the microscopic unit cell the problem is reduced to six similar problems of antiplane deformation on an equilateral circular triangle (see forthcoming Figure 2). These problems are solved in closed form by the complex variable method, and the solution is used to determine the longitudinal shear moduli, and to study their dependence on the microscopic damage caused by the circumferential debonding at the fiber–matrix interface. Subsequently, the damage evolution is investigated under the hypothesis that the microcracks propagate according to the Griffiths energy criterion. The elastic domain, where there is no damage propagation, is determined and it is shown that it is a polygonal convex set symmetric with respect to the origin. The overall damage evolution is discussed in detail and illustrated with some examples which highlight the very rich nature of the proposed model.     

Thermal buckling and post-buckling of pinned–fixed Euler–Bernoulli beams on an elastic foundation

In this article, both thermal buckling and post-buckling of pinned–fixed beams resting on an elastic foundation are investigated. Based on the accurate geometrically non-linear theory for Euler–Bernoulli beams, considering both linear and non-linear elastic foundation effects, governing equations for large static deformations of the beam subjected to uniform temperature rise are derived. Due to the large deformation of the beam, the constraint forces of elastic foundation in both longitudinal and transverse directions are taken into account. The boundary value problem for the non-linear ordinary differential equations is solved effectively by using the shooting method. Characteristic curves of critical buckling temperature versus elastic foundation stiffness parameter corresponding to the first, the second, and the third buckling mode shapes are plotted. From the numerical results it can be found that the buckling load-elastic foundation stiffness curves have no intersection when the value of linear foundation stiffness parameter is less than 3000, which is different from the behaviors of symmetrically supported (pinned–pinned and fixed–fixed) beams. As we expect that the non-linear foundation stiffness parameter has no sharp influence on the critical buckling temperature and it has a slight effect on the post-buckling temperature compared with the linear one.     

A note on the extensional viscosity of elastic liquids under strong flows

In this article a parametric study based on a balance between viscous drag and restoring Brownian forces is used in order to construct a nonlinear dumbbell model with a finite spring and a drag correction for a dilute polymer solution. The constitutive equations used are reasonable approximation for describing flows of very dilute polymer solutions such as those used in turbulent drag reduction. We investigate the response of an elastic liquid under extensional flows in order to explore the roles of a stress anisotropy and of elasticity in strong flows. It is found that for low Reynolds numbers, the extensional viscosity of a dilute polymer solution is governed by two parameters: a Deborah number representing the importance of the elasticity on the flow and the macromolecule extensibility that accounts for the viscous anisotropic effects caused by the macromolecule orientation. Two different asymptotic regimes are described.The first corresponds to an elastic limit in which the extensional viscosity is a function of the Deborah number and the particle volume fraction. The second is an anisotropic regime with the extensional viscosity independent of Deborah number but strongly dependent on macromolecule aspect ratio. The analysis may explain from a phenomenological point of view why few ppms of macromolecules of high molecule weight or a small volume fraction of long fibres produce important attenuation of the pressure drop in turbulent flows. On the basis of our analysis it is seen that the anisotropic limit of the extensional viscosity caused by extended polymers under strong flows should play a key role in the attenuation of flow instability and in the mechanism of drag reduction by polymer additives.     

Hertz contact at finite friction and arbitrary profiles

Axisymmetric contact at finite Coulomb friction and arbitrary profiles is examined analytically and numerically for dissimilar linear elastic solids. Invariance and generality are aimed at and an incremental procedure is developed resulting in a reduced benchmark problem corresponding to a rigid flat indentation of an elastic half-space. The reduced problem, being independent of loading and contact region, was solved by a finite element method based on a stationary contact contour and characterized by high accuracy. Subsequently, a tailored cumulative superposition procedure was developed to resolve the original problem to determine global and local field values. Save for the influence of the coefficients of friction and contraction ratio, it is shown that at partial slip the evolving relative stick-slip contour is independent of any convex and smooth contact profile at monotonic loading. For flat and conical profiles with rounded edges and apices, results are illustrated for relations between force, depth and contact contours together with surface stress distributions. The solution for dissimilar solids in a full space is transformed to a half-space problem and solved for a combination of material parameters in order to first determine interface traction distributions. Subsequently, full field values for the two solids were computed individually. In order to predict initiation of fracture and plastic flow, results are reported for the location and magnitude of maximum tensile stress and effective stress, respectively, for a range of geometrical and material parameters. In two illustrations, predicted results are compared with experimental findings related to initiation of brittle fracture and load-depth relations at nanoindentation.