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.     

Accurate measurement of Poisson's ratio in small samples

A method is described whereby Poisson's ratio was measured in metallic and plastic materials to an accuracy of ±0.003 (3σ limits). A size limitation was imposed in that the test specimens had to be manufactured from a 50.8 mm (2 in.)-diam bar with the maximum stress direction across a diameter.     

闭孔泡沫铝的塑性泊松比

在表征闭孔泡沫铝的力学性能中,塑性泊松比是较为重要的参数之一。本文应用Kelvin十四面体模型构建出不同相对密度的闭孔泡沫铝三维细观模型并采用LS-DYNA对所得细观模型进行单轴准静态压缩计算。数值模拟分析发现,随着轴向应变的增加,泡沫铝泊松比-轴向应变曲线呈倒S形,存在峰值和极小值,曲线变化规律与泡沫铝胞孔的变形有密切关系。根据泊松比-轴向应变曲线与胞孔变形之间的关系,给出了平均塑性泊松比的定义。计算结果显示,随着相对密度的提高,闭孔泡沫铝的平均塑性泊松比增大。当闭孔泡沫铝的相对密度低于0.1时,其平均塑性泊松比接近于零,计算中可以忽略;当闭孔泡沫铝相对密 度大于0.1时,其平均塑性泊松比随相对密度的增加而呈线性从0.17增加到0.5     

Elastic-modulus variations in concrete

This paper presents the results of an experimental study to determine the variations of axial strains in concrete under a uniform uniaxial stress. Surface-bonded and especially developed embeddable-strain-gage units are used for measuring axial strains in concrete specimens of rectangular cross sections. The test results show that the elastic modulus in compression increases with the distance from the nearest specimen face, said increase reaching about 60 percent in this investigation. These results are confirmed by tests on drilled core cylinders obtained from the test specimens. The variations in the elastic modulus are explained by the decrease in the cement content with the distance from the nearest specimen face. Recommendations for further investigations are given.     

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.     

Independence of Poisson's ratio in classical elastostatics with generalized boundary conditions

Elastic states solving the general boundary value problem of classical elasticity, and being partially or completely independent of Poisson's ratio, are characterized in terms of conditions on the accompanying dilatation field.     

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.     

Determination of young's modulus or Poisson's ratio using eddy currents

Combined a-c and d-c magnetic fields cause strains in a conducting sample. The amplitude of this strain is dependent on the value of Young's modulus and Poisson's ratio. The strain amplitude, being in the order of 10 pm, can be measured with a stabilized Michelson interferometer, described elsewhere.^1,2 An expression is derived, relating the axial strain in cylindrical samples to the magnetic-field quantities, the elastic properties and the electrical resistivity of the sample. The finite-element method is used to treat more complicated configurations. Samples of aluminum, copper, gold and tin are used for comparing the measured and calculated results. To this end, the elastic properties of the copper samples were also determined from measurement of the ultrasonic-wave velocity. The agreement between both methods is very satisfactory.     

Note on the expansion in powers of Poisson's ratio of solutions in elastostatics

In this paper we examine the power-series development with respect to Poisson's ratio of the solution to the second boundary-value problem (surface tractions prescribed) in three-dimensional classical elastostatics for the case of vanishing body forces. The individual terms of this expansion, by means of steady-state thermoelasticity theory, are found to admit an independent physical interpretation. This interpretation, in turn, permits certain conclusions concerning the dependence upon the elastic constants of solutions to space problems. In particular, it is shown that for a body of arbitrary connectivity all stresses are independent of the elastic constants if and only if the dilatation (and the mean normal stress) is a linear function of the cartesian coordinates. The feasibility of successive approximations of solutions appropriate to sufficiently small values of Poisson's ratio is also considered.The results communicated in this paper were obtained in the course of an investigation conducted under Contract Nonr 562(25) of Brown University with the Office of Naval Research, Washington, D.C.     

Interpretation of experimental data for Poisson's ratio of highly nonlinear materials

The Poisson's ratio of a material is strictly defined only for small strain linear elastic behavior. In practice, engineering strains are often used to calculate Poisson's ratio in place of the mathematically correct true strains with only very small differences resulting in the case of many engineering amterials. The engineering strain definition is often used even in the inelastic region, for example, in metals during plastic yielding. However, for highly nonlinear elastic materials, such as many biomaterials, smart materials and microstructured materials, this convenient extension may be misleading, and it becomes advantageous to define a strainvarying Poisson's function. This is analogous to the use of a tangent modulus for stiffness. An important recent application of such a Poisson's function is that of auxetic materials that demonstrate a negative Poisson's ratio and are often highly strain dependent. In this paper, the importance of the use of a Poisson's function in appropriate circumstances is demonstrated. Interpretation methods for coping with error-sensitive data or small strains are also described.     

负泊松比蜂窝材料的动力学响应及能量吸收特性

针对传统正方形蜂窝,通过用更小的双向内凹结构胞元替代原蜂窝材料的结构节点,得到了一种具有负泊松比特性的节点层级蜂窝材料模型。利用显式动力有限元方法,研究了冲击荷载作用下该负泊松比蜂窝结构的动力学响应及能量吸收特性。研究结果表明,除了冲击速度和相对密度,负泊松比蜂窝材料的动力学性能亦取决于胞元微结构。与正方形蜂窝相比,该负泊松比层级蜂窝材料的动态承载能力和能量吸收能力明显增强。在中低速冲击下,试件表现为拉胀材料明显的"颈缩"现象,并展示出负泊松比材料独特的平台应力增强效应。基于能量吸收效率方法和一维冲击波理论,给出了负泊松比蜂窝材料的密实应变和动态平台应力的经验公式,以预测该蜂窝材料的动态承载能力。本文的研究将为负泊松比多胞材料冲击动力学性能的多目标优化设计提供新的设计思路。     

泡沫金属的微惯性效应和动态塑性泊松比

采用三维Voronoi技术和显式有限元方法来研究闭孔和开孔两种泡沫金属的动态塑性泊松比问题和微惯性效应。细观数值模拟的结果表明:塑性泊松比随着轴向应变的增加而下降,塑性泊松比的峰值随着冲击速度的增加而下降;相对密度增加时,泡沫金属塑性泊松比增加;微惯性对平台应力的影响不大。该数值模拟结果能够解释侧向约束情况下闭孔泡沫金属的压溃应力随着加载速率的提高而下降的实验现象。     

The homogenization method for the study of variation of Poisson's ratio in fiber composites

Summary Materials with specific microstructural characteristics and composite structures are able to exhibit negative Poisson's ratio. This fact has been shown to be valid for certain mechanisms, composites with voids and frameworks and has recently been verified for microstructures optimally designed by the homogenization approach. For microstructures composed of beams, it has been postulated that nonconvex shapes (with reentrant corners) are responsible for this effect. In this paper, it is numerically shown that mainly the shape, but also the ratio of shear-to-bending rigidity of the beams do influence the apparent (phenomenological) Poisson's ratio. The same is valid for continua with voids, or for composites with irregular shapes of inclusions, even if the constituents are quite usual materials, provided that their porosity is strongly manifested. Elements of the numerical homogenization theory and first attempts towards an optimal design theory are presented in this paper and applied for a numerical investigation of such types of materials. Received 11 March 1997; accepted for publication 12 September 1997     

Effects of orthotropy and variation of Poisson's ratio on the behaviour of tubes in pure flexure

The behaviour of tubes under conditions of pure bending is investigated for the cases where the material of which they are constructed is either orthotropic or of various Poisson's ratios. Large deflections and moderate nonlinear strains are considered and the modelling incorporates Timoshenko beam theory thereby allowing non-zero shear strains to develop. This in turn makes axially inhomogeneous deformation of the cross-section possible and, in particular, the compressed side can develop wrinkling. Numerical solutions are presented for various material types and tube dimensions and some interesting phenomena, such as mode interaction and jumping, are demonstrated.     

Analytical parametric analysis of the contact problem of human buttocks and negative Poisson's ratio foam cushions

Analytical investigations on the contact problems between two homogeneous and isotropic soft bodies were performed to simulate the contact of human buttocks and seat cushions. The cushion materials' Poisson's ratio were allowed to be negative. The human buttocks were modeled as an ideal sphere with radius 15 cm, and assumed to have a low Young's modulus and a Poisson's ratio close to 0.5. These parameters were held constant during our analysis. Peak contact pressure was reduced by adjusting the contour curvature of cushions according to Hertz theory, as expected. Moreover, analysis by both the Hertz model and a finite thickness 3D elasticity model showed that using negative Poisson's ratio cushions could further reduce the pressure. Negative Poisson's ratio cushions may be beneficial in the prevention of pressure sores or ulcers in the sick and in reduction of pressure-induced discomfort in seated people.     

Measuring Poisson's ratios in wood

Poisson's ratios and Young's moduli were measured for five sugar pine (Pinus lambertiana Douglas) boards in a plane delineated by the grain direction and a tangent to the growth increments. One test specimen per board was loaded in a direction parallel to the grain; a second one was loaded perpendicular to the grain in the tangential direction. Test results from four of the five boards fulfilled theoretical expectations with a maximum deviation of ±8 percent for the quotients of Poisson's ratios divided by Young's moduli. Linear relationships were found to exist between the rate of stress parallel to the load, the rate of strain parallel to the load, and the rate of strain perpendicular to the load. With increasing magnitudes of strain rate, values for Poisson's ratios and Young's moduli approached limit values. It was speculated that at least some of the elastic constants are time dependent. However, the term in the equations which describes that property had large errors.     

Effective elastic moduli of a soft medium with hard polygonal inclusions and extremal behavior of effective Poisson's ratio

We consider two-dimensional, two-phase, elastic composites consisting of a soft isotropic medium into which hard elastic inclusions have been placed, requiring that the inclusions be interconnected only at corner points. Denoting by the ratio of Young's modulus for the soft and hard phases, we show that the leading term in the asymptotic expansion as 0 for the effective moduli can be calculated from a finite-dimensional algebraic minimization problem. For several composites with either hexagonal symmetry or orthotropic symmetry, we explicitly solve this algebraic problem. In particular, from the above constituents we construct an isotropic material with maximal positive Poisson's ratio, as well as an orthotropic material with Poisson's ratio less than –1. We also recover in a simple way, Milton's isotropic composite with Poisson's ratio close to –1.     

Near-zero Poisson's ratio and suppressed mechanical anisotropy in strained black phosphorene/SnSe van der Waals heterostructure: a first-principles study

Black phosphorene (BP) and its analogs have attracted intensive attention due to their unique puckered structures, anisotropic characteristics, and negative Poisson's ratio. The van der Waals (vdW) heterostructures assembly by stacking different materials show novel physical properties, however, the parent materials do not possess. In this work, the first-principles calculations are performed to study the mechanical properties of the vdW heterostructure. Interestingly, a near-zero Poisson's ratio v_zx is found in BP/SnSe heterostructure. In addition, compared with the parent materials BP and SnSe with strong in-plane anisotropic mechanical properties, the BP/SnSe heterostructure shows strongly suppressed anisotropy. The results show that the vdW heterostructure has quite different mechanical properties compared with the parent materials, and provides new opportunities for the mechanical applications of the heterostructures.