Generalized Plane Strain of Pressurized Orthotropic Tubes

1965 ◽  
Vol 87 (3) ◽  
pp. 337-343 ◽  
Author(s):  
Bernard W. Shaffer
Keyword(s):  
Plane Strain ◽  
The Other ◽  
Cylindrical Coordinates ◽  
Incompressible Materials ◽  
Hooke's Law ◽  
Poisson's Ratios ◽  
Poisson’S Ratios ◽  
Moduli Of Elasticity ◽  
Compressible Materials ◽  
Generalized Plane Strain

The generalized Hooke’s law in cylindrical coordinates is presented in terms of directional moduli of elasticity and Poisson’s ratios. It is used in deriving a solution for long pressurized orthotropic tubes with closed ends. Two sets of equations are found; one set is applicable to the study of compressible materials and the other to incompressible materials. The distinction is also described in terms of the moduli of elasticity and Poisson’s ratios.

Edge-Bonded Dissimilar Orthogonal Elastic Wedges Under Normal and Shear Loading

1968 ◽  
Vol 35 (3) ◽  
pp. 460-466 ◽  
Author(s):  
David B. Bogy
Keyword(s):  
Asymptotic Behavior ◽  
Plane Strain ◽  
Elastic Constants ◽  
Plane Stress ◽  
Shear Loading ◽  
The Other ◽  
Stress Fields ◽  
Shear Moduli ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

The plane-strain and generalized plane stress problems of two materially dissimilar orthogonal elastic wedges, which are bonded together on one of their faces while arbitrary normal and shearing tractions are prescribed on their remaining faces, are treated within the theory of classical elastostatics. The asymptotic behavior of the solution in the vicinity of the intersection of the bonded and loaded planes is investigated. The stress fields are found to be singular there with singularities of the type r−α, where α depends on the ratio of the two shear moduli and on the two Poisson’s ratios. This dependence is shown graphically for physically relevant values of the elastic constants. The largest value of α for the range of constants considered is 0.311 and occurs when one material is rigid and the other is incompressible.

Plane strain rotation moduli for soft elastic blocks

1979 ◽  
Vol 14 (1) ◽  
pp. 17-21 ◽  
Author(s):  
P B Lindley
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Plane Strain ◽  
Elastic Material ◽  
Analysis Data ◽  
Simple Relation ◽  
Theoretical Solution ◽  
The Other ◽  
Element Analysis ◽  
Poisson's Ratios

Making assumptions similar to these used to obtain compression moduli, a simple relation is developed for the plane strain rotation moduli for blocks of soft elastic material bonded to rigid end plates. The deformation arises when one plate rotates relative to the other plane about an axis along the centre of its width. The approximate theoretical solution compares well with finite-element analysis data for materials with Poisson's ratios of 0.333, 0.483 87 and 0.499 83 and blocks having width-to-thickness ratios between 0.25 and 64.

Three-Dimensional Constraint Effects on the Slitting Method for Measuring Residual Stress

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
C. Can Aydıner ◽  
Michael B. Prime
Keyword(s):  
Residual Stress ◽  
Plane Strain ◽  
Plane Stress ◽  
Three Dimensional ◽  
Poisson's Ratio ◽  
Out Of Plane ◽  
Sample Width ◽  
Poisson's Ratios ◽  
Poisson’S Ratios ◽  
Calibration Coefficients

The incremental slitting or crack compliance method determines a residual stress profile from strain measurements taken as a slit is incrementally extended into the material. To date, the inverse calculation of residual stress from strain data conveniently adopts a two-dimensional, plane strain approximation for the calibration coefficients. This study provides the first characterization of the errors caused by the 2D approximation, which is a concern since inverse analyses tend to magnify such errors. Three-dimensional finite element calculations are used to study the effect of the out-of-plane dimension through a large scale parametric study over the sample width, Poisson's ratio, and strain gauge width. Energy and strain response to point loads at every slit depth is calculated giving pointwise measures of the out-of-plane constraint level (the scale between plane strain and plane stress). It is shown that the pointwise level of constraint varies with slit depth, a factor that makes the effective constraint a function of the residual stress to be measured. Using a series expansion inverse solution, the 3D simulated data of a representative set of residual stress profiles are reduced with 2D calibration coefficients to yield the error in stress. The sample width below which it is better to use plane stress compliances than plane strain is shown to be about 0.7 times the sample thickness; however, even using the better approximation, the rms stress errors sometimes still exceed 3% with peak errors exceeding 6% for Poisson's ratio 0.3, and errors increase sharply for larger Poisson's ratios. The error is significant, yet, error magnification from the inverse analysis in this case is mild compared to, e.g., plasticity based errors. Finally, a scalar correction (effective constraint) over the plane-strain coefficients is derived to minimize the root-mean-square (rms) stress error. Using the posed scalar correction, the error can be further cut in half for all widths and Poisson's ratios.

Cellular Materials With Extremely High Negative and Positive Poisson’s Ratios: A Mechanism Based Material Design

2013 ◽  
Author(s):  
Kwangwon Kim ◽  
Jaehyung Ju ◽  
Doo-Man Kim
Keyword(s):  
Porous Materials ◽  
Analytical Model ◽  
Compliant Mechanisms ◽  
Constitutive Relations ◽  
Functional Materials ◽  
Material Design ◽  
The Other ◽  
Yield Strain ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

In an effort to tailor functional materials with customized anisotropic properties — stiffness and yield strain, we propose porous materials consisting of flexible mesostructures designed from the deformation of a re-entrant auxetic honeycomb and compliant mechanisms. Using an analogy between compliant mechanisms and a cellular material’s deformation, we can tailor in-plane properties of mesostructures; low stiffness and high strain in one direction and high stiffness and low strain in the other direction. Two mesostructures based on hexagonal honeycombs with positive and negative cell angles are generated. An analytical model is developed to obtain effective moduli and yield strains of the porous materials by combining the kinematics of a rigid link mechanism and deformation of flexure hinges. A numerical technique is implemented to the analytical model for nonlinear constitutive relations of the mesostructures and their strain dependent Poisson’s ratios. A Finite Element Analysis (FEA) is used to validate the analytical and numerical model. The moduli and yield strain of a porous aluminum alloy are about 6.3GPa and 0.26% in one direction and about 2.8MPa and 12% in the other direction. The mesostructures have extremely high positive and negative Poisson’s ratios, νxy* (∼ ±40) due to the large rotation of the link member in the transverse direction caused by the input displacement in the longitudinal direction. The mesostructures also show higher moduli for compressive loading due to the contact of slit edges at the center region. This paper demonstrates that compliant mesostructures can be used for a next generation material design in terms of tailoring mechanical properties; moduli, strength, strain, and Poisson’s ratios. The proposed mesostructures can also be easily manufactured using a conventional cutting method.

Compression moduli for blocks of soft elastic material bonded to rigid end plates

1979 ◽  
Vol 14 (1) ◽  
pp. 11-16 ◽  
Author(s):  
P B Lindley
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Plane Strain ◽  
Elastic Material ◽  
Analysis Data ◽  
Theoretical Solution ◽  
Element Analysis ◽  
Incompressible Materials ◽  
Simplifying Assumptions ◽  
Poisson's Ratios

Using simplifying assumptions based on a theoretical solution for incompressible materials, simple relations are developed for the plane strain and axisymmetric compression moduli for blocks of compressible soft elastic material bonded to rigid end plates. The approximate theoretical solutions compare well with finite-element analysis data for materials with Poisson's ratios between 0.125 and 0.499 83 and blocks having width-to-thickness or diameter-to-thickness ratios between 0.25 and 128.

scholarly journals Bond-based peridynamics: A tale of two Poisson's ratios

2019 ◽  
Author(s):  
Jeremy Trageser ◽  
Pablo Seleson
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Two Dimensional ◽  
Isotropic Materials ◽  
Stress Models ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

This paper explores the restrictions imposed by bond-based peridynamics, particularly with respect to plane strain and plane stress models. We begin with a review of the derivations in [2] wherein for isotropic materials a Poisson's ratio restriction of 1/4 for plane strain and 1/3 for plane stress is deduced. Next, we show Cauchy's relations are an intrinsic limitation of bond-based peridynamics and specialize this result to plane strain and plane stress models, generalizing the results of [2] and demonstrating the Poisson's ratio restrictions in [2] are simply a consequence of Cauchy's relations. We conclude with a discussion of the validity of peridynamic plane strain and plane stress models formulated from two-dimensional bond-based peridynamic models.

scholarly journals Giant negative Poisson’s ratio in two-dimensional V-shaped materials

2021 ◽  
Author(s):  
Xikui Ma ◽  
Jian Liu ◽  
Yingcai Fan ◽  
Weifeng Li ◽  
Jifan Hu ◽  
...  
Keyword(s):  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Negative Poisson’S Ratio ◽  
Two Dimensional ◽  
Auxetic Materials ◽  
Negative Poisson's Ratio ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

Two-dimensional (2D) auxetic materials with exceptional negative Poisson’s ratios (NPR) are drawing increasing interest due to the potentials in medicine, fasteners, tougher composites and many other applications. Improving the auxetic...

Continuum Description of the Time- and Strain-Dependent Poisson’s Ratio of Ligament Under Finite Deformation

2013 ◽  
Author(s):  
Aaron M. Swedberg ◽  
Shawn P. Reese ◽  
Steve A. Maas ◽  
Benjamin J. Ellis ◽  
Jeffrey A. Weiss
Keyword(s):  
Large Scale ◽  
Mechanical Response ◽  
Tensile Deformation ◽  
Large Strain ◽  
Fiber Direction ◽  
Strain Behavior ◽  
Nonlinear Stress ◽  
Poisson's Ratios ◽  
Poisson’S Ratios ◽  
Strain Dependent

Ligament volumetric behavior controls fluid and thus nutrient movement as well as the mechanical response of the tissue to applied loads. The reported Poisson’s ratios for tendon and ligament subjected to tensile deformation loading along the fiber direction are large, ranging from 0.8 ± 0.3 in rat tail tendon fascicles [1] to 2.98 ± 2.59 in bovine flexor tendon [2]. These Poisson’s ratios are indicative of volume loss and thus fluid exudation [3,4]. We have developed micromechanical finite element models that can reproduce both the characteristic nonlinear stress-strain behavior and large, strain-dependent Poisson’s ratios seen in tendons and ligaments [5], but these models are computationally expensive and unfeasible for large scale, whole joint models. The objectives of this research were to develop an anisotropic, continuum based constitutive model for ligaments and tendons that can describe strain-dependent Poisson’s ratios much larger than the isotropic limit of 0.5. Further, we sought to demonstrate the ability of the model to describe experimental data, and to show that the model can be combined with biphasic theory to describe the rate- and time-dependent behavior of ligament and tendon.

Carbon nanotube films change Poisson’s ratios from negative to positive

2010 ◽  
Vol 97 (6) ◽  
pp. 061909 ◽  
Author(s):  
Yin Ji Ma ◽  
Xue Feng Yao ◽  
Quan Shui Zheng ◽  
Ya Jun Yin ◽  
Dong Jie Jiang ◽  
...  
Keyword(s):  
Carbon Nanotube ◽  
Poisson's Ratios ◽  
Poisson’S Ratios ◽  
Nanotube Films

scholarly journals Theoretical and practical differences between creep and relaxation Poisson’s ratios in linear viscoelasticity

2015 ◽  
Vol 19 (4) ◽  
pp. 537-555 ◽  
Author(s):  
Abudushalamu Aili ◽  
Matthieu Vandamme ◽  
Jean-Michel Torrenti ◽  
Benoit Masson
Keyword(s):  
Linear Viscoelasticity ◽  
Poisson's Ratios ◽  
Poisson’S Ratios
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