The linear theory of ellasticity in anisotropic materials is essentialy based on the fourth order stiffness tensor C. Such a tensor is represented in MTEX by a variable of type stiffnessTensor. Such a variable can either by set up using a symmetric 6x6 matrix or by importing it from an external file. The following examples does so for the stiffness tensor for Olivine
The linear theory of elasticity in anisotropic materials is essentially based on the fourth order stiffness tensor C. Such a tensor is represented in MTEX by a variable of type stiffnessTensor. Such a variable can either by set up using a symmetric 6x6 matrix or by importing it from an external file. The following examples does so for the stiffness tensor for Olivine
{% highlight matlab %}
% file name
fname = fullfile(mtexDataPath,'tensor','Olivine1997PC.GPa');
-% crytsal symmetry
+% crystal symmetry
cs = crystalSymmetry('mmm',[4.7646 10.2296 5.9942],'mineral','Olivin');
% define the tensor
@@ -37,7 +37,7 @@
0 0 0 0 77 0
0 0 0 0 0 78.7
{% endhighlight %}
-
Hooke's Law
The stiffness tensor tensor of a material is defined as the stress the material expreances for a given strain
+
Hooke's Law
The stiffness tensor tensor of a material is defined as the stress the material experiences for a given strain
{% highlight matlab %}
eps = strainTensor(diag([1,1.1,0.9]),cs)
{% endhighlight %}
@@ -78,7 +78,7 @@
Hooke's Law
The stiffness tensor tensor of a material is defin
0 1.1 0
0 0 0.9
{% endhighlight %}
-
The ellastic energy of the strain eps can be computed equivalently by the following equations
+
The elastic energy of the strain eps can be computed equivalently by the following equations
{% highlight matlab %}
% the elastic energy
U = sigma : eps
@@ -101,7 +101,7 @@
Young's Modulus
Young's modulus is also known as the tensile m
E =
286.9284
{% endhighlight %}
-
If the direction d is ommited Youngs modulus is returned as a spherical function.
+
If the direction d is omitted Youngs modulus is returned as a spherical function.
{% highlight matlab %}
% compute Young's modulus as a directional dependent function
E = C.YoungsModulus
@@ -116,7 +116,6 @@
Young's Modulus
Young's modulus is also known as the tensile m
{% highlight plaintext %}
E = S2FunHarmonicSym (Olivin)
- mineral: Olivin (mmm)
bandwidth: 128
antipodal: true
isReal: true
@@ -140,7 +139,6 @@
Young's Modulus
Young's modulus is also known as the tensile m
{% highlight plaintext %}
beta = S2FunHarmonicSym (Olivin)
- mineral: Olivin (mmm)
bandwidth: 2
antipodal: true
isReal: true
@@ -166,14 +164,13 @@
Young's Modulus
Young's modulus is also known as the tensile m
nu =
0.1515 0.3383
{% endhighlight %}
-
If we ommit in the call to PoissonRatio the last argument
+
If we omit in the call to PoissonRatio the last argument
{% highlight matlab %}
nu = C.PoissonRatio(p)
{% endhighlight %}
{% highlight plaintext %}
nu = S2FunHarmonicSym (Olivin)
- mineral: Olivin (mmm)
bandwidth: 4
antipodal: true
isReal: true
@@ -233,4 +230,33 @@
Young's Modulus
Young's modulus is also known as the tensile m
{% endhighlight %}
{% include inline_image.html file="AnisotropicTheory_04.png" %}
-Wave Velocities
Since elastic compression and decompression is mechanics of waves traveling through a medium anisotropic compressibility causes also anisotropic waves speeds. The analysis of this anisotropy is explained in the section wave velocities.
+