Elasticity Theory for Indentation of a Rubber Plate

1968 ◽  
Vol 41 (5) ◽  
pp. 1122-1131 ◽  
Author(s):  
S. D. Gehman
Keyword(s):  
Elasticity Theory ◽  
Thickness Dependence ◽  
Classical Elasticity ◽  
Rubber Specimen ◽  
Empirical Correction ◽  
Classical Elasticity Theory ◽  
Rubber Plate

Abstract Rubber hardness readings with an indenter depend upon thickness of the rubber specimen. This effect has been known and studied since first attempts to develop precision methods to determine hardness. Classical elasticity theory accounted satisfactorily for indentation relations with thick rubber but thickness dependence was treated as an empirical correction.

Lattice Spacings in Some Transition Metal Terminal Solid Solutions

1962 ◽  
Vol 6 ◽  
pp. 121-135 ◽  
Author(s):  
Henry Chessin ◽  
Sigurds Arajs ◽  
D. S. Miller
Keyword(s):  
Transition Metal ◽  
Size Effect ◽  
Elasticity Theory ◽  
Solid Solutions ◽  
Calculated Data ◽  
Lattice Parameter ◽  
Lattice Parameters ◽  
Classical Elasticity ◽  
Atomic Size ◽  
Classical Elasticity Theory

AbstractThe lattice parameter-composition curves for several nickel solid solutions and for some chromium and. iron solid solutions are discussed. It is shown that the size effect may be the predominating influence on the change of lattice parameters in these systems. This is demonstrated by comparing observed and calculated data employing various methods. A new scheme for evaluating the atomic size in solid solutions is proposed, based on regarding the atom, as an incompressible core surrounded by a smeared-out compressible volume. The suggestion that classical elasticity theory may be used as a basis for understanding the size effect in solid solutions is justified by examination of the Ag-Pd system for additions of Ag from 0 to 100 at. %.

Stiffness characteristics of rubber impact absorbers

1972 ◽  
Vol 7 (1) ◽  
pp. 33-40 ◽  
Author(s):  
E A Bakirzis
Keyword(s):  
Elasticity Theory ◽  
Classical Elasticity ◽  
Cross Sectional ◽  
Wide Range ◽  
Stiffness Characteristics ◽  
Classical Elasticity Theory

Classical elasticity theory, together with a knowledge of the behaviour of solid-rubber pads under compression, is employed to predict the force-deflection characteristics of hollow rubber units used as impact absorbers. Various parameters are predicted theoretically and agreement with theory is found to be satisfactory for a wide range of shapes and ratios of cross-sectional dimensions.

The Analysis of the Effect of Surface Stresses at Nanoscale

2015 ◽  
Vol 1102 ◽  
pp. 169-172
Author(s):  
Zhi Ying Ou ◽  
Ya Wen Wu
Keyword(s):  
Contact Problem ◽  
Elasticity Theory ◽  
Function Method ◽  
Classical Elasticity ◽  
Complex Variable Function ◽  
Surface Stresses ◽  
Variable Function ◽  
Complex Variable Function Method ◽  
Classical Elasticity Theory ◽  
Effect Of Surface

Based on classical elasticity theory, the effects of surface stresses on the nanosized contact problem in an elastic half-plane which contains a nanocylindrical hole are analyzed. Meanwhile, the effects of surface energy of the contact nanosized surface are considered. The complex variable function method is applied to derive the fundamental solution of the contact problem. As example, the deformation induced by a distributed traction of cosine function on the nanosized surface is analyzed in detail. The results tell some interesting characteristics in contact mechanics, which are different from those in classical elasticity theory.

Bending of a Cosserat Elastic Bar of Square Cross Section: Theory and Experiment

2015 ◽  
Vol 82 (9) ◽  
Author(s):  
Roderic Lakes ◽  
W. J. Drugan
Keyword(s):  
Elasticity Theory ◽  
Cross Section ◽  
Surface Deformation ◽  
Length Scale ◽  
Polymer Foam ◽  
Pure Bending ◽  
Classical Elasticity ◽  
Dimensional Solution ◽  
Cosserat Elasticity ◽  
Classical Elasticity Theory

Pure bending experiments on prismatic bars of square cross section composed of reticulated polymer foam exhibit deformation behavior not captured by classical elasticity theory. Perhaps the clearest example of this is the observed sigmoidal deformation of the bars' lateral surfaces, which are predicted by classical elasticity theory to tilt but remain planar upon pure moment application. Such foams have a non-negligible length scale compared to the bars' cross-sectional dimensions, whereas classical elasticity theory contains no inherent length scale. All these facts raise the intriguing question: is there a richer, physically sensible, yet still continuum and relatively simple elasticity theory capable of modeling the observed phenomenon in these materials? This paper reports our exploration of the hypothesis that Cosserat elasticity can. We employ the principle of minimum potential energy for homogeneous isotropic Cosserat linear elastic material in which the microrotation vector is taken to be independent of the macrorotation vector (as prior experiments indicate that it should be in general to model such materials) to obtain an approximate three-dimensional solution to pure bending of a prismatic bar having a square cross section. We show that this solution, and hence Cosserat elasticity, captures the experimentally observed nonclassical deformation feature, both qualitatively and quantitatively, for reasonable values of the Cosserat moduli. A further interesting conclusion is that a single experiment—the pure bending one—suffices to reveal directly, via the observation of surface deformation, the presence of nonclassical elastic effects describable by Cosserat elasticity.

Modeling of Deformations in a Ring Shaped Workpiece Due to Chucking and Cutting Forces

Manufacturing ◽  
2002 ◽  
Author(s):  
John A. Malluck ◽  
Shreyes N. Melkote
Keyword(s):  
Finite Element ◽  
Theoretical Model ◽  
Finite Element Model ◽  
Cutting Forces ◽  
Element Model ◽  
Outer Diameter ◽  
Classical Elasticity ◽  
Elastic Deformations ◽  
The Finite Element Model ◽  
Classical Elasticity Theory

This paper presents a theoretical model for predicting the elastic deformations of ring-type workpieces due to in-plane chucking and cutting forces applied in turning processes. The model is derived from classical elasticity theory for bending of thin rings. Experimental results are presented to verify the strengths and limitations of this model. The results from a finite element model are also presented for comparison. For the ring diameters and radial chucking loads considered in this work, it is shown that the theoretical model is accurate to within 11% of the measured radial deformations for rings with inner-to-outer diameter ratio (Din/Dout) of 0.881. The finite element model is shown to yield slightly better results. The applicability of the theoretical model is illustrated by using it to predict the surface error produced in turning of a ring.

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