# Compliance matrix from strain matrix, Matlab

1. Sep 18, 2016

### grepecs

1. The problem statement, all variables and given/known data
(I'm trying to replicate some results in an academic paper where they have calculated elastic properties of a crystal. Because I'm going to do a lot of similar time-consuming calculations following this one, I need to learn how to do them using a computer.)

The compliance matrix C is the inverse of the strain matrix S. I want to calculate C for a given S. I thought it would be easy to do this in Matlab using the command C=inv(S), but for some reason most of the resulting compliance matrix elements are wrong.

2. Relevant equations

C=S^-1

where S is the 6x6 matrix

[209 114 102 0 1 0;
0 234 139 0 -7 0;
0 0 238 0 27 0;
0 0 0 77 0 -5;
0 0 0 0 23 0;
0 0 0 0 0 72]

3. The attempt at a solution
In Matlab:

C=inv(S)

which gives me

C=[0.0048 -0.0023 -0.0007 0 -0.0001 0;
0 0.0043 -0.0025 0 0.0042 0;
0 0 0.0042 0 -0.0049 0;
0 0 0 0.0130 0 0.0009;
0 0 0 0 0.0435 0;
0 0 0 0 0 0.0139]

However, the correct answer is supposed to be (the elements below have been multiplied by 10^3)

C=[6.8 -2.3 -1.7 0 1 0;
0 8.8 -5.2 0 9.2 0;
0 0 9.5 0 -13 0;
0 0 0 13 0 0.9;
0 0 0 0 62.5 0;
0 0 0 0 0 13.9]

As you can see, the only elements that I get right are C(1,2), C(4,4), C(4,6), and C(6,6), i.e., only 4 out of the 13 nonzero elements. It seemed like such a simple task, but at the moment I'm stuck. Any hints as to what I'm doing wrong? I have already double checked S.

2. Sep 21, 2016

### grepecs

Ok, I solved it. For potential future persons with a similar problem: the matrix elements (in this case the elastic constants and compliance coefficients) are symmetric about the diagonal, which means that c12=c21, c13=c31 etc. I wrongly assumed that all elements below the diagonal were zero, since only those above the diagonal were explicitly listed in the paper I read (which is of course a perfectly reasonable thing to do -- I should have known better).