Some Applications of Integrated Elasticity

[+] Author and Article Information
A. T. Assaad

 Blue Slide Systems LLC, Pittsburgh, PA 15219-3120

G. B. Sinclair1

Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803-6413glennsinclair@cox.net

This sort of approach belongs to a class of rate-of-deformation theories, early versions of which were also advanced in Jaumann (5) and Hencky (6).

For δL012, there are six reported measurements in Ref. 11: Eq. 19 can fit these six to within 5%.

For plane strain, exchange E for 2(1+ν)G then replace the remaining occurrences of ν with ν(1ν).


Author to whom correspondence should be addressed.

J. Appl. Mech 74(2), 210-222 (Nov 30, 2005) (13 pages) doi:10.1115/1.2188537 History: Received February 18, 2005; Revised November 30, 2005

This paper examines the effects of relaxing the assumption of classical linear elasticity that the loads act in their entirety on the undeformed shape. Instead, loads here are applied incrementally as deformation proceeds, and resulting fields are integrated. A formal statement of the attendant integrated elasticity theory is provided. A class of problems is identified for which this formulation is amenable to solution in closed form. Some results from these configurations are compared with linear elasticity and experimentally measured data. The comparisons indicate that, as deformation increases, integrated elasticity is capable of tracking the physical response better than linear elasticity.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 3

Comparison of stress versus force response of linear and integrated elasticity

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Figure 4

Comparison of force versus deflection response of linear and integrated elasticity

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Figure 5

Force-deflection response of rubber band specimens

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Figure 6

Force-deflection response of latex tubes

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Figure 7

Spherical vessel under internal pressure

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Figure 8

Comparison of stress versus pressure response of linear and integrated elasticity

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Figure 9

Comparison of pressure versus radius response of linear and integrated elasticity

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Figure 10

Pressure-radius response of rubber balloons

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Figure 11

Plate weakened by an elliptical hole under tension at infinity

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Figure 13

Crack length response of a rubber sheet under tension (data from Mansfield (17))

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Figure 14

Cross section of a thick-walled spherical pressure vessel

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Figure 1

Coordinate systems for elastic regions: (a) initial and final regions, (b) intervening regions for successive load increments

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Figure 2

Cylindrical bar under uniaxial tension

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Figure 12

Comparison of peak stress versus applied stress for linear and integrated elasticity



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