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evaluate an odf at orientation g

Syntax

-{% highlight matlab %} -ori = discreteSample(SO3F,npoints,varargin) -{% endhighlight %} -
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overloads SO3F1 .* SO3F2

Syntax

-{% highlight matlab %} -sF = SO3F1 .* SO3F2 -sF = a .* SO3F2 -sF = SO3F1 .* a -{% endhighlight %} -

Input

- - - - - - - - - -
- SO3F1, SO3F2 - - SO3FunRBF -
- a - - double -
-

Output

- - - - - -
- SO3F - - SO3Fun -
-

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b/pages/documentation_matlab/EBSDPlotting.html index e429d4654..a180b9ff2 100644 --- a/pages/documentation_matlab/EBSDPlotting.html +++ b/pages/documentation_matlab/EBSDPlotting.html @@ -61,7 +61,7 @@

Phase Plots

ans = 0.8549 0.6471 0.1255 {% endhighlight %} -

These values are RGB values which can be altered to any other RGB triple. A more convinient way for changing the color is the function str2rgb which converts color names into RGB triplets

+

These values are RGB values which can be altered to any other RGB triple. A more convenient way for changing the color is the function str2rgb which converts color names into RGB triplets

{% highlight matlab %} ebsd('Diopside').color = str2rgb('salmon'); @@ -84,7 +84,7 @@

Visualizing arbitrary properties

{% highlight matlab %} plot(ebsd,ebsd.bc) -colormap gray % make the image grayscale +colormap gray % make the image gray-scale mtexColorbar {% endhighlight %}
@@ -99,7 +99,7 @@

Visualizing orientations

{% include inline_image.html file="EBSDPlotting_05.png" %}
-

Obviously, the rotational angle is not a very distintive representative for orientations. A more common approach is to define a colorization of the fundamental secor of the inverse pole figure, a so called ipf color key, and to colorize orientations according to their position in a fixed inverse pole figure. Let's consider the following standard key.

+

Obviously, the rotational angle is not a very distinctive representative for orientations. A more common approach is to define a colorization of the fundamental sector of the inverse pole figure, a so called ipf color key, and to colorize orientations according to their position in a fixed inverse pole figure. Let's consider the following standard key.

{% highlight matlab %} % this defines an ipf color key for the Forsterite phase ipfKey = ipfColorKey(ebsd('Forsterite')); @@ -111,7 +111,7 @@

Visualizing orientations

{% include inline_image.html file="EBSDPlotting_06.png" %}
-

Next we may utilize this key to turn the orientations into colors, which are than passed to the plot command.

+

Next we may utilize this key to turn the orientations into colors, which are than passed to the plot command.

{% highlight matlab %} colors = ipfKey.orientation2color(ebsd('Forsterite').orientations); plot(ebsd('Forsterite'),colors) @@ -119,16 +119,16 @@

Visualizing orientations

{% include inline_image.html file="EBSDPlotting_07.png" %}
-

The above ipf color key can be largely customizied. This is explained in more detail in IPF Maps. Beside IPF maps there are also more specific ways to colorize orientations as they are discussed in Advanced Plotting.

+

The above ipf color key can be largely customized. This is explained in more detail in IPF Maps. Beside IPF maps there are also more specific ways to colorize orientations as they are discussed in Advanced Plotting.

Superposing different plots

-

Combining different plots can be done either by plotting only subsets of the EBSD data or via the option 'faceAlpha'. Note that the option 'faceAlpha' requires the renderer of the figure to be set to 'opengl'.

+

Combining different plots can be done either by plotting only subsets of the EBSD data or using the option 'faceAlpha' to control transparency.

{% highlight matlab %} close all; plot(ebsd,ebsd.bc) mtexColorMap black2white hold on -plot(ebsd('fo'),'FaceAlpha',0.5) +plot(ebsd('Forsterite'),colors,'FaceAlpha',0.5) hold off {% endhighlight %}
diff --git a/pages/documentation_matlab/FibreODFs.html b/pages/documentation_matlab/FibreODFs.html index 59eec3b16..8d6c33f43 100644 --- a/pages/documentation_matlab/FibreODFs.html +++ b/pages/documentation_matlab/FibreODFs.html @@ -1,5 +1,5 @@ --- -title: Fibre ODFs +title: Fiber ODFs sidebar: documentation_sidebar permalink: FibreODFs.html @@ -13,7 +13,7 @@ This HTML was auto-generated from MATLAB code. To make changes, update the MATLAB code and republish this document. --> -Fibre ODFs +Fiber ODFs @@ -26,7 +26,7 @@

A fibre is represented in MTEX by a variable of type fibre.

{% highlight matlab %} -cs = crystalSymmetry.load('Ti-Titanium-alpha.cif') +cs = crystalSymmetry('cubic') % define the fibre to be the beta fibre f = fibre.beta(cs) @@ -41,22 +41,20 @@ {% highlight plaintext %} cs = crystalSymmetry - mineral : Titanium - symmetry : 6/mmm - elements : 24 - a, b, c : 3, 2.9, 4.7 - reference frame: X||a*, Y||b, Z||c* + symmetry: m-3m + elements: 48 + a, b, c : 1, 1, 1 -f = fibre (Titanium → xyz) +f = fibre (m-3m → xyz) - h || r: (11 7 -18 12) || (0.16606,0.13548,0.97676) - o1 → o2: (348.4°,57.8°,60°) → (90°,77.1°,60°) + h || r: (12 6 11) || (1,1,4) + o1 → o2: (0°,35.3°,45°) → (90°,62.8°,45°) -odf = SO3FunCBF (Titanium → xyz) +odf = SO3FunCBF (m-3m → xyz) kernel: de la Vallee Poussin, halfwidth 10° - fibre : (11 7 -18 12) || 0.16606,0.13548,0.97676 + fibre : (12 6 11) || 1,1,4 weight: 1 {% endhighlight %}
diff --git a/pages/documentation_matlab/IsotropicTheory.html b/pages/documentation_matlab/IsotropicTheory.html index 3acfe2da2..d232f498d 100644 --- a/pages/documentation_matlab/IsotropicTheory.html +++ b/pages/documentation_matlab/IsotropicTheory.html @@ -60,7 +60,7 @@

The single crystal stiffness tensor

-0.9 -6.4 -9.4 -7.2 0.6 33.6 {% endhighlight %}

The effective isotropic stiffness tensor

-

An isotropic Albite material we assume here to consist of randomly oriented grains forming an uniform (isotropic) texture. In this case the Voigt and Reuss avarages provide upper and lower bounds for the elastic properties of the material.

+

An isotropic Albite material we assume here to consist of randomly oriented grains forming an uniform (isotropic) texture. In this case the Voigt and Reuss averages provide upper and lower bounds for the elastic properties of the material.

{% highlight matlab %} [C_iso_Voigt,C_iso_Reuss,C_iso_Hill] = mean(C,uniformODF(C.CS)) {% endhighlight %} @@ -203,7 +203,7 @@

Formulas between the elastic moduli

101.9764 {% endhighlight %}

Lame constants

-

The second way to represent the elastic behaviour of an isotropic medium is by means of the Lame constants

+

The second way to represent the elastic behavior of an isotropic medium is by means of the Lame constants

{% highlight matlab %} lambda = nu/(1-2*nu) /(1+nu) * E; mu =G; @@ -258,7 +258,7 @@

Lame constants

Hashin Shtrikman Bounds

While the Voigt and Reuss bounds are tight without additional assumptions, the extreme cases require a very specific layered microstructure. If one additionally assumes that the material is quasihomogeneous, i.e., it is constant elastic properties within each subregion that is significantly larger then the grain size, then the Voigt and Reuss bounds are to wide. More narrow bounds for this settings have been established by Hashin and Shtrikman in 1962.

The following deviation follows the paper by J.M. Brown (2015) Determination of Hashin-Shtrikman bounds on the isotropic effective elastic moduli of polycrystals of any symmetry, Computers & Geosciences, 80 (2015) 95-99.

-

The upper and lower Hashin-Shtrikman bounds for the bulk and shear moduli are found as a solution of an optimzation problem. Lets first set up the search domain

+

The upper and lower Hashin-Shtrikman bounds for the bulk and shear moduli are found as a solution of an optimization problem. Lets first set up the search domain

{% highlight matlab %} % define a 2 dimensional domain of bulk and shear moduli KMin = 1; KMax = 150; % minimum and maximum bulk moduli @@ -267,7 +267,7 @@

Hashin Shtrikman Bounds

Go = linspace(GMin,GMax,300); [G0Mesh,K0Mesh] = meshgrid(Go,Ko); {% endhighlight %} -

Next the initial stiffness tensor is updated such that the residual stiffness tensor R remains either possitve or negative definite.

+

Next the initial stiffness tensor is updated such that the residual stiffness tensor R remains either positive or negative definite.

{% highlight matlab %} tic [khs, ghs, def] = HashinShtrikmanModulus(C,K0Mesh,G0Mesh); @@ -302,7 +302,9 @@

Hashin Shtrikman Bounds

{% endhighlight %} {% highlight plaintext %} -Elapsed time is 1.776948 seconds. +Warning: Tensor is not positive definite +Warning: Tensor is not positive definite +Elapsed time is 2.440417 seconds. {% endhighlight %}
{% include inline_image.html file="IsotropicTheory_01.png" %} diff --git a/pages/documentation_matlab/SO3FunSymmetricFunctions.html b/pages/documentation_matlab/SO3FunSymmetricFunctions.html index c6785b315..58482238d 100644 --- a/pages/documentation_matlab/SO3FunSymmetricFunctions.html +++ b/pages/documentation_matlab/SO3FunSymmetricFunctions.html @@ -159,7 +159,7 @@
{% include inline_image.html file="SO3FunSymmetricFunctions_03.png" %}
-

Symmetrising the Fourier coefficients transforms the coefficients. So we symmetrise the function and it is no longer possible to go back to the non symmetrized function from before.

+

Symmetrising the Fourier coefficients transforms the coefficients. So we symmetrise the function and it is no longer possible to go back to the non symmetrised function from before.

{% highlight matlab %} SO3F2 = SO3F2.symmetrise SO3F2.fhat(1:10)