Ferroelectric material hysteresis In COMSOL Multiphysics®

Parameters are useful in the following context:

•As parameters in dimensions for geometric primitives or other geometry operations

•As parameters for the mesh generators too, for example, specify the mesh size

•As parameters to control some aspects of the solution process

•To quickly evaluate a mathematical expression, including unit conversion

•In physics interface and feature settings, expressions, and coupling operators

•In expressions when evaluating results

Create the Geometry

The Jiles–Atherton model of magnetic hysteresis was introduced in 1984 by David Jiles and D. L. Atherton. This is one of the most popular models of magnetic hysteresis. Its main advantage is the fact that this model enables connection with physical parameters of the magnetic material.
Please check attached PDF for the theory details

The model is studied and results are plotted

An Infinite Element Domain node applies a real-valued coordinate scaling to a layer of virtual domains surrounding the physical region of interest. When the dependent variables vary slowly with radial distance from the center of the physical domain, the finite elements can be stretched in the radial direction such that boundary conditions on the outside of the infinite element layer are effectively applied at a very large distance from any region of interest.

The Ampère’s Law node adds Ampère’s law for the magnetic field and provides an interface for defining the constitutive relation and its associated properties as well as electric properties.

Select the Hysteresis Jiles–Atherton model to use in the constitutive relation B = μ0H + μ0M with the magnetization M (SI unit: A/m) computed from the solution of the five parameters Jiles–Atherton model. Specify the five parameters Ms, a, k, c, and α either from the material (default) or as user defined.

The Coil node can be used to model coils, cables and other conductors subject to a lumped excitation, such as an externally applied current or voltage. The Coil feature transforms this lumped excitation into local quantities (electric field and electric current density), and computes lumped parameters of interest such as impedance, and inductance.
The Coil feature supports two different Conductor models:

•Single conductor, which models a conductive body such as a wire, busbar, or other metallic conductor in which the current flows freely due to the material’s conductivity. This model can be used when the current flow has a well-defined beginning and end (for example, connections to an external source) or is closed in a loop.

•Homogenized multiturn, which models a bundle of tiny wires tightly wound together but separated by an electrical insulator. In this scenario, the current flows only in the direction of the wires and is negligible in other directions.

The Time Dependent study and study step are used when field variables change over time.

For example, in electromagnetics, it is used to compute transient electromagnetic fields, including electromagnetic wave propagation in the time domain. In heat transfer, it is used to compute temperature changes over time. In solid mechanics, it is used to compute the time-varying deformation and motion of solids subject to transient loads. In acoustics, it is used to compute the time-varying propagation of pressure waves. In fluid flow, it is used to compute unsteady flow and pressure fields. In chemical species transport, it is used to compute chemical composition over time. In chemical reactions, it is used to compute the reaction kinetics and the chemical composition of a reacting system.

Maximum step constraint. By default, the solver chooses a maximum time step automatically. Select Constant as the maximum step constraint for manual specification of a fixed maximum time step. A constant maximum step constraint is a positive scalar value, which can be an expression that evaluates to a numerical value before entering the solver. The expression can include global parameters. Select Expression as the maximum step constraint for more general expressions of the allowed maximum time step. These expressions are evaluated while solving and can, for instance, depend on the time parameter itself.