added comment on computing the inverse of an stiffness tensor explicitly

TensorAnalysis/@complianceTensor/inv.m

@@ -8,4 +8,36 @@
 %  C - @stiffnessTensor
 %
 
-C = stiffnessTensor(inv@tensor(S));
+C = stiffnessTensor(inv@tensor(S));
+
+end
+
+% this can be done more explicitely by
+function test
+
+M = matrix(S,'voigt');
+
+D = M(1,1,:) .* M(2,2,:) .* M(3,3,:) ...
+  - M(1,1,:) .* M(2,3,:).^2 ...
+  - M(2,2,:) .* M(1,3,:) .* M(1,3,:) ...
+  - M(3,3,:) .* M(1,2,:).^2 ...
+  + 2 * M(1,2,:) .* M(2,3,:) .* M(1,3,:);
+
+C11 = (M(2,2,:) .* M(3,3,:)-M(2,3,:) .* M(2,3,:))/D;
+C12 = (M(1,3,:) .* M(2,3,:)-M(1,2,:) .* M(3,3,:))/D;
+C13 = (M(1,2,:) .* M(2,3,:)-M(1,3,:) .* M(2,2,:))/D;
+C22 = (M(1,1,:) .* M(3,3,:)-M(1,3,:) .* M(1,3,:))/D;
+C23 = (M(1,2,:) .* M(1,3,:)-M(2,3,:) .* M(1,1,:))/D;
+C33 = (M(1,1,:) .* M(2,2,:)-M(1,2,:) .* M(1,2,:))/D;
+
+% Enter tensor as 6 by 6 matrix,M line by line.
+M = [[  C11   C12   C13    0     0     0];...
+    [   C12   C22   C23    0     0     0];...
+    [   C13   C23   C33    0     0     0];...
+    [   0      0      0   1./M(4,4,:)    0     0];...
+    [   0      0      0    0    1./M(5,5,:)    0];...
+    [   0      0      0    0     0   1./M(6,6,:)]];
+% 
+C = reshape(stiffnessTensor(M,cs_tensor,'density',rho),size(S));
+
+end