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Non-elliptic elastic materials and the modeling of elastic-plastic behavior for finite deformation

Abeyaratne, Rohan and Knowles, James K. (1987) Non-elliptic elastic materials and the modeling of elastic-plastic behavior for finite deformation. Journal of the Mechanics and Physics of Solids, 35 (3). pp. 343-365. ISSN 0022-5096. https://resolver.caltech.edu/CaltechAUTHORS:20141112-121650858

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Abstract

For illustrative purposes this paper treats a special problem in the theory of finite deformations of elastic materials whose associated displacement equations of equilibrium do not remain elliptic at all strains. The typical deformation arising in this problem possesses a discontinuous gradient, so that quasi-static motions involving such equilibrium states may be dissipative. For a special class of such “non-elliptic” elastic materials, it is shown that the macroscopic response in the problem treated may be precisely of the form associated with elastic—perfectly plastic behavior. The counterparts of yield, plastic strain and plastic strain rate are determined by the underlying elastic strain energy function.


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http://dx.doi.org/10.1016/0022-5096(87)90012-3DOIArticle
http://www.sciencedirect.com/science/article/pii/0022509687900123PublisherArticle
Additional Information:© 1987 Pergamon Journals Ltd. Received 14 August 1986; In revised form 28 October 1986. The authors are grateful to James R. Rice for some most helpful comments on an earlier draft of this paper. The results communicated in this paper were obtained in the course of an investigation supported in part by the U.S. National Science Foundation.
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Issue or Number:3
Record Number:CaltechAUTHORS:20141112-121650858
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20141112-121650858
Official Citation:Abeyaratne, R., & Knowles, J. K. (1987). Non-elliptic elastic materials and the modeling of elastic-plastic behavior for finite deformation. Journal of the Mechanics and Physics of Solids, 35(3), 343-365. doi: http://dx.doi.org/10.1016/0022-5096(87)90012-3
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:51660
Collection:CaltechAUTHORS
Deposited By: Joanne McCole
Deposited On:12 Nov 2014 21:10
Last Modified:03 Oct 2019 07:35

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