Poisson's Ratio Of Material Research Articles

Lamb Wave Basis for Impact-Echo Method Analysis

The impact-echo method has been developed over the past 20 years and is now widely used in the nondestructive evaluation of concrete. However, some practical issues remain unresolved, such as the physical basis for the empirical correction factor sbd used to obtain thickness mode frequency. A new approach based on guided wave theory is proposed in this paper: that the impact-echo resonance in plates corresponds to the zero-group-velocity frequency of the S1 Lamb mode. A numerical model is developed, verified by experiment, and then shown to adequately simulate the dynamic response of a concrete plate. Using this model the thickness resonance mode is identified and found to accurately match that particular Lamb mode in terms of shape and frequency. New values forb based on the Lamb mode model are computed and dependence on material Poisson's ratio is demonstrated.

Making and Characterizing Negative Poisson's Ratio Materials

We present an introduction to the use of negative Poisson's ratio materials to illustrate various aspects of mechanics of materials. Poisson's ratio is defined as minus the ratio of transverse strain to longitudinal strain in simple tension. For most materials, Poisson's ratio is close to 1/3. Negative Poisson's ratios are counter-intuitive but permissible according to the theory of elasticity. Such materials can be prepared for classroom demonstrations, or made by students.

Poisson's Ratio in Linear Viscoelasticity – A Critical Review

Poisson's ratio is an elastic constant defined as the ratio of thelateral contraction to the elongation in the infinitesimal uniaxialextension of a homogeneous isotropic body. In a viscoelastic materialPoisson's ratio is a function of time (or frequency) that depends on thetime regime chosen to elicit it. It is important as one of the materialfunctions that characterize bulk behavior. This paper develops the linear theory of the time- orfrequency-dependent Poisson's ratio, and it reviews work on itsexperimental determination. The latter poses severe difficulties in viewof the high accuracy required. Thus, reliable information on theviscoelastic Poisson's ratio is as yet rather scanty. The paper also reports on attempts to measure the Poisson's ratioof a viscoelastic material as a function of temperature. Lateralcontraction in creep and at constant rate of extension receivesattention as well.

MR validation of soft tissue mimicing phantom deformation as modeled by nonlinear finite element analysis.

A study of the applicability of nonlinear finite element analysis (FEA) to predict soft tissue deformation was validated with phase contrast magnetic resonance velocity imaging. A phantom of varying stiffness was placed in a special purpose, computer controlled MR compatible compression apparatus which provided precise, time varying compression with surface deformations on the order of 11%. The resulting motion was measured with MR velocity images acquired throughout the cycle of compression. The phantom geometry was modeled with a finite element mesh and the mechanical properties of the phantom material were measured and incorporated in the FEA model. The motion as calculated by the FEA model was compared to the motion measured with MRI and the results were found to vary with the material's Poisson's ratio and the coefficient of friction. A minimum difference was reached when the Poisson's ratio and coefficient of friction were set to 0.485 and 0.3, respectively. Under these conditions, the root mean square difference was found to be 14.4%.

Influence of Cell Size on Re-Entrant Transformation of Negative Poisson's Ratio Reticulated Polyurethane Foams

Several foams of different cell-size, including Scott Industrial polyurethane foam with large cells (20 pores per inch, ppi, or 1.2 mm per pore, black), medium cells (65 ppi, or 0.4 mm per pore, green), and near-microcellular (100 ppi, 0.25 mm per pore, white), were processed over various time and temperature regimes to ascertain the role of cell size in transformation to negative Poisson's ratio materials. These foams were transformed successfully, and exhibited negative Poisson's ratio behavior. Poisson's ratio was measured using a new laser based setup. For all as-received (unprocessed) foams with different cell sizes, Poisson's ratio decreased with compressive axial strain and increased with tensile strain up to a maximum. The maximum Poisson's ratio in tension decreased as cell size increases. The strain at which maximum Poisson's ratio occurs, increased with cell size. In negative Poisson's ratio foams, minimum Poisson's ratios of −0.8, −0.5, and −0.4 for 20 ppi, 65 ppi, and 100 ppi foams, respectively were observed. Furthermore, the cell size effects on transformation parameters were also found.

Properties of a chiral honeycomb with a poisson's ratio of — 1

A theoretical and experimental investigation is conducted of a two-dimensionally chiral honeycomb. The honeycomb exhibits a Poisson's ratio of —1 for deformations in-plane. This Poisson's ratio is maintained over a significant range of strain, in contrast to the variation with strain seen in known negative Poisson's ratio materials.

Error Limitations in the Determination of Mechanical Properties of Thin Films

This study addresses the ability to determine stiffness parameters and Poisson's ratio of ultrathin films in terms of isotropic material description. A primary concern is the precision with which such determinations can be made by means of certain continuum analyses. Starting from previously published results and drawing on energy methods for modeling the load-deflection relationship of rectangular membranes of arbitrary aspect ratio an analysis improvement reduces the error from the 40% range to 2-10% values. Further precision can only be derived from numerical analysis. By comparing the numerical data of load-versus-deflection behavior to that for the energy based approximation, Young's modulus can be determined to within 2% of the value specified, provided that Poisson's ratio, v, is known. If the latter is not the case, the error increases to 7 to 10%, if a limited range of Poisson's ratio is admitted. In addition, a method to determine Poisson's ratio is pursued by considering membranes of various aspect ratios. This method, which may also be readily applied for "exact" numerical analyses, was found to be particularly useful for materials with Poisson's ratio in the range from 0.25 to 0.5. Finally, this study is then extended to bimaterial films in two different fashions: through the use of an effective thickness defined in terms of a stretch equivalent, and through the use of effective material properties. The first method was found useful for low Poisson's ratio material whereas the second method was successful for high Poisson's ratio materials. Young's modulus of the material under test was retrieved on average within 3 %.

On the Effect of Triaxial State of Stress on Ductility Using Nonlinear CDM Model

Ductility takes into account the material capability to plastically deform. This parameter is not only modified by temperature but it is strongly affected by the stress triaxiality that, in the case of positive hydrostatic stress, reduces the material strain to failure. Due to the importance of this parameter in engineering design many attempts to predict the evolution of ductility with stress triaxiality have been done. Here, a nonlinear continuum damage model, as proposed by the author, is used to obtain the evolution of material ductility with stress triaxiality. The expression found relates the strain to failure in multi-axial state of stress regime only to the uniaxial strain to failure, to the damage strain threshold, to the material Poisson's ratio, and, of course, to stress triaxiality. The proposed model was successfully verified comparing the predicted evolution of material ductility with the experimental data relative to several metals. The procedure for the damage parameters identification is also discussed in details.

Modeling the tensile behavior of human Achilles tendon

Uniaxial quasi-static tensile stress, sigma versus strain, epsilon, data were obtained from 29 cadaveric Achilles tendons (donor ages: 36 to 100 years), at a strain rate of either 10 or 100%/s. These results were then used in modeling the elastic component of the tensile deformational behavior of this tissue. Two approaches were taken. In the first, it was shown that the following constitutive relation provided an excellent fit to the elastic section of the sigma-epsilon curve, sigma = C epsilon exp[D epsilon + F epsilon 2], with C, D and F being material constants, whose values for the present dataset were found to be C = 2.00 +/- 0.99, D = 0.089 +/- 0.087 and F = -0.0047 +/- 0.0095. The values of these coefficients were not statistically significantly affected by either donor age or test strain rate. In the second approach, the value of the modulus of elasticity of a filamentary polymer matrix composite material was computed as a function of various combinations of values of the modulus of elasticity of the fiber, the modulus of elasticity of the matrix, and angle of orientation of the principal material axes with respect to the reference coordinate axes (theta) for a fiber volume fraction of 0.6 and a material Poisson's ratio of 0.4. By comparing these results with the experimentally-obtained values of the tangent modulus of elasticity of the tendons (defined as the slope of the linear section of the post-toe zone in the sigma-epsilon plot), and assuming that the tendon may be idealized as a filamentary polymer matrix composite material, the suggestion is made that the winding angle of the fibers (collagen fibrils) in the tendon (taken to be equal to theta) is about 6 degrees.

The effect of the processing parameters on the fabrication of auxetic polyethylene

A novel fibrillated particulate microstructure has been fabricated in ultra high molecular weight polyethylene (UHMWPE) that produces a negative Poisson's ratio (auxetic) material. The processing route involves compaction, sintering and extrusion of a UHMWPE fine powder. The first, compaction stage is examined in this paper in detail in order to ascertain the compaction conditions required to produce, as an end-product, an auxetic polymer and to assess the importance of this stage in the processing route. It was found that while part of the function of the compaction stage was to impart structural integrity to the processed polymers, the conditions for optimizing the production of auxetic UHMWPE were not identical to those for optimum structural integrity of the compact. Both sets of conditions were examined, with compaction pressure and temperature being the most important of the variables examined.

The effect of the processing parameters on the fabrication of auxetic polyethylene

A novel fibrillated particulate microstructure has been fabricated in ultra high molecular weight polyethylene (UHMWPE) that produces a negative Poisson's ratio (auxetic) material. The processing route involves compaction, sintering and extrusion of a UHMWPE fine powder. The first, compaction stage is examined in this paper in detail in order to ascertain the compaction conditions required to produce, as an end-product, an auxetic polymer and to assess the importance of this stage in the processing route. It was found that while part of the function of the compaction stage was to impart structural integrity to the processed polymers, the conditions for optimizing the production of auxetic UHMWPE were not identical to those for optimum structural integrity of the compact. Both sets of conditions were examined, with compaction pressure and temperature being the most important of the variables examined.

Three-dimensional evaluation of the T-stress in centre cracked plates

Thick three-dimensional (3-D) finite element models of centre cracked plates are used to study the variation in the biaxiality factor β with the crack aspect ratio a/w. The use of two widely accepted methods to evaluate the T-stress in two-dimensions, namely the boundary layer method and the displacement field method, to calculate the T-stress in three-dimensions is studied. It is shown that the boundary layer method gives results that compare rather well with the two-dimensional plane strain values (maximum difference of 6 percent), while the displacement field method results are about 15 percent lower. Two parameters are shown to affect the three-dimensional evaluation of the biaxiality factor, namely the material's Poisson's ratio ν and the specimen's thickness t. The biaxiality factor is directly proportional to ν and inversely proportional to t. Three-dimensional analysis is required to assess correctly the effect of ν and t on β.

The limits of Poisson's ratio in polycrystalline bodies

While it has been established that the elastic moduli and compliances of anisotropic and isotropic materials should be positive for thermodynamic reasons, no condition related to the values of Poisson's ratio has yet been established. However, it is generally accepted that for isotropic materials Poisson's ratio should vary between — 1.0 and 0.5, whereas for orthotropic materials various conditions have been introduced relating the different components of the anisotropic Poisson's ratio with the remaining elastic constants of the material. In this paper, limits for Poisson's ratio of body-centred cubic (bcc) polycrystalline materials are determined, based on the modes of deformation of a typical unit cell of the material subjected to a uniform external loading arbitrarily oriented relative to the principal axes of the crystal. It is shown that the values of Poisson's ratio thus established correlate satisfactorily with experimental values of this constant. The procedure can be readily applied to other structural units of polycrystalline bodies.

Examination of acoustic behavior of negative poisson's ratio materials

Negative Poisson's ratio (NPR) foams have been predicted to have unusual acoustic properties. To measure these, polyurethane foam was chosen to serve as a model system. Negative Poisson ratios were produced in open cell, reticulated polyurethane foams by heat setting the foam which had been three-dimensionally compressed 3·7-fold. Acoustic reflection measurements were made on unconverted foam, NPR uncovered foam, and on NPR foam with an unattached and attached cover. Foams tested had pore densities ranging from 25·4 to 254 pores per linear cm. NPR foams absorbed better than unconverted foams at all frequencies. Smaller pore-size NPR foams absorbed sound more efficiently at frequencies above 630 Hz than did those with larger pores, and those with covers were better sound absorbers in the frequency range 250–1000 Hz than the uncovered NPR foams. Unidirectional compression to one quarter of the original thickness reduced the Poisson ratio to zero and caused the foam to absorb nearly as well as did creation of the negative Poisson's ratio.

Effective Elastic Moduli of Porous Ceramic Materials

This paper compares the applicability of a few theoretical models for determining effective elastic moduli, using published experimental data on ceramic materials in a porosity range of 0–40% and on a cellular material with a porosity of about 90%. As the experimental data for the effective Poisson's ratio involve a large scatter, a set of numerical experiments using the finite element method was carried out to obtain the variation of the effective Poisson's ratio with porosity. These variations show that the effective Poisson's ratio approaches 0.25 with increasing porosity, irrespective of the material Poisson's ratio. The effect of pore shapes on the effective elastic moduli and the Poisson's ratio has also been analyzed using FEM.

Advances in negative Poisson's ratio materials

Solids that become fatter in cross‐section when stretched are rare, but do exist. How such materials—which have a negative Poisson's ratio—can be created with specific properties, the implications of these unusual properties, and recent advances are discussed. The Figure shows an example of a negative Poisson's ratio structure with mechanical isotropy in two dimensions: the laminate of Milton. magnified image

Acoustic properties of materials with reduced Poisson ratio.

Reduced Poisson ratio materials present an interesting opportunity for altering acoustic properties. Relationship of material morphology with Poisson ratio will be explored. The effect of Poisson ratio on mechanical properties will be reviewed. Relationship with moduli, flexural rigidity, and fracture toughness will be examined. Reduced Poisson materials have low cutoff frequencies and low wave dispersion constants compared to analogous conventional materials. Development of a variety of materials for specific applications will be discussed. The generic approach to the fabrication of reduced Poisson ratio materials, such as foams, honeycombs, laminates, and composites, provides application engineers added flexibility in choosing appropriate materials.

Design of a Fastener Based on Negative Poisson's Ratio Foam

In this article we make use of the negative Poisson's ratio of recently developed cellular solids in the design of a press-fit fastener. Insertion of the fastener is facilitated by the lateral contraction which negative Poisson's ratio materials exhibit under compression. Removal of the fastener is resisted by the corre¬sponding elastic expansion under tension.

Deformation mechanisms in negative Poisson's ratio materials: structural aspects

Poisson's ratio in materials is governed by the following aspects of the microstructure: the presence of rotational degrees of freedom, non-affine deformation kinematics, or anisotropic structure. Several structural models are examined. The non-affine kinematics are seen to be essential for the production of negative Poisson's ratios for isotropic materials containing central force linkages of positive stiffness. Non-central forces combined with pre-load can also give rise to a negative Poisson's ratio in isotropic materials. A chiral microstructure with noncentral force interaction or non-affine deformation can also exhibit a negative Poisson's ratio. Toughness and damage resistance in these materials may be affected by the Poisson's ratio itself, as well as by generalized continuum aspects associated with the microstructure.

Stress intensity factor extraction using moiré interferometry based on a two-parameter displacement eigenfunction: Validity criteria and comparison with ASTM E-399 K IC plane strain test methods

Validity criteria are presented for use of moiré interferometry as a means to obtain near tip crack data combined with the use of a truncated two parameter, displacement based, K IC eigenfunction extraction method. Comparison is made with standard ASTM plane strain fracture toughness test methods for a three point bend specimen of 15V-3Cr titanium. Agreement between the experimental and ASTM plane strain K IC is found even though surface data were used. Quantitative explanations of this agreement are postulated, based on extreme near tip data extraction, the theoretical three-dimensional free surface crack tip eigenvalue for a relatively low Poisson ratio material and a direct measurement of this eigenvalue based on measured displacement.