Why are some hysteresis loops shaped like a butterfly?

Authors:
Bojana Drincic;Dennis S. Bernstein
Affiliations:
Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI;Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI
Venue:
ACC'09 Proceedings of the 2009 conference on American Control Conference
Year:
2009

Citing 1
Cited 1

On domain switching in deformable ferroelectrics, seen as continua with microstructure

Zeitschrift für Angewandte Mathematik und Physik (ZAMP)

Brief paper: Why are some hysteresis loops shaped like a butterfly?

Automatica (Journal of IFAC)

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Abstract

In this paper we investigate the origins of butterfly-shaped hysteresis maps. In particular, we show that there exist 2-to-1 maps that transform oriented simple closed curves into multi-loop closed curves with loops of opposite orientations. As an illustrative application, the hysteretic input-output map of the preloaded two-bar linkage mechanism becomes a butterfly when a 2-to-1 map is applied to it. In this case, the application of the 2-to-1 map to the hysteresis loop is equivalent to plotting an alternative output variable. We also investigate the hysteretic maps of ferroelectric materials that are transformed into a butterfly through a 2-to-1 map.