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TECHNICAL PAPERS

# Some Applications of Integrated Elasticity

[+] Author and Article Information

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 $δ∕L0⩽1∕2$, 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 $ν∕(1−ν)$.

1

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

## Abstract

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.

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## Figures

Figure 3

Comparison of stress versus force response of linear and integrated elasticity

Figure 4

Comparison of force versus deflection response of linear and integrated elasticity

Figure 5

Force-deflection response of rubber band specimens

Figure 6

Force-deflection response of latex tubes

Figure 7

Spherical vessel under internal pressure

Figure 8

Comparison of stress versus pressure response of linear and integrated elasticity

Figure 9

Comparison of pressure versus radius response of linear and integrated elasticity

Figure 10

Figure 11

Plate weakened by an elliptical hole under tension at infinity

Figure 13

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

Figure 14

Cross section of a thick-walled spherical pressure vessel

Figure 1

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

Figure 2

Cylindrical bar under uniaxial tension

Figure 12

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

## Errata

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