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TensorAnalysis.html
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<!DOCTYPE html
PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN">
<html xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<title>Tensors (DocHelp Toolbox)
</title>
<!-- DOCNAME: DocHelp Toolbox -->
<meta name="chunktype" content="refpage">
<!-- CHUNKNAME: TensorAnalysis -->
<!-- HEADSTUFF: TensorAnalysis -->
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<meta name="refentity" content="method:TensorAnalysis">
<meta http-equiv="Content-Script-Type" content="text/javascript">
<meta name="toctype" content="fcn">
<link rel="stylesheet" href="up.css"><script language="JavaScript" src="docscripts.js"></script></head>
<body><a name="top_of_page"></a><div class="navbar navbar-inverse navbar-fixed-top">
<div class="navbar-inner">
<div class="container"><a class="brand" href="/">MTEX Toolbox</a><ul class="nav">
<li><a href="/download.html">Downloads</a></li>
</ul>
<ul class="nav">
<li><a href="/documentation.html">Documentation</a></li>
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<li><a href="/team.html">People</a></li>
</ul>
<ul class="nav">
<li><a href="/publications.html">Publications</a></li>
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<li><a href="/support.html">Support</a></li>
</ul>
</div>
</div>
</div>
<div class="container">
<h1>Tensors</h1>
<div class="subheading">
<p>Explains how to work with material tensors in MTEX, i.e. how to compute mean material tensors according to an ODF or to EBSD
data, how to compute rotate and visualize tensors and how to calculate with elasticity tensors.
</p>
</div>
<p>
<table class="ref" width="90%">
<tr>
<td valign="top" width="15">
<div align="center">
<a href="#"
onClick="return toggleexpander('TensorArithmetics_block','TensorArithmetics_expandable_text');"
valign="top"
width="15">
<img id="TensorArithmetics_expandable_text" src="arrow_right.gif" style="border:0px"/></a>
</div>
</td>
<td valign="top" width="250px">
<a href="TensorArithmetics.html">Tensor Arithmetics<td valign="top" width="75%">how to calculate with tensors in MTEX</td></a>
</td>
</tr>
<tr>
<td/>
<td colspan="2">
<div class="expander" id="TensorArithmetics_block"
style="display:none; background:#e7ebf7; padding-left:2ex;">
<table>
<tr>
<td>
<a href="TensorArithmetics.html#4">Defining a Tensor</a>
</td>
</tr>
<tr>
<td>
<a href="TensorArithmetics.html#7">Importing a Tensor from a File</a>
</td>
</tr>
<tr>
<td>
<a href="TensorArithmetics.html#8">Visualization</a>
</td>
</tr>
<tr>
<td>
<a href="TensorArithmetics.html#10">Rotating a Tensor</a>
</td>
</tr>
<tr>
<td>
<a href="TensorArithmetics.html#13">The Inverse Tensor</a>
</td>
</tr>
<tr>
<td>
<a href="TensorArithmetics.html#14">Tensor Products</a>
</td>
</tr>
</table>
</div>
</td>
</tr>
<tr>
<td valign="top" width="15">
<div align="center">
<a href="#"
onClick="return toggleexpander('MeanTensors_block','MeanTensors_expandable_text');"
valign="top"
width="15">
<img id="MeanTensors_expandable_text" src="arrow_right.gif" style="border:0px"/></a>
</div>
</td>
<td valign="top" width="250px">
<a href="MeanTensors.html">Average Material Tensors<td valign="top" width="75%">how to calculate average material tensors
from ODF and EBSD data</td></a>
</td>
</tr>
<tr>
<td/>
<td colspan="2">
<div class="expander" id="MeanTensors_block"
style="display:none; background:#e7ebf7; padding-left:2ex;">
<table>
<tr>
<td>
<a href="MeanTensors.html#5">Import EBSD Data</a>
</td>
</tr>
<tr>
<td>
<a href="MeanTensors.html#7">Data Correction</a>
</td>
</tr>
<tr>
<td>
<a href="MeanTensors.html#8">Define Elastic Stiffness Tensors for Glaucophane and Epidote</a>
</td>
</tr>
<tr>
<td>
<a href="MeanTensors.html#10">The Average Tensor from EBSD Data</a>
</td>
</tr>
<tr>
<td>
<a href="MeanTensors.html#12">ODF Estimation</a>
</td>
</tr>
<tr>
<td>
<a href="MeanTensors.html#13">The Average Tensor from an ODF</a>
</td>
</tr>
</table>
</div>
</td>
</tr>
<tr>
<td valign="top" width="15">
<div align="center">
<a href="#"
onClick="return toggleexpander('PlasticDeformation_block','PlasticDeformation_expandable_text');"
valign="top"
width="15">
<img id="PlasticDeformation_expandable_text" src="arrow_right.gif"
style="border:0px"/></a>
</div>
</td>
<td valign="top" width="250px">
<a href="PlasticDeformation.html">Schmid Factor Analysis<td valign="top" width="75%">This script describes how to analyze
Schmid factors.</td></a>
</td>
</tr>
<tr>
<td/>
<td colspan="2">
<div class="expander" id="PlasticDeformation_block"
style="display:none; background:#e7ebf7; padding-left:2ex;">
<table>
<tr>
<td>
<a href="PlasticDeformation.html#3">Geometric Definition</a>
</td>
</tr>
<tr>
<td>
<a href="PlasticDeformation.html#11">Stress Tensor</a>
</td>
</tr>
<tr>
<td>
<a href="PlasticDeformation.html#13">Active Slip System</a>
</td>
</tr>
<tr>
<td>
<a href="PlasticDeformation.html#20">The Schmid factor for EBSD data</a>
</td>
</tr>
<tr>
<td>
<a href="PlasticDeformation.html#28">Strain based analysis on the same data set</a>
</td>
</tr>
</table>
</div>
</td>
</tr>
<tr>
<td valign="top" width="15">
<div align="center">
<a href="#"
onClick="return toggleexpander('PiezoElectricity_block','PiezoElectricity_expandable_text');"
valign="top"
width="15">
<img id="PiezoElectricity_expandable_text" src="arrow_right.gif" style="border:0px"/></a>
</div>
</td>
<td valign="top" width="250px">
<a href="PiezoElectricity.html">The Piezoelectricity Tensor<td valign="top" width="75%">how to work with piezoelectricity</td></a>
</td>
</tr>
<tr>
<td/>
<td colspan="2">
<div class="expander" id="PiezoElectricity_block"
style="display:none; background:#e7ebf7; padding-left:2ex;">
<table>
<tr>
<td>
<a href="PiezoElectricity.html#5">Plotting the magnitude surface</a>
</td>
</tr>
<tr>
<td>
<a href="PiezoElectricity.html#11">Mean Tensor Calculation </a>
</td>
</tr>
</table>
</div>
</td>
</tr>
<tr>
<td valign="top" width="15">
<div align="center">
<a href="#"
onClick="return toggleexpander('SeismicsMultiplot_block','SeismicsMultiplot_expandable_text');"
valign="top"
width="15">
<img id="SeismicsMultiplot_expandable_text" src="arrow_right.gif" style="border:0px"/></a>
</div>
</td>
<td valign="top" width="250px">
<a href="SeismicsMultiplot.html">Seismic velocities and anisotropy<td valign="top" width="75%">Calculalating and plotting
elastic velocities from elastic stiffness Cijkl tensor and density (by David Mainprice).</td></a>
</td>
</tr>
<tr>
<td/>
<td colspan="2">
<div class="expander" id="SeismicsMultiplot_block"
style="display:none; background:#e7ebf7; padding-left:2ex;">
<table>
<tr>
<td>
<a href="SeismicsMultiplot.html#3">Crystal Symmetry and definition of the elastic stiffness tensor</a>
</td>
</tr>
<tr>
<td>
<a href="SeismicsMultiplot.html#6">Plotting section</a>
</td>
</tr>
<tr>
<td>
<a href="SeismicsMultiplot.html#8">AVS : Plot S-wave anisotropy percentage for each proppagation direction</a>
</td>
</tr>
<tr>
<td>
<a href="SeismicsMultiplot.html#9">S1 Polarization: Plot fastest S-wave (Vs1) polarization directions</a>
</td>
</tr>
<tr>
<td>
<a href="SeismicsMultiplot.html#10">Vs1 : Plot Vs1 velocities (km/s)</a>
</td>
</tr>
<tr>
<td>
<a href="SeismicsMultiplot.html#11">Vs2 : Plot Vs2 velocities (km/s)</a>
</td>
</tr>
<tr>
<td>
<a href="SeismicsMultiplot.html#12">dVs : Plot Velocity difference Vs1-Vs2 (km/s) plus Vs1 polarizations</a>
</td>
</tr>
<tr>
<td>
<a href="SeismicsMultiplot.html#13">Vp/Vs1 : Plot Vp/Vs1 ratio (no units)</a>
</td>
</tr>
<tr>
<td>
<a href="SeismicsMultiplot.html#14">Vp/Vs2 : Plot Vp/Vs2 ratio (no units)</a>
</td>
</tr>
</table>
</div>
</td>
</tr>
<tr>
<td valign="top" width="15">
<div align="center">
<a href="#"
onClick="return toggleexpander('SlipSystems_block','SlipSystems_expandable_text');"
valign="top"
width="15">
<img id="SlipSystems_expandable_text" src="arrow_right.gif" style="border:0px"/></a>
</div>
</td>
<td valign="top" width="250px">
<a href="SlipSystems.html">Slip Systems<td valign="top" width="75%">How to analyze slip transmission at grain boundaries</td></a>
</td>
</tr>
<tr>
<td/>
<td colspan="2">
<div class="expander" id="SlipSystems_block"
style="display:none; background:#e7ebf7; padding-left:2ex;">
<table>
<tr>
<td>
<a href="SlipSystems.html#4">Burgers vector and normal directions</a>
</td>
</tr>
<tr>
<td>
<a href="SlipSystems.html#11">Rotating slip systems</a>
</td>
</tr>
</table>
</div>
</td>
</tr>
<tr>
<td valign="top" width="15">
<div align="center">
<a href="#"
onClick="return toggleexpander('SlipTransmition_block','SlipTransmition_expandable_text');"
valign="top"
width="15">
<img id="SlipTransmition_expandable_text" src="arrow_right.gif" style="border:0px"/></a>
</div>
</td>
<td valign="top" width="250px">
<a href="SlipTransmition.html">Slip Transmission<td valign="top" width="75%">How to analyze slip transmission at grain boundaries</td></a>
</td>
</tr>
<tr>
<td/>
<td colspan="2">
<div class="expander" id="SlipTransmition_block"
style="display:none; background:#e7ebf7; padding-left:2ex;">
<table>
<tr>
<td>
<a href="SlipTransmition.html#4">Import Titanium data</a>
</td>
</tr>
<tr>
<td>
<a href="SlipTransmition.html#5">Schmid Factor</a>
</td>
</tr>
<tr>
<td>
<a href="SlipTransmition.html#9">Resolved shear stress</a>
</td>
</tr>
<tr>
<td>
<a href="SlipTransmition.html#10">Compatibility of slip systems</a>
</td>
</tr>
<tr>
<td>
<a href="SlipTransmition.html#11">Plot m' in misorientation space</a>
</td>
</tr>
</table>
</div>
</td>
</tr>
<tr>
<td valign="top" width="15">
<div align="center">
<a href="#"
onClick="return toggleexpander('StrainAnalysis_block','StrainAnalysis_expandable_text');"
valign="top"
width="15">
<img id="StrainAnalysis_expandable_text" src="arrow_right.gif" style="border:0px"/></a>
</div>
</td>
<td valign="top" width="250px">
<a href="StrainAnalysis.html">Slip Transmition<td valign="top" width="75%">How to analyse slip transmission at grain boundaries</td></a>
</td>
</tr>
<tr>
<td/>
<td colspan="2">
<div class="expander" id="StrainAnalysis_block"
style="display:none; background:#e7ebf7; padding-left:2ex;">
<table>
<tr>
<td>
<a href="StrainAnalysis.html#3">Import Titanium data</a>
</td>
</tr>
<tr>
<td>
<a href="StrainAnalysis.html#4">Taylor model</a>
</td>
</tr>
</table>
</div>
</td>
</tr>
<tr>
<td valign="top" width="15">
<div align="center">
<a href="#"
onClick="return toggleexpander('TaylorModel_block','TaylorModel_expandable_text');"
valign="top"
width="15">
<img id="TaylorModel_expandable_text" src="arrow_right.gif" style="border:0px"/></a>
</div>
</td>
<td valign="top" width="250px">
<a href="TaylorModel.html">Taylor Model<td valign="top" width="75%"/></a>
</td>
</tr>
<tr>
<td/>
<td colspan="2">
<div class="expander" id="TaylorModel_block"
style="display:none; background:#e7ebf7; padding-left:2ex;">
<table>
<tr>
<td>
<a href="TaylorModel.html#5">Set up</a>
</td>
</tr>
<tr>
<td>
<a href="TaylorModel.html#6">The orientation dependence of the Taylor factor</a>
</td>
</tr>
<tr>
<td>
<a href="TaylorModel.html#7">The orientation dependence of the spin</a>
</td>
</tr>
<tr>
<td>
<a href="TaylorModel.html#9">Most active slip direction</a>
</td>
</tr>
<tr>
<td>
<a href="TaylorModel.html#13">Texture evolution during rolling</a>
</td>
</tr>
<tr>
<td>
<a href="TaylorModel.html#15">restore MTEX preferences</a>
</td>
</tr>
<tr>
<td>
<a href="TaylorModel.html#16">Inverse Taylor</a>
</td>
</tr>
</table>
</div>
</td>
</tr>
<tr>
<td valign="top" width="15">
<div align="center">
<a href="#"
onClick="return toggleexpander('GND_demo_block','GND_demo_expandable_text');"
valign="top"
width="15">
<img id="GND_demo_expandable_text" src="arrow_right.gif" style="border:0px"/></a>
</div>
</td>
<td valign="top" width="250px">
<a href="GND_demo.html">Dislocation Density Estimation<td valign="top" width="75%">This example sheet describes how to estimate
dislocation densities in MTEX following the reference paper Pantleon, Resolving the geometrically necessary dislocation content
by conventional electron backscattering diffraction, Scripta Materialia, 2008</td></a>
</td>
</tr>
<tr>
<td/>
<td colspan="2">
<div class="expander" id="GND_demo_block"
style="display:none; background:#e7ebf7; padding-left:2ex;">
<table>
<tr>
<td>
<a href="GND_demo.html#1">Data import and grain reconstruction</a>
</td>
</tr>
<tr>
<td>
<a href="GND_demo.html#3">Data cleaning</a>
</td>
</tr>
<tr>
<td>
<a href="GND_demo.html#5">The incomplete curvature tensor</a>
</td>
</tr>
<tr>
<td>
<a href="GND_demo.html#6">The components of the curvature tensor</a>
</td>
</tr>
<tr>
<td>
<a href="GND_demo.html#8">The incomplete dislocation density tensor</a>
</td>
</tr>
<tr>
<td>
<a href="GND_demo.html#10">Crystallographic Dislocations</a>
</td>
</tr>
<tr>
<td>
<a href="GND_demo.html#12">The Energy of Dislocations</a>
</td>
</tr>
<tr>
<td>
<a href="GND_demo.html#15">Fitting Dislocations to the incomplete dislocation density tensor</a>
</td>
</tr>
<tr>
<td>
<a href="GND_demo.html#19">The total dislocation energy </a>
</td>
</tr>
</table>
</div>
</td>
</tr>
</table>
</p>
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