A theory of finite deformation magneto-viscoelasticity

TL;DR

This paper develops a mathematical framework for large strain magneto-viscoelastic deformations, incorporating energy dissipation from mechanical and magnetic effects, and provides solutions illustrating the influence of model parameters.

Contribution

It introduces a thermodynamically consistent model for finite deformation magneto-viscoelasticity with internal damping mechanisms and solves specific relaxation problems.

Findings

Model captures the interplay of mechanical and magnetic relaxation.

Solutions demonstrate parameter effects on deformation and magnetisation.

Graphical results illustrate the model's predictions.

Abstract

This paper deals with the mathematical modelling of large strain magneto-viscoelastic deformations. Energy dissipation is assumed to occur both due to the mechanical viscoelastic effects as well as the resistance offered by the material to magnetisation. Existence of internal damping mechanisms in the body is considered by decomposing the deformation gradient and the magnetic induction into `elastic' and `viscous' parts. Constitutive laws for material behaviour and evolution equations for the non-equilibrium fields are derived that agree with the laws of thermodynamics. To illustrate the theory the problems of stress relaxation, magnetic field relaxation, time dependent magnetic induction and strain are formulated and solved for a specific form of the constitutive law. The results, that show the effect of several modelling parameters on the deformation and magnetisation process, are illustrated graphically.