A Multiphysics Internal State Variable (ISV) Magneto Thermo-Visco-Plastic Model


Mounia Malki


Liu, Yucheng

Committee Member

Horstemeyer, Mark F.

Committee Member

Baskes, Michael I.

Committee Member

Dickel, Doyl

Date of Degree


Original embargo terms

Visible to MSU only for 2 years||5/16/2022

Document Type

Dissertation - Open Access


Mechanical Engineering

Degree Name

Doctor of Philosophy


James Worth Bagley College of Engineering


Department of Mechanical Engineering


A macroscale Internal State Variable (ISV) constitutive model coupling magnetism effects with thermal, elastic, and damage effects is developed. Previous models for magnetic and mechanical fields included constitutive equations describing their effects on the material system studied independently. Some models explain the mechanisms behind mechanical deformations caused by magnetization changes that are presented in the literature. They mainly focus on the nanoscale level. Other models, describe the behavior of one specific magnet that is mostly a permanent magnet. However permanent magnets are made of rare-earth elements that are subjected to a high supply risk. In attempt to find an alternative to permanent magnets, a mathematical model that captures the physical behavior of magnets is needed, to help develop a tool to create a new permanent magnet. The ISV constitutive model herein describes the macroscale mechanical deformation caused by magnetic fields on ferromagnetic materials, Iron (Fe), Cobalt (Co) and Nickel (Ni) precisely. The ISV model internally coheres the kinematic, thermodynamic, and kinetic relationships of deformation using the evolving histories of internal variables. For the kinematics, a multiplicative decomposition of deformation gradient is employed including a magnetization term, and the Jacobian that represents the conservation of mass and conservation of momentum. The First and Second Law of Thermodynamics are used to constrain the appropriate constitutive relations through the Clausius-Duhem inequality. The kinetic framework employs a stress-strain relationship with a flow rule that couples the thermal, mechanical, and damage terms. To determine the ISVs needed to mimic the behavior of magnetic materials, we conducted various magnetic experiments on three different specimens made of Iron, Nickel and Cobalt. Experiments captured the mechanical deformation of a rod sample when subjected to a magnetic field using the Michelson Interferometer. To study the magnetic hysteresis of Iron, Nickel, and Cobalt, previous literature data were used. It was shown that the magnetization equation modeled the hysteresis of Iron, Nickel, and Cobalt. The magnetostrictive strain equation shows good agreement for Nickel and Cobalt, but further investigation should be done for Iron.




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