A Semigroup Theory of Rate Independent Hysteresis

TL;DR

This paper develops an algebraic semigroup framework to analyze rate independent hysteresis, revealing new relations between return point memory, partial order, and variational principles, and discussing erasing properties of field histories.

Contribution

It introduces a novel semigroup-based algebraic approach to model and analyze rate independent hysteresis, connecting it with existing theories and properties.

Findings

Identifies the semigroup structure of hysteresis history space.

Discovers the relation between return point memory and partial order.

Characterizes erasing properties of field histories.

Abstract

We explore a macroscopic, algebraic approach to rate independent hysteresis using semigroup theory. A macroscopic description of metastable states relevant to rate independent hysteresis is introduced using field history. The semigroup structure of the history space is identified. Using semigroup theory and related mathematical techniques, the general relation between return point memory (RPM) and partial order is discovered. For hysteresis system with RPM, a variational principle is identified. The erasing properties of field histories are also characterized. The connection between this semigroup approach and other models are also discussed.