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On the dissipative response due to discontinuous strains in bars of unstable elastic material

Abeyaratne, Rohan and Knowles, James K. (1988) On the dissipative response due to discontinuous strains in bars of unstable elastic material. International Journal of Solids and Structures, 24 (10). pp. 1021-1044. ISSN 0020-7683. http://resolver.caltech.edu/CaltechAUTHORS:20141029-093857845

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Abstract

Some elastic materials are capable of sustaining finite equilibrium deformations with discontinuous strains. Boundary-value problems for such “unstable” elastic materials often possess an infinite number of solutions, suggesting that the theory suffers from a constitutive deficiency. In the setting of the one-dimensional theory of bars in tension, the present paper explores the consequences of supplementing the theory with further constitutive information. This additional information pertains to the surface of strain discontinuity and consists of a ‘kinetic relation’ and a criterion for the “initiation” of such a surface. We show that the quasi-static response of the bar to a prescribed force history is then fully determined. In particular, we observe how unstable clastic materials can he used to model macroscopic behavior similar to that associated with viscoplasticity.


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http://dx.doi.org/10.1016/0020-7683(88)90105-9 DOIArticle
http://www.sciencedirect.com/science/article/pii/0020768388901059PublisherArticle
Additional Information:© 1988 Pergamon Press plc. Received 16 November 1987; in revised form 24 March 1988. The results communicated in this paper were obtained in the course of an investigation supported in part by the Office of Naval Research.
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Office of Naval Research (ONR)UNSPECIFIED
Record Number:CaltechAUTHORS:20141029-093857845
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20141029-093857845
Official Citation:Rohan Abeyaratne, James K. Knowles, On the dissipative response due to discontinuous strains in bars of unstable elastic material, International Journal of Solids and Structures, Volume 24, Issue 10, 1988, Pages 1021-1044, ISSN 0020-7683, http://dx.doi.org/10.1016/0020-7683(88)90105-9. (http://www.sciencedirect.com/science/article/pii/0020768388901059)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:50992
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:29 Oct 2014 16:44
Last Modified:29 Oct 2014 16:44

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