Available Materials in Electromagnetic Solutions

Introduction

The solving of an electromagnetic problem consists of solving a set of equations:

the Maxwell equations, which represent the backbone of the theory
the constitutive equations of the matter, which model the material properties.


Material	Constitutive equation	Material property
magnetic		μ: permeability (H/m)
dielectric		ε: permittivity (F/m)
electric/conductive		ρ: resistivity (Ω.m) σ: conductivity (Ω^-1.m^-1)

Soft Magnetic Material


Model		Formula	Parameters
Linear isotropic	Soft Magnetic Analytical BH model	B= μ.H	μ_r: initial relative permeability
Nonlinear isotropic saturation (analytic with knee adjustment)*	Soft Magnetic Analytical BH model with Saturation	B= μ(H).H	μ_r: initial relative permeability Js: saturation magnetization (T) a: adjustment coefficient of the B(H) curve knee
Nonlinear isotropic saturation (spline)	Soft Magnetic Raw data BH model	B= μ(H).H	list of coordinates of points (H,B)

Note: In MT 2D and 3D and in MAC 2D and 3D, it is possible to specify a model to compute the iron losses. Only modified Bertotti model is available at this time, characterised by 3 coefficients and 3 exponents:

$k_{1}$ is the hysteresis losses coefficient;
$k_{2}$ is the classical losses coefficient;
$k_{3}$ is the excess losses coefficient;
$α_{1}$ is the hysteresis losses exponent;
$α_{2}$ is the classical losses exponent;
$α_{3}$ is the excess losses exponent.

Note: A material with modified Bertotti model is needed to compute iron losses in a Sheet Lamination part.

Hard Magnetic Material

Warning: In MAC 2D and 3D, Hard Magnetic material cannot be used.


Model		Formula	Parameters
Linear magnet described by the Br module*	Hard Magnetic Linear	B= [μ].H + Br	μ_r//: relative permeability (recoil line slope) Br: remanent flux density (T)
Nonlinear magnet described by Hc and the Br module *	Hard Magnetic Nonlinear	B= [μ(H)].H + Br	μ_rmax: maximal relative permeability μ_r⊥: transverse relative permeability B_r: remanent flux density (T) J_s: saturation magnetization (T)
Nonlinear magnet described by spline	Hard Magnetic Raw data	B= μ(H).H	list of coordinates of points (H,B)

Dielectric Material


Model		Formula	Parameters
Linear Isotropic	Dielectric properties → Linear	D = ε₀ε_rE	ε_r: relative permittivity
Isotropic Spline	Dielectric properties → Spline

Electric Material


Model		Formula	Parameters
Linear Isotropic resistivity*	Electric properties → Electric resistivity	J = (1/ρ)E	ρ: electric resistivity

Note: the * indicates the possibility to use this material model depending of the temperature