Simulation of field effects on the mechanical hysteresis of Terfenol rods and magnetic shape memory materials using vector Preisach-type models

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Abstract

Materials exhibiting gigantic magnetostriction and magnetic shape memory are currently being widely used in various applications. Recently, an approach based on simulating 1-D magnetostriction using 2-D anisotropic Preisach-type models has been introduced. The purpose of this paper is to present a detailed formulation and quantitative assessment for the simulation of field effects on the mechanical hysteresis of Terfenol rods and magnetic shape memory materials using this recently proposed model. Details of the model formulation, identification procedure and experimental testing are given in the paper.

Introduction

Magnetic materials exhibiting gigantic magnetostriction, especially Terfenol, and shape memory are currently being widely used in various devices and applications. Obviously, using accurate magnetostriction simulation models during design stages of such devices can lead to a significant enhancement in their precision.

Recently, several magnetostriction models having good qualitative agreement with experimentally observed data have been proposed (see, for instance, Refs. [1], [2], [3], [4]). Among these recently developed models, an approach based on simulating 1-D magnetostriction using 2-D anisotropic Preisach-type models has been presented [5]. According to this approach, 1-D magnetostriction experimentally observed data may be simply realized by mapping the inputs and outputs of the 2-D anisotropic Preisach-model easy and hard axes to the magnetic field H, flux density B, stress value σs and strain λ. In other words, a 2-D anisotropic vector Preisach model may give good agreement with well-known and experimentally observed 1-D magnetostriction data. It should be pointed out here that while many previous publications investigated the accuracy of such models in simulating magnetization and strain variations caused by magnetic field changes, few publications assessed such models for mechanical hysteresis simulations.

The purpose of this paper is to present a detailed formulation and quantitative assessment for the simulation of field effects on the mechanical hysteresis of Terfenol rods and magnetic shape memory materials using the model proposed in Ref. [5]. The proposed model has been numerically implemented and its identification has been obtained. Model simulations were performed and comparisons were carried out between experimentally measured and computed Terfenol and magnetic shape memory material stress–strain (σλ) curves derived under the application of a magnetic field (H). Details of the model formulation, identification procedure and experimental testing are given in the following sections of the paper.

Section snippets

The adopted model and its identification

Focusing on the mechanical hysteresis and its dependency on magnetic field variations, the model proposed in Ref. [5] can be mathematically reformulated as follows:λ(t)ex=-π/2+π/2eφΓ^(eφ·(σ(t)ex+H(t)ey))dφ,Γ^(eφ·(σ(t)ex+H(t)ey))=αβν(α,β,φ)γ^αβ(eφ·(σ(t)ex+H(t)ey))dαdβ,where ν is the model unknown, t represents the input–output time instant, H is the applied field, σ is the applied stress, λ is the strain, γ^αβ are elementary hysteresis operators represented by rectangular loops

Simulations and experimental results

The proposed model, as given by Eqs. (1), (2), (3) and Eq. (8), has been numerically implemented and several computer simulations have been performed and compared with experimentally observed data for; a Terfenol rod and a magnetic shape memory material produced by Adaptamat (www.adaptamat.com).

For the case of the Terfenol rod stress–strain (σλ) first-order-reversal curves measured at zero field were acquired as shown in Fig. 1. Using these curves solution of the identification problem was

Conclusions

It can be concluded from the presented results that the proposed simulation approach can lead to good qualitative agreement with experimentally measured stress–strain (σλ) data subject to different magnetic field H variations. As indicated before, this can be mainly attributed to the fact that the model identification is implicitly carried out using σλ curves for different H values.

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