Relaxed nonlocal models of hysteresis

Deborah Brandon; Tao Lin; Robert C. Rogers

doi:10.1117/12.174243

1 May 1994 Relaxed nonlocal models of hysteresis

Deborah Brandon, Tao Lin, Robert C. Rogers

Proceedings Volume 2192, Smart Structures and Materials 1994: Mathematics and Control in Smart Structures; (1994) https://doi.org/10.1117/12.174243
Event: 1994 North American Conference on Smart Structures and Materials, 1994, Orlando, FL, United States

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.

Citation Download Citation

Deborah Brandon, Tao Lin, and Robert C. Rogers "Relaxed nonlocal models of hysteresis", Proc. SPIE 2192, Smart Structures and Materials 1994: Mathematics and Control in Smart Structures, (1 May 1994); https://doi.org/10.1117/12.174243

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available