Three-dimensional analytical elasticity solution for loaded functionally graded coated half-space

In the present paper, a three-dimensional problem of elasticity of normal and tangential loading of surface of the functionally graded coated half-space is considered. In case when Poisson's ratio is constant and the Young's modulus is a power or exponential function of the distance from the surface of the half-space, analytical solution using Fourier transform is obtained. Stress field due to Hertz contact pressure in an elliptical region are studied as a function of the parameter b/a (where a and b are axes of the contact ellipse) and coating thickness.     

Waterhammer modelling of viscoelastic pipes with a time-dependent Poisson's ratio

Poisson's ratio in viscoelastic materials is a function of time. However, recently developed waterhammer models of viscoelastic pipes consider it constant. This simplifying assumption avoids cumbersome calculations of double convolution integrals which appear if Poisson's ratio is time-dependent. The present research develops a mathematical model taking the time dependency of Poisson's ratio into account for linear viscoelastic pipes. Poisson's ratio is written in terms of relaxation function and bulk modulus which is assumed to be constant. The relaxation function is obtained from creep function given as the viscoelastic property data of pipe material. The results obtained from the present waterhammer model are compared with the experimental data for two different flow rates. The comparison reveals that with the application of the time-dependent Poisson's ratio and unsteady friction, the viscoelastic data of mechanical tests can directly be used for waterhammer analysis with less need for the calibration of the flow configuration. It was also shown that the creep curve calibrated based on the present model is closer to the actual creep curve than that calibrated based on previous models.     

EFFECTS OF POISSON’S RATIO ON SCALING LAW IN HERTZIAN FRACTURE

In this paper the Auerbach＇s scaling law of Hertzian fracture induced by a spherical indenter pressing on a brittle solid is studied. In the analysis, the singular integral equation method is used to analyze the fracture behavior of the Hertzian contact problem. The results show that the Auerbach＇s constant sensitively depends on the Poisson＇s ratio, and the effective Auerbach＇s domain is also determined for a given value of the Poisson＇s ratio.     

Vibration of thick auxetic plates

This short communication investigates the effect of negative Poisson's ratio on the natural frequency of thick plates of arbitrary shape. Using the Mindlin plate theory, it was generally found that as the plate's Poisson's ratio becomes more negative, the Mindlin-to-Kirchhoff natural frequency ratio increases with decreasing rate. Upon comparing (a) the use of the simplified constant shear correction factor and the more accurate variable shear correction factor, (b) with and without rotary inertia, it was found that all the four combinations stated in (a) and (b) do not give appreciable difference when the Poisson's ratio of the plate is positive. However in the case of plates with negative Poisson's ratio, results reveal that when at least one of the simplifying assumptions is used, the Mindlin-to-Kirchhoff natural frequency ratio is overestimated, and that the overestimation further increases when both the simplifying assumptions are used. When benchmarked against Reddy plate theory, the use of variable shear correction factor has almost the same effect as the inclusion of rotary inertia. Hence the use of either variable shear correction factor or rotary inertia is proposed for modeling the vibrational frequencies of conventional and auxetic isotropic plates.     

A class of auxetic three-dimensional lattices

We propose a class of auxetic three-dimensional lattice structures. The elastic microstructure can be designed to have an omnidirectional Poisson's ratio arbitrarily close to the stability limit of −1. The cubic behaviour of the periodic system has been fully characterized; the minimum and maximum Poisson's ratio and the associated principal directions are given as a function of the microstructural parameters.The initial microstructure is then modified into a body-centred cubic system that can achieve Poisson's ratio lower than −1 and that can also behave as an isotropic three-dimensional auxetic structure.     

Effect of rolling friction on wall pressure,discharge velocity and outflow of granular material from a flat-bottomed bin

The present paper provides both experimental and DEM analyses of the filling and discharge of pea grains from a 3D flat-bottomed bin. In the DEM model, the fixed mean values of the experimentally determined single particle data, such as the particle density, Young's modulus, Poisson's ratio as well as the sliding and rolling friction coefficients were incorporated to analyse their effects on the macroscale indicators, such as the wall pressure, discharge velocities and material outflow parameters. The effect of rolling friction was studied based on the experimentally measured single particle rolling friction coefficient. This analysis is aimed at the quantitative prediction of flow parameters as related to the identification of material parameters.     

The elastic contact of two disks by the method of caustics

An experimental technique based on the optical method of caustics for the solution of the two-dimensional problem of a narrow contact between two elastic disks was developed. In particular, an elliptical pressure distribution of the Hertz type was assumed, as well as a rectilinear contact form according to Muskhelishvili's solution. The method presents the advantage of yielding directly the contact length, from which the load applied on the disks can be readily evaluated.     

Two-dimensional sliding frictional contact of functionally graded materials

A multi-layered model for sliding frictional contact analysis of functionally graded materials (FGMs) with arbitrarily varying shear modulus under plane strain-state deformation has been developed. Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into several sub-layers and in each sub-layers the shear modulus is assumed to be a linear function while the Poisson's ratio is assumed to be a constant. In the contact area, it is assumed that the friction is one of Coulomb type. With this model the fundamental solutions for concentrated forces acting perpendicular and parallel to the FGMs layer surface are obtained. Then the sliding frictional contact problem of a functionally graded coated half-space is investigated. The transfer matrix method and Fourier integral transform technique are employed to cast the problem to a Cauchy singular integral equation. The contact stresses and contact area are calculated for various moving stamps by solving the equations numerically. The results show that appropriate gradual variation of the shear modulus can significantly alter the stresses in the contact zone.     

Winkler地基模型上功能梯度材料涂层的摩擦接触问题

研究Winker地基模型上功能梯度材料涂层在一刚性圆柱形冲头作用下的摩擦接触问题。功能梯度材料涂层表面作用有法线向和切线向集中作用力。假设材料非均匀参数呈指数形式变化,泊松比为常量,利用Fourier积分变换技术将求解模型的接触问题转化为奇异积分方程组,再利用切比雪夫多项式对所得奇异积分方程组进行数值求解。最后,给出了功能梯度材料非均匀参数、摩擦系数、Winker地基模型刚度系数及冲头曲率半径对接触应力分布和接触区宽度的影响情况。     

An analytical solution for a linear viscoelastic layer loaded with a cylindrical punch: Evaluation of the rebound indentation test with application for assessing viability of articular cartilage

A general closed-form solution for the so-called rebound indentation test’ is obtained for a cylindrical flat-ended punch indenting a linear viscoelastic layer lying on a rigid substrate. Under the assumption of time-independent Poisson's ratio, we derive closed-form analytical expressions for the contact force (in a displacement controlled regime) and for the indentation displacement (in a load-controlled regime) and we consider in detail the case of standard viscoelastic solid. Our results indicate that the rebound displacement (in other words the indentation displacement in the load-controlled stage) is independent of the relaxed elastic modulus and Poisson's ratio, and also of the layer's thickness. Our analytical solution can be used for layered samples of arbitrary materials exhibiting viscoelastic properties; however, since the rebound indentation test has been recently suggested for assessing the viability of biomedical materials, we have applied our theoretical framework to the identification of materials parameters from experiments on articular cartilage. In this context, we have found a pretty good agreement for the rebound deformation, even until the strain becomes relatively large.     

A nonlinear contact pressure distribution model for wear calculation of planar revolute joint with clearance

As various errors result from manufacture and assembly processes or wear effect, clearance joint widely exists in mechanical system as a base component. The coupling analysis of tribology and dynamics of clearance joint is important to the reliability of mechanical system. A nonlinear contact pressure distribution mode (NLCP) is proposed to combine dynamics analysis with wear calculation together in this paper. The discrete thought of Winkler model is adopted to deal with contact problem with a high conformal rate. The contact relationship in a local microcontact area can be regarded as the contact between cylinder and plane. And the local contact pressure is acquired based on Hertz contact theory. The NLCP model has not only described the nonlinear relationship between contact pressure and penetration depth, but also avoided the complexity in contact pressure computation. The performance of NLCP model is demonstrated in comparison with asymmetric Winkler model, revealing that NLCP model has enhanced the calculation accuracy with a good efficiency. A comprehensive experimental study on the wear calculation of a slider–crank mechanism with clearance joint is presented and discussed to provide an experimental verification for NLCP model. The paper’s work has solved the contact problem with a high conformal rate and has described the nonlinear relationship between contact pressure and penetration depth. It has great value to the wear analysis of clearance joint.     

Singularities in auxetic elastic bimaterials

In this paper we study the effects of negative Poisson's ratios on elastic problems containing singularities. Materials with a negative Poisson's ratio are termed auxetic. We present a brief review of such materials. The elasticity problem of a bimateral wedge is presented, then two particular cases of this problem are investigated: the free-edge problem and the interface crack problem. We study the effect on the stress singularity due to one portion of the bimaterial becoming auxetic. We find that the auxetic material has a significant effect on the singularity order, even causing the singularity to vanish for certain values of the elastic constants.     

Scaling laws of nanoporous gold under uniaxial compression: Effects of structural disorder on the solid fraction,elastic Poisson's ratio,Young's modulus and yield strength

In this work the relationship between the structural disorder and the macroscopic mechanical behavior of nanoporous gold under uniaxial compression was investigated, using the finite element method. A recently proposed model based on a microstructure consisting of four-coordinated spherical nodes interconnected by cylindrical struts, whose node positions are randomly displaced from the lattice points of a diamond cubic lattice, was extended. This was done by including the increased density as result of the introduced structural disorder. Scaling equations for the elastic Poisson's ratio, the Young's modulus and the yield strength were determined as functions of the structural disorder and the solid fraction. The extended model was applied to identify the elastic–plastic behavior of the solid phase of nanoporous gold. It was found, that the elastic Poisson's ratio provides a robust basis for the calibration of the structural disorder. Based on this approach, a systematic study of the size effect on the yield strength was performed and the results were compared to experimental data provided in literature. An excellent agreement with recently published results for polymer infiltrated samples of nanoporous gold with varying ligament size was found.     

STRENGTH CRITERION FOR PLAIN CONCRETE UNDER MULTIAXIAL STRESS BASED ON DAMAGE POISSON＇S RATIO

A new unified strength criterion in the principal stress space has been proposed for use with normal strength concrete （NC） and high strength concrete （HSC） in compressioncompression-tension, compression-tension-tension, triaxial tension, and biaxial stress states. The study covers concrete with strengths ranging from 20 to 130 MPa. The conception of damage Poisson＇s ratio is defined and the expression for damage Poisson＇s ratio is determined basically. The failure mechanism of concrete is illustrated, which points out that damage Poisson＇s ratio is the key to determining the failure of concrete. Furthermore, for the concrete under biaxial stress conditions, the unified strength criterion is simplified and a simplified strength criterion in the form of curves is also proposed. The strength criterion is physically meaningful and easy to calculate, which can be applied to analytic solution and numerical solution of concrete structures.     

Poisson's ratio determined with strain rosettes

Poisson's ratio appears in general stress-strain equations and is essential to experimental stress analysis. An experimental method using bonded electrical-resistance strain rosettes is described in this paper. The standard use of two strain sensing elements at 90 deg was replaced with “rectangular rosettes” installed back-to-back. The third strain-sensing element was used to calculate the gage alignment error and “true” longitudinal and transver e strains. For 2024-T351 sheet material, an average measured value of 0.312 for Poisson's ratio was obtained.     

On the measurement of Poisson's ratio for modeling clay

Resonance testing of Plasticine clay indicates that, for small strains (≤10^?5) in the frequency range 100–3000 Hz, the material can be considered to be a linear viscoelastic solid with parameters which depend on temperature, frequency and prior large-strain history. In order to measure Poisson's ratio, it is necessary to take special precautions to eliminate large straining between small-strain tests of different tensorial character. A simple but effective test configuration for measuring Poisson's ratio is described and test results are displayed.     

Poisson's ratio variations in concrete

This paper presents the results of an investigation relating to the variations in the Poisson's ratio in compression of concrete. An embeddable strain-gage unit has been developed for use in this investigation, and the readings from this gage unit proved quite reliable. With embeddable gage units, and surface-bonded strain gages, concrete test specimens were prepared and tested under uniform load in compression. The test results from this investigation prove that the Poisson's ratio of concrete is minimum at the faces of the test specimens, and it increases as the point moves towards the specimens' axes, where it reaches a value about 56 percent larger than that at the faces of these specimens.     

Out-of-plane modulus of semi-auxetic laminates

Materials that possess negative Poisson's ratio are termed “auxetic solids”. The out-of-plane modulus of a laminate consisting of alternating positive and negative isotropic laminas (semi-auxetic laminate) is investigated in this paper. It is herein shown that the use of the inverse rule-of-mixture for obtaining the out-of-plane Young's modulus of a laminate is valid only for conventional laminates and fully auxetic laminates. The Young's modulus by inverse rule-of mixture significantly underestimates the out-of-plane Young's modulus of a semi-auxetic laminate. It is also shown that under certain conditions, the out-of-plane Young's modulus of a semi-auxetic laminate exceeds even the direct rule-of-mixture. A correction term is developed herein for incorporation into the inverse rule-of-mixture.     

Numerical perturbation method for approximate solution of poisson's equation on a moderately deforming grid

In problems such as the computation of incompressible flows with moving boundaries, it may be necessary to solve Poisson's equation on a large sequence of related grids. In this paper the LU decomposition of the matrix A ₀ representing Poisson's equation discretized on one grid is used to efficiently obtain an approximate solution on a perturbation of that grid. Instead of doing an LU decomposition of the new matrix A , the RHS is perturbed by a Taylor expansion of A ^?1 about A ₀. Each term in the resulting series requires one ‘backsolve’ using the original LU . Tests using Laplace's equation on a square/rectangle deformation look promising; three and seven correction terms for deformations of 20% and 40% respectively yielded better than 1% accuracy. As another test, Poisson's equation was solved in an ellipse (fully developed flow in a duct) of aspect ratio 2/3 by perturbing about a circle; one correction term yielded better than 1% accuracy. Envisioned applications other than the computation of unsteady incompressible flow include: three-dimensional parabolic problems in tubes of varying cross-section, use of ‘elimination’ techniques other than LU decomposition, and the solution of PDEs other than Poisson's equation.