Adhesion Performances Between Two Orthotropic Solids Influenced by Temperature Increment

The classical adhesive contact models belong to isothermal adhesion theories,where the effect of temperature on adhesion was neglected.However,a number of experimental results indicated that the adhesion behaviors can be significantly affected by temperature.In this paper,the two-dimensional non-slipping anisothermal adhesion behaviors between two orthotropic elastic cylinders are investigated within the framework of the Johnson-Kendall-Roberts theory.The stated problem is reduced to the coupled singular integral equations by virtue of the Fourier integral transform,which are solved analytically with the analytical function theory.The closed-form solutions for the stress fields in the presence of thermoelastic effect are obtained.The stable equilibrium state of contact system is determined by virtue of the Griffith energy balance.The effect of temperature difference on adhesion behaviors between orthotropic solids is discussed.It is found that the difference between the oscillatory and non-oscillatory solutions increases with increasing the degree of anisotropy of orthotropic materials.The oscillatory solution cannot be well approximated by the non-oscillatory solution for the orthotropic materials with relatively high anisotropy.     

Adhesive contact on power-law graded elastic solids: The JKR–DMT transition using a double-Hertz model

A cohesive zone model of axisymmetric adhesive contact between a rigid sphere and a power-law graded elastic half-space is established by extending the double-Hertz model of Greenwood and Johnson (1998). Closed-form solutions are obtained analytically for the surface stress, deformation fields and equilibrium relations among applied load, indentation depth, inner and outer radii of the cohesive zone, which include the corresponding solutions for homogeneous isotropic materials and the Gibson solid as special cases. These solutions provide a continuous transition between JKR and DMT type contact models through a generalized Tabor parameter μ$\mu$. Our analysis reveals that the magnitude of the pull-off force ranges from (3+k)πRΔγ/2$(3+k)\pi R\mathrm{\Delta }\gamma /2$ to 2πRΔγ$2\pi R\mathrm{\Delta }\gamma$, where k$k$, R$R$ and Δγ$\mathrm{\Delta }\gamma$ denote the gradient exponent of the elastic modulus for the half-space, the radius of the sphere and the work of adhesion, respectively. Interestingly, the pull-off force for the Gibson solid is found to be identically equal to 2πRΔγ,$2\pi R\mathrm{\Delta }\gamma ,$ independent of the corresponding Tabor parameter. The obtained analytical solutions are validated with finite element simulations.     

Investigation on effect of drag models on flow behavior of power-law fluid–solid two-phase flow in fluidized bed

In this study, a Eulerian-Eulerian two-fluid model combined with the kinetic theory of granular flow is adopted to simulate power-law fluid–solid two-phase flow in the fluidized bed. Two new power-law liquid–solid drag models are proposed based on the rheological equation of power-law fluid and pressure drop. One called model A is a modified drag model considering tortuosity of flow channel and ratio of the throat to pore, and the other called model B is a blending drag model combining drag coefficients of high and low particle concentrations. Predictions are compared with experimental data measured by Lali et al., where the computed porosities from model B are closer to the measured data than other models. Furthermore, the predicted pressure drop rises as liquid velocity increases, while it decreases with the increase of particle size. Simulation results indicate that the increases of consistency coefficient and flow behavior index lead to the decrease of drag coefficient, and particle concentration, granular temperature, granular pressure, and granular viscosity go down accordingly.     

任意轴对称弹性体吸附接触的广义Maugis模型

通过线性叠加Sneddon方法和Lowengrub-Sneddon方法分别给出的解, 得到了一个弹性半空间轴对称混合边值问题的一般解,进而研究了两个一般轴对称弹性体的正向无摩擦吸附接触问题. 考虑任意有效的表面形状(要求中心部分首先进入接触)和任意的表面吸附作用,推广得到了广义Maugis模型. 该模型是一个半解析的模型,它可以分解成表面形状和表面吸附作用的分别独立影响的两部分,以及一个关联变形和吸附作用的式子. 利用Dugdale模型近似表面吸附作用,得到了具有任意有效的表面形状的广义M-D模型. 它在强吸附或软材料条件下的极限形式是广义JKR模型,而在弱吸附或硬材料下的另一个极限形式是广义DMT模型.     

Adhesive contact between a rigid nanofiber and an incompressible elastic substrate

Adhesive contact between a rigid nanofiber and an incompressible elastic substrate is studied. A new expression of adhesive pressure, which accounts for the exact geometry of the fiber and the deformation of the substrate, is derived from the elementary Lennard–Jones (L–J) potential. This enables that the phenomenon of adhesion saturation for small fiber radii is predicted in a natural way. Numerical computations also show the validity of the well-known Derjaguin’s approximation in a quite broad region down to fiber radii of a few nanometers. These results are expected useful for such applications as nanoindentation, nanopunch, and bio-inspired adhesion.     

Asymptotic models of contact interaction among elliptic punches on a semiclassical foundation

Consideration is given to the contact without friction among an arbitrary number of elliptic punches or punches in the form of an elliptic paraboloid and an elastic half-space with Young's modulus as a power-law function of the distance from the edge. Asymptotic models of contact interaction are designed assuming that the distance between punches is large compared with their dimensions __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 78–96, January 2006.     

On the contact width in generalized plain strain JKR model for isotropic solids

Adhesive contact model between an elastic cylinder and an elastic half space is studied in the present paper, in which an external pulling force is acted on the above cylinder with an arbitrary direction and the contact width is assumed to be asymmetric with respect to the structure. Solutions to the asymmetric model are obtained and the effect of the asymmetric contact width on the whole pulling process is mainly discussed. It is found that the smaller the absolute value of Dundurs＇ parameter 13 or the larger the pulling angle O, the more reasonable the symmetric model would be to approximate the asymmetric one.     

A Whitham–Boussinesq long-wave model for variable topography

We study the propagation of water waves in a channel of variable depth using the long-wave asymptotic regime. We use the Hamiltonian formulation of the problem in which the non-local Dirichlet–Neumann operator appears explicitly in the Hamiltonian, and propose a Hamiltonian model for bidirectional wave propagation in shallow water that involves pseudo-differential operators that simplify the variable-depth Dirichlet–Neumann operator. The model generalizes the Boussinesq system, as it includes the exact dispersion relation in the case of constant depth. Analogous models were proposed by Whitham for unidirectional wave propagation. We first present results for the normal modes and eigenfrequencies of the linearized problem. We see that variable depth introduces effects such as a steepening of the normal modes with the increase in depth variation, and a modulation of the normal mode amplitude. Numerical integration also suggests that the constant depth nonlocal Boussinesq model can capture qualitative features of the evolution obtained with higher order approximations of the Dirichlet–Neumann operator. In the case of variable depth we observe that wave-crests have variable speeds that depend on the depth. We also study the evolutions of Stokes waves initial conditions and observe certain oscillations in width of the crest and also some interesting textures and details in the evolution of wave-crests during the passage over obstacles.     

Contact Problems for Prestressed Elastic Bodies and Rigid and Elastic Punches

Contact problems for prestressed bodies and rigid and elastic punches are discussed. The influence of the prestresses on the contact characteristics is analyzed numerically     

The relation between a microscopic threshold-force model and macroscopic models of adhesion

This paper continues our recent work on the relationship between discrete contact interactions at the microscopic scale and continuum contact interactions at the macroscopic scale(Hulikal et al., J. Mech. Phys. Solids 76,144–161, 2015). The focus of this work is on adhesion. We show that a collection of a large number of discrete elements governed by a threshold-force based model at the microscopic scale collectively gives rise to continuum fracture mechanics at the macroscopic scale. A key step is the introduction of an efficient numerical method that enables the computation of a large number of discrete contacts. Finally,while this work focuses on scaling laws, the methodology introduced in this paper can also be used to study roughsurface adhesion.     

Thermoelastic State of a Transversely Isotropic Layer between Two Annular Punches

A technique is developed to solve contact problems for annular punches interacting with a transversely isotropic layer. The contact problem for two heated annular punches interacting with a layer is solved. The formulas for the contact stresses under the punches are derived, and the effect of the shape of the punches on the magnitude and distribution of these stresses is analyzed     

A unified treatment of axisymmetric adhesive contact problems using the harmonic potential function method

A unified treatment of axisymmetric adhesive contact problems is provided using the harmonic potential function method for axisymmetric elasticity problems advanced by Green, Keer, Barber and others. The harmonic function adopted in the current analysis is the one that was introduced by Jin et al. (2008) to solve an external crack problem. It is demonstrated that the harmonic potential function method offers a simpler and more consistent way to treat non-adhesive and adhesive contact problems. By using this method and the principle of superposition, a general solution is derived for the adhesive contact problem involving an axisymmetric rigid punch of arbitrary shape and an adhesive interaction force distribution of any profile. This solution provides analytical expressions for all non-zero displacement and stress components on the contact surface, unlike existing ones. In addition, the newly derived solution is able to link existing solutions/models for axisymmetric non-adhesive and adhesive contact problems and to reveal the connections and differences among these solutions/models individually obtained using different methods at various times. Specifically, it is shown that Sneddon’s solution for the axisymmetric punch problem, Boussinesq’s solution for the flat-ended cylindrical punch problem, the Hertz solution for the spherical punch problem, the JKR model, the DMT model, the M-D model, and the M-D-n model can all be explicitly recovered by the current general solution.