crack tip functions

XFEM: crack tip function derivatives

Hi,

I am using a X-FEM Matlab code found here http://people.civil.gla.ac.uk/~bordas/xfemMatlab.html"]http://people.civil.gla.ac.uk/~bordas/xfemMatlab.html

In branch.m/branch_node.m (both functions of radius r and angle theta) crack tip fields are defined...and questions arise.

% Functions

f(1) = r2 * st2 ;
f(2) = r2 * ct2;
f(3) = r2 * st2 * ct;
f(4) = r2 * ct2 * ct;

-these functions are not the same defined e.g. in (Fleming,1997) or (Sukumar,2000) etc...why?

 their derivatives are then considered:

(here for function f(3))


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