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Proceedings Paper

Relaxed nonlocal models of hysteresis
Author(s): Deborah Brandon; Tao Lin; Robert C. Rogers
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Paper Abstract

In this paper we present energy minimization problems for deformations of materials whose bulk energies have two potential wells. (Two-well models have often been used in simple models of shape memory alloys.) The higher-dimensional models feature relaxed bulk energies derived from double-well potentials with two compatible quadratic wells. The relaxation of the double quadratic well can be calculated explicitly. The relaxed minimization problems are regularized through the use of spatially nonlocal forces. These forces are related to Van der Waals capillary forces and interfacial or coherence forces used in phase fraction theories. We describe an algorithm for computing stationary points of the energy, and do a number of calculations on 1-D static deformations. Our calculations show a rich class of metastable states that form themselves into hysteresis loops and subloops.

Paper Details

Date Published: 1 May 1994
PDF: 12 pages
Proc. SPIE 2192, Smart Structures and Materials 1994: Mathematics and Control in Smart Structures, (1 May 1994); doi: 10.1117/12.174243
Show Author Affiliations
Deborah Brandon, Carnegie Mellon Univ. (United States)
Tao Lin, Virginia Polytechnic Institute and State Univ. (United States)
Robert C. Rogers, Virginia Polytechnic Institute and State Univ. (United States)


Published in SPIE Proceedings Vol. 2192:
Smart Structures and Materials 1994: Mathematics and Control in Smart Structures
H. Thomas Banks, Editor(s)

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