Knowles, James K. (2001) Nonlinear Waves in Thermoelastic Solids Undergoing Phase Transitions. In: Acoustic interactions with submerged elastic structures, Part II. Series on stability, vibration, and control of systems., Series B. No.5. World Scientific , River Edge, NJ, pp. 348-364. ISBN 9789812811950. https://resolver.caltech.edu/CaltechAUTHORS:20141029-083903820
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Abstract
This paper is concerned with continuum modeling of the macroscopic dynamical response of one-dimensional thermoelastic bars undergoing phase transitions. The specific model considered involves a particular "two-well" Helmholtz free energy potential governing the bulk response of the material as well as a nucleation criterion and kinetic relation controlling the initiation and evolution of the phase transition. Inertia is taken into account, and the discussion is based on an adiabatic theory. In contrast to models in which the free energy involves only a single well, the entropy inequality at propagating strain discontinuities is not sufficient to assure the uniqueness of solutions to the boundary-initial value problems of interest: kinetics and nucleation must be imposed as well.
| Item Type: | Book Section | |||||||||
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| Additional Information: | © 2001 World Scientific Publishing Company. The research summarized here was supported in part by the U.S. Office of Naval Research and the U.S. Army Research Office. | |||||||||
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| Series Name: | Series on stability, vibration, and control of systems., Series B | |||||||||
| Issue or Number: | 5 | |||||||||
| DOI: | 10.1142/9789812811950_0012 | |||||||||
| Record Number: | CaltechAUTHORS:20141029-083903820 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20141029-083903820 | |||||||||
| Official Citation: | NONLINEAR WAVES IN THERMOELASTIC SOLIDS UNDERGOING PHASE TRANSITIONS James K. Knowles Acoustic Interactions with Submerged Elastic Structures. July 2001, 348-364 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 50983 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 29 Oct 2014 16:18 | |||||||||
| Last Modified: | 10 Nov 2021 19:03 |
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