Summary for: InhomogeneousMaterial < Material

Class summary

InhomogeneousMaterial Inhomogeneous material properties class.

This class implements some simple functionality for analysing materials with non-homogeneous yet isotropic material properties.

The class supports setting the following mechanical properties

• Young’s modulus
• Poisson’s ratio
• Density independently for each element. Please note that the properties must be set either for all of the elements, or none of them. In other words, the size of e.g. this.elementwise_Youngs_modulus_values must equal the size of this.elements, or be empty. Likewise, the indexing is obviously local, i.e. setting the n:th entry of this.elementwise_Youngs_modulus_values corresponds to the Young’s modulus of this.elements(n) in the global indexing scheme.

For magnetic inhomohenuity, two options are offered.

The simpler and faster method uses two coefficient for the H and B values, transforming the elementwise H(B) behaviour into Hnew = H_coefficient ** H(B** B_coefficient). The two coefficients are defined elementwise, in this.elementwise_H_coefficient and this.elementwise_B_coefficient.

The more general method is to set custom BH curves for sets of elements using this.set_elementwise_BH_data. While it is possible to set different properties for each and every element, this can result in slow evaluation times.

The method used is defined by this.BH_mode. Setting “simple” uses the two-coefficient approach, while “general” uses the elementwise properties.

Custom behaviour can most easily by implemented by subclassing and then overloading the interpolate_elementwise_reluctivity method.

Properties

.BH_mode Method of BH evaluation.

Either “simple” or “general”. See interpolate_elementwise_reluctivity.

.elementwise_B_coefficient B-coefficient for BH evaluation.

See interpolate_elementwise_reluctivity.

.elementwise_H_coefficient H-coefficient for BH evaluation.

See interpolate_elementwise_reluctivity.

.elementwise_Poissons_ratio_values Elementwise Poisson’s ratio.

.elementwise_Youngs_modulus_values Elementwise Young’s modulus.

.elementwise_density_values Elementwise density.

Methods

Class methods are listed below. Inherited methods are not included.

.basic copy stuff

.clear_elementwise_BH_data(this) Clears custom BH data.

.elementwise_density Return elementwise density.

Returns this.elementwise_density_values if set, and this.density otherwise.

.elementwise_poissons_ratio Return elementwise Poisson’s ratio.

Returns this.elementwise_Poissons_ratio_values if set, and this.density Poissons_ratio.

.elementwise_stiffness_tensor Plane-strain stiffness tensor.

Returns the elementwise stiffness tensor, for plane-strain formulation, using Voigt notation in column-major format.

If this.elementwise_Youngs_modulus_values has not been set, reverts to the method implementation in Material.

.InhomogeneousMaterial/from_material is a function.

this = from_material(this_dummy, mat)

.interpolate_elementwise_reluctivity Return elementwise reluctivities.

[nu, dnu] = interpolate_elementwise_reluctivity(this, Bsquared) returns the arrays of elementwise reluctivities and differential reluctivities, the latter defined as dnu/dB^2.

Two options are supported:

The simpler and faster method uses two coefficient for the H and B values, transforming the elementwise H(B) behaviour into Hnew = H_coefficient ** H(B** B_coefficient). The two coefficients are defined elementwise, in this.elementwise_H_coefficient and this.elementwise_B_coefficient.

The more general method is to set custom BH curves for sets of elements using this.set_elementwise_BH_data. While it is possible to set different properties for each and every element, this can result in slow evaluation times.

The method used is defined by this.BH_mode. Setting “simple” uses the two-coefficient approach, while “general” uses the elementwise properties.

.set_elementwise_BH_data Sets elementwise BH behaviour.

set_elementwise_BH_data(this, B, H, element_indices) sets the given BH behaviour for the set of elements given in element_indices. Note that local indexing is used, i.e. global_index = this.elements(local_index)

Please also note that you should always call this.clear_elementwise_BH_data once before calling this method, to avoid accumulating old data.

Please also note that the BH data must be set for all elements, even if the default behaviour is assumed for some of them.