Matrix Diagonalization
Add a Matrix Diagonalization node () under Definitions>Variable Utilities (if Group by Type is active; otherwise, directly under Definitions) to define variables representing the diagonalization of a symmetric 3x3 input matrix. You add it by right-clicking the Definitions node and choosing Variable Utilities>Matrix Diagonalization or by right-clicking the Variable Utilities node and choosing Matrix Diagonalization.
You can define a Label for the node, and a namespace for variables using the Name field. For the Geometric Entity Selection, see About Selecting Geometric Entities.
In addition, the Settings window for a Matrix Diagonalization node contains the following sections:
Input Matrix
Enter the symmetric matrix elements for the 3x3 input matrix in the table. The matrix diagonalization is primarily intended for extracting principal components of 3D tensor quantities such as principal stresses and strains.
Output
Select the Compute exponential check box to compute also the matrix eT, where T is the input matrix.
Select the Ignore Jacobian contributions check box (selected by default) to ignore any solution dependencies during the solution process.
The principal values become available as variables <name>.e<i>, where <name> is the namespace set in the Name field, and <i> is the principal component index, ordered from largest to smallest absolute value. Components of the corresponding principal vectors are called <name>.e<i><j>, where <j> are integer indices. If Compute exponential was selected, the result can be evaluated as a list of variables with names <name>.expT<i><j>. The input matrix with names <name>.T<i><j>, as well as its determinant <name>.detT are also made available. Note that the determinant is not computed for matrices of size 4x4 or larger; if required, use a Matrix Decomposition node instead.
You can use individual components where variable expressions are allowed, but also evaluate complete vectors and matrices at once using a matrix evaluation node under Derived Values. For example, to evaluate the first principal vector, select matdiag1.e1_vec under Model>Component 1>Definitions>Matrix Diagonalization 1>Principal vector 1if it the node has been defined as Matrix Diagonalization 1 with the name matdiag1 in Component 1.