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materialProperties

Material properties for structural, thermal, and electromagnetic analysis

Since R2023a

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Description

A materialProperties object contains the description of material properties for structural, thermal, and electromagnetic analysis. An femodel object contains an array of materialProperties objects in its MaterialProperties property.

Creation

Syntax

model.MaterialProperties = materialProperties(Name=Value)
model.MaterialProperties(RegionID) = materialProperties(Name=Value)

Description

model.MaterialProperties = materialProperties(Name=Value) creates a material properties object and sets properties using one or more name-value arguments. This syntax assigns the specified structural, thermal, or electromagnetic material properties to the entire geometry of the femodel object model.

example

model.MaterialProperties(RegionID) = materialProperties(Name=Value) assigns material properties to the specified geometry region.

example

Input Arguments

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Cell or face IDs, specified as a vector of positive integers. Find the region IDs using pdegplot with the CellLabels (3-D) or FaceLabels (2-D) value set to "on".

Data Types: double

Properties

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Young's modulus of the material, specified as a positive number, three-element vector of positive numbers (for both 2-D and 3-D geometries), or function handle. Use a function handle to specify Young's modulus that depends on space. For details, see Nonconstant Parameters of Finite Element Model.

Specifying Young's modulus as a three-element vector of positive numbers (or a function handle returning a three-row matrix of positive numbers) means that the material is orthotropic. A matrix of positive numbers specifies the orthotropic Young's modulus along the Cartesian coordinates x, y, and z as [Ex Ey Ez]. For orthotropic materials, you must also specify a shear modulus and Poisson's ratio as three-row matrices of positive numbers or function handles returning three-row matrices of positive numbers.

Data Types: double

Poisson's ratio of the material, specified as a positive number, three-element vector of positive numbers (for both 2-D and 3-D geometries), or function handle. Use a function handle to specify Poisson's ratio that depends on space. For details, see Nonconstant Parameters of Finite Element Model. For isotropic materials, the value must be in the range (0,0.5).

Specifying Poisson's ratio as a three-element vector of positive numbers (or a function handle returning a three-row matrix of positive numbers) means that the material is orthotropic. A matrix of positive numbers specifies the orthotropic Poisson's ratio along the Cartesian coordinates x, y, and z as [νxy νyz νxz]. For orthotropic materials, you must also specify Young's modulus and a shear modulus as three-element vectors of positive numbers or function handles returning three-row matrices of positive numbers.

Data Types: double

Shear modulus of the material, specified as a three-element vector of positive numbers (for both 2-D and 3-D geometries), or function handle. Specify shear modulus for orthotropic materials. Use a function handle to specify shear modulus that depends on space. For details, see Nonconstant Parameters of Finite Element Model.

Specifying a shear modulus indicates that the material is orthotropic. A matrix of positive numbers specifies the orthotropic shear modulus along the Cartesian coordinates x, y, and z as [Gxy Gyz Gxz]. For orthotropic materials, you must also specify Young's modulus and Poisson's ratio as three-element vectors of positive numbers or function handles returning three-row matrices of positive numbers.

Data Types: double

Mass density of the material, specified as a positive number or function handle. Use a function handle to specify mass density that depends on space. For details, see Nonconstant Parameters of Finite Element Model. This property is required when modeling gravitational effects.

Data Types: double

Coefficient of thermal expansion of the material, specified as a real number. This property is required for thermal stress analysis. Thermal stress analysis requires the structural model to be static.

Data Types: double

Thermal conductivity of the material, specified as a nonnegative number, matrix, or function handle. You can specify thermal conductivity for a steady-state or transient analysis. For orthotropic thermal conductivity, use a thermal conductivity matrix. Use a function handle to specify a thermal conductivity that depends on space, time, or temperature. For details, see Nonconstant Parameters of Finite Element Model.

Data Types: double | function_handle

Specific heat of the material, specified as a positive number or function handle. Specify this property for a transient thermal conduction analysis. Use a function handle to specify a specific heat that depends on space, time, or temperature. For details, see Nonconstant Parameters of Finite Element Model.

Data Types: double | function_handle

Hysteretic damping of the material, specified as a nonnegative number. This type of damping is also called structural damping.

Data Types: double

Relative permittivity of the material, specified as a number or function handle.

  • Use a positive number to specify a relative permittivity for an electrostatic analysis.

  • Use a real or complex number to specify a relative permittivity for a harmonic electromagnetic analysis.

  • Use a function handle to specify a relative permittivity that depends on the coordinates and, for a harmonic analysis, on the frequency. For details, see Nonconstant Parameters of Finite Element Model.

Data Types: double | function_handle
Complex Number Support: Yes

Relative permeability of the material, specified as a number or function handle. For a magnetostatic analysis:

  • Use a positive number to specify a constant relative permeability.

  • Use a function handle to specify a relative permeability that depends on the coordinates, magnetic potential and its gradients, and the norm of the magnetic flux density. For details, see Nonconstant Parameters of Finite Element Model.

For a harmonic analysis:

  • Use a real or complex number to specify a constant relative permeability.

  • Use a function handle to specify a relative permeability that depends on the coordinates and on the frequency. For details, see Nonconstant Parameters of Finite Element Model.

Data Types: double | function_handle
Complex Number Support: Yes

Conductivity of the material, specified as a nonnegative number or function handle. Use a function handle to specify a conductivity that depends on the coordinates and, for a harmonic analysis, on the frequency. For details, see Nonconstant Parameters of Finite Element Model.

Data Types: double | function_handle

Examples

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Open Live Script

Specify relative permeability for an femodel object representing a magnetostatic problem.

Create an femodel object for solving a magnetostatic problem, and assign a geometry representing a plate with a hole to the model.

model = femodel(AnalysisType="magnetostatic", ...
                Geometry="PlateHolePlanar.stl");

Plot the geometry with the face labels.

pdegplot(model.Geometry,FaceLabels="on");

Figure contains an axes object. The axes object contains an object of type line.

Specify the vacuum permeability value in the SI system of units.

model.MaterialProperties = materialProperties(RelativePermeability=5000);
model.MaterialProperties
ans = 
  1x1 materialProperties array

Properties for analysis type: magnetostatic

Index    RelativePermeability
  1              5000        

  Show all properties
Open Live Script

Specify Young's modulus, Poisson's ratio, and the mass density for an femodel object representing a static structural problem.

Create and plot a bimetallic beam geometry.

H = 0.1;
gm = multicuboid(0.5,0.1,[H,H],Zoffset=[0,H]);
pdegplot(gm,CellLabels="on");

Figure contains an axes object. The axes object contains 6 objects of type quiver, text, patch, line.

Create an femodel object for solving a static structural problem, and assign the geometry to the model.

model = femodel(AnalysisType="structuralStatic", ...
                Geometry=gm);

Specify different values of Young's modulus, Poisson's ratio, and the mass density for cells 1 and 2.

model.MaterialProperties(1) = materialProperties(YoungsModulus=210e9, ...
                                              PoissonsRatio=0.28, ...
                                              MassDensity=1.3e-5);
model.MaterialProperties(2) = materialProperties(YoungsModulus=110e9, ...
                                              PoissonsRatio=0.37, ...
                                              MassDensity=2.4e-5);
model.MaterialProperties
ans = 
  1x2 materialProperties array

Properties for analysis type: structuralStatic

Index    CTE    PoissonsRatio    YoungsModulus    MassDensity    ShearModulus
  1      []        0.2800         2.1000e+11      1.3000e-05          []     
  2      []        0.3700         1.1000e+11      2.4000e-05          []     

  Show all properties
Open Live Script

Use function handles to specify a thermal conductivity that depends on temperature and a specific heat that depends on coordinates.

Create a rectangular geometry.

gm = decsg([3 4 -1.5 1.5 1.5 -1.5 0 0 .2 .2]');

Create an femodel object for solving a transient thermal problem, and assign the geometry to the model.

model = femodel(AnalysisType="thermalTransient", ...
                Geometry=gm);

Specify the thermal conductivity as a linear function of temperature, k = 40 + 0.003T.

k = @(location,state)40 + 0.003*state.u;

Specify the specific heat as a linear function of the y-coordinate, cp = 500y.

cp = @(location,state)500*location.y;

Specify the thermal conductivity, mass density, and specific heat of the material.

model.MaterialProperties = materialProperties(ThermalConductivity=k, ...
                                              MassDensity=2.7*10^(-6), ...
                                              SpecificHeat=cp);
model.MaterialProperties
ans = 
  1x1 materialProperties array

Properties for analysis type: thermalTransient

Index           ThermalConductivity           MassDensity             SpecificHeat          
  1      @(location,state)40+0.003*state.u    2.7000e-06     @(location,state)500*location.y

  Show all properties
Open Live Script

Use a function handle to specify a relative permeability that depends on the magnetic flux density.

Create an femodel object for solving a magnetostatic problem, and assign a geometry representing a plate with a hole to the model.

model = femodel(AnalysisType="magnetostatic", ...
                Geometry="PlateHolePlanar.stl");

Plot the geometry with the face labels.

pdegplot(model.Geometry,FaceLabels="on");

Figure contains an axes object. The axes object contains an object of type line.

Specify the vacuum permeability value in the SI system of units.

model.VacuumPermeability = 1.2566370614e-6;

Specify the data for the magnetic flux density, B, and the corresponding magnetic field strength, H.

B = [0 .3 .8 1.12 1.32 1.46 1.54 1.61875 1.74];
H = [0 29.8 79.6 159.2 318.31 795.8 1591.6 3376.7 7957.8];

From the data for B and H, interpolate the H(B) dependency (B-H curve) using the modified Akima cubic Hermite interpolation method.

HofB = griddedInterpolant(B,H,"makima","linear");
muR = @(B) B./HofB(B)/mu0;

Specify the relative permeability that depends on the magnetic flux density.

model.MaterialProperties = materialProperties(RelativePermeability=muR);
model.MaterialProperties
ans = 
  1x1 materialProperties array

Properties for analysis type: magnetostatic

Index    RelativePermeability
  1       @(B)B./HofB(B)/mu0 

  Show all properties
Open Live Script

Use vector values to specify Young's modulus, Poisson's ratio, and shear modulus representing an orthotropic material.

Create an femodel object for solving a static structural problem, and assign a geometry representing a cube with a cylindrical hole to the model.

model = femodel(AnalysisType="structuralStatic", ...
                Geometry="BlockWithHole.step");

Plot the geometry.

pdegplot(model.Geometry,FaceAlpha=0.3);

Figure contains an axes object. The axes object contains 6 objects of type quiver, text, patch, line.

Specify Young's modulus, Poisson's ratio, shear modulus, and the mass density. For an orthotropic material, all parameters, except the mass density, must be 1-by-3 vector of positive numbers.

E = [22E9,9.8E9,22E9];
nu = [0.28,0.28,0.11];
G = [3.5E9,3.5E9,2.5E9];
rho = 1.3e-5;
model.MaterialProperties = materialProperties(YoungsModulus=E, ...
                                              PoissonsRatio=nu, ...
                                              ShearModulus=G, ...
                                              MassDensity=rho);
model.MaterialProperties
ans = 
  1x1 materialProperties array

Properties for analysis type: structuralStatic

Index    CTE        PoissonsRatio                   YoungsModulus               MassDensity               ShearModulus           
  1      []     [0.2800 0.2800 0.1100]    [2.2000e+10 9.8000e+09 2.2000e+10]    1.3000e-05     [3.5000e+09 3.5000e+09 2.5000e+09]

  Show all properties

Version History

Introduced in R2023a

See Also

Functions

Objects