principal strains using eig function
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I am trying to use the eig function to calculate the principal strains from 3D strain tensor. Unfortunately I do get different results than from another tool (<http://www.continuummechanics.org/cm/techforms/Eigen.html>) For
A1 = [4.420000000000000 1.350000000000000 3.509000000000000;
1.350000000000000 3.832000000000000 0;
3.509000000000000 0 3.207000000000000]
Matlab eig function yields
>> [V1, D1] = eig(A1)
V1 =
-0.651153549926562 0.054428335246106 0.756991816825237
0.232116359059687 -0.935349177129471 0.266915553499784
0.722579442189515 0.349513194551449 0.596422230101738
D1 =
0.044859378106921 0 0
0 3.753442970840320 0
0 0 7.660697651052759
while the Web tool gives:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/151321/image.jpeg)
The Values look pretty the same, but their position in vector/matrix is different. As far I understand, the columns of the V1 represent the cosines of the angle between the a principal strain and the Cartesian axis. But which corresponds to which principal strain and how to calculate angles between the principal strains and the Cartesian strain axis?
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Eric Lin
2015 年 6 月 19 日
What is happening is the web app is displaying the eigenvectors by row whereas MATLAB is displaying them by column. The relative order of the eigenvectors is not significant.
I am not familiar with the domain but from a quick search it seems that the vectors are related to the strains based on their eigenvalue, i.e. the max principal strain is the eigenvector with the largest eigenvalue. Again, I am not familiar with the domain but angles between vectors can be computed by dot product.
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