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.

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.

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.

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 Characterisation of cubic oak specimens from the Vasa ship and recent wood by means of quasi-static loading and resonance ultrasound spectroscopy (RUS)

Holzforschung ◽  
2016 ◽  
Vol 70 (5) ◽  
pp. 457-465 ◽  
Author(s):  
Alexey Vorobyev ◽  
Olivier Arnould ◽  
Didier Laux ◽  
Roberto Longo ◽  
Nico P. van Dijk ◽  
...  
Keyword(s):  
Static Loading ◽  
Resonant Ultrasound Spectroscopy ◽  
Shear Moduli ◽  
Additional Information ◽  
Cylindrical Orthotropy ◽  
Engineering Parameters ◽  
Resonant Ultrasound ◽  
The Difference ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

Abstract The cylindrical orthotropy, inherent time-dependency response, and variation between and within samples make the stiffness characterisation of wood more challenging than most other structural materials. The purpose of the present study is to compare static loading with resonant ultrasound spectroscopy (RUS) and to investigate how to combine the advantages of each of these two methods to improve the estimation of the full set of elastic parameters of a unique sample. The behavior of wood as an orthotropic mechanical material was quantified by elastic engineering parameters, i.e. Poisson’s ratios and Young’s and shear moduli. Recent and waterlogged archaeological oak impregnated with polyethylene glycol (PEG) from the Vasa warship built in 1628 was in focus. The experimental results were compared, and the difference between RUS and static loading was studied. This study contributes additional information on the influence of PEG and degradation on the elastic engineering parameters of wood. Finally, the shear moduli and Poisson’s ratios were experimentally determined for Vasa archaeological oak for the first time.

Cavities vis-a`-vis Rigid Inclusions and Some Related General Results in Plane Elasticity

1989 ◽  
Vol 56 (4) ◽  
pp. 786-790 ◽  
Author(s):  
John Dundurs
Keyword(s):  
Stress Field ◽  
Plane Strain ◽  
Elastic Constants ◽  
Plane Stress ◽  
Poisson Ratio ◽  
Plane Elasticity ◽  
By Products

There is a strange feature of plane elasticity that seems to have gone unnoticed: The stresses in a body that contains rigid inclusions and is loaded by specified surface tractions depend on the Poisson ratio of the material. If the Poisson ratio in this stress field is set equal to +1 for plane strain, or +∞ for plane stress, the rigid inclusions become cavities for elastic constants within the physical range. The paper pursues this circumstance, and in doing so also produces several useful by-products that are connected with the stretching and curvature change of a boundary.

First-principles study on the structural, elastic and electronic properties of the four Si3Sb4 compounds

2019 ◽  
Vol 33 (05) ◽  
pp. 1950047
Author(s):  
Ruike Yang ◽  
Bao Chai ◽  
Qun Wei ◽  
Minhua Xue ◽  
Ye Zhou
Keyword(s):  
Electronic Properties ◽  
First Principles ◽  
Density Functional ◽  
Phonon Dispersion ◽  
Elastic Anisotropy ◽  
Functional Theory ◽  
Shear Moduli ◽  
Young’S Moduli ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

For novel [Formula: see text]-Si3Sb4, pseudocubic-Si3Sb4, cubic-Si3Sb4 and [Formula: see text]-Si3Sb4, the structural, elastic and electronic properties are investigated using first-principles density functional theory (DFT). The elastic constants and phonon dispersion spectra show that they are mechanically and dynamically stable. The bulk moduli, shear moduli, Young’s moduli, Poisson’s ratios and Pugh ratios for the four compounds have been calculated. The bulk moduli indicate that the bond strength of [Formula: see text]-Si3Sb4 is stronger than others. The values of the Poisson’s ratios and Pugh ratios show that pseudocubic-Si3Sb4 is the stiffest among the four Si3Sb4 compounds. Tetragonal Si3Sb4 are more brittle than cubic Si3Sb4. For the four Si3Sb4 compounds, the elastic anisotropies are analyzed via the anisotropic indexes and the 3D surface constructions. The [Formula: see text]-Si3Sb4 elastic anisotropy is stronger than others and the [Formula: see text]-Si3Sb4 is weaker than others. The calculated band structures show that they exhibit metallic features. The results of their TDOS show that there are many similarities. The peaks of TDOS are derived from the contributions of Si “s”, Si “p”, Sb “s” and Sb “p” states.

A crack at the interface between two power-law materials under plane strain loading

1991 ◽  
Vol 432 (1886) ◽  
pp. 547-553 ◽  
Keyword(s):  
Energy Density ◽  
Asymptotic Solution ◽  
Plane Strain ◽  
Power Law ◽  
Arbitrary Constant ◽  
Perturbation Technique ◽  
Radial Distance ◽  
The Other ◽  
Stress Fields ◽  
Hardening Parameter

The stress fields at the tip of a crack lying along the interface between two incompressible power-law materials is considered for the case of plane strain loading. An asymptotic solution is constructed which has the property that the energy density W is of the order of 1/ r , as r →0, in the material with the largest hardening parameter (material 1), where r denotes the radial distance from the crack tip. The solution in the other material (material 2) is such that W = o(1/ r ) as r →0. The solution in material 1 behaves, asymptotically, as if the other material is rigid. It is shown numerically that the near-tip fields are functions containing only one arbitrary constant, and this is corroborated analytically by using a small perturbation technique.

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.

Solutions for Axisymmetric Problems of Layered Generalized Gibson Subgrade

2014 ◽  
Vol 574 ◽  
pp. 53-57
Author(s):  
Jian Ming Jin
Keyword(s):  
Half Space ◽  
Hankel Transform ◽  
Surface Load ◽  
Shear Moduli ◽  
Space Solution ◽  
Axisymmetric Surface ◽  
Axisymmetric Problems ◽  
The Relationship ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

This article presents the solutions for displacements and stress of layered generalized Gibson subgrade subjected to an axisymmetric surface load. We assume that the material has constant Poisson’s ratios (μ=0.5), and its shear moduli varies linearly with depth. During the solutions, the Hankel transform in a cylindrical co-ordinate system is employed. The relationship between the solution and half-space solution is also examined and discussed. At last, the analysis flow is presented .

Sign in / Sign up

Export Citation Format

Share Document