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Research Papers

# On the Theory of Elastic Undamageable Materials

[+] Author and Article Information

Boyd Professor
Department of Civil and
Environmental Engineering,
Louisiana State University,
Baton Rouge, LA 70803;
Department of Civil and
Environmental Engineering,
Hanyang University,
Seoul 133-791, Republic of Korea

Peter I. Kattan

Visiting Professor
Department of Civil and
Environmental Engineering,
Louisiana State University,
Baton Rouge, LA 70803
email: pkattan@orange.jo

Contributed by the Materials Division of ASME for publication in the Journal of Engineering Materials and Technology. Manuscript received May 26, 2012; final manuscript received October 3, 2012; published online March 25, 2013. Assoc. Editor: Xi Chen.

J. Eng. Mater. Technol 135(2), 021002 (Mar 25, 2013) (6 pages) Paper No: MATS-12-1107; doi: 10.1115/1.4023770 History: Received May 26, 2012; Revised October 03, 2012

## Abstract

In this work, both the concepts of Voyiadjis–Kattan materials and undamageable materials are introduced. The Voyiadjis–Kattan material of order $n$ is defined as a nonlinear elastic material that has a higher-order strain energy form in terms of $n$. The undamageable material is obtained as the limit of the Voyiadjis–Kattan material of order $n$ as $n$ goes to infinity. The relations of these types of materials to other nonlinear elastic materials from the literature are outlined. Also, comparisons of these types of materials with rubber materials are presented. Finally, a proof is given to show that the value of the damage variable remains zero in an undamageable material throughout the deformation process. It is hoped that these proposed new types of materials will open the way to new areas of research in both damage mechanics and materials science.

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## References

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## Figures

Fig. 1

Valid stress-strain curves for various values of n

Fig. 2

Stress-strain curve for silicon rubber

Fig. 3

Stress-strain curve for gum rubber

Fig. 4

Stress-strain curve for neoprene rubber

Fig. 5

Damaged and effective moduli of elasticity

Fig. 6

Relation between ℓ1 and the ratio of the stresses

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