exact_griffith.asv

efg code with matlab

% *************************************************************************
%                 TWO DIMENSIONAL ELEMENT FREE GALERKIN CODE
%                            Nguyen Vinh Phu
%                        LTDS, ENISE, Juillet 2006
% *************************************************************************

function [ux,uy] = exact_Griffith(x,E,nu,stressState,sigmato,xTip,adv,cracklength)
% Compute the exact di



%  inclination of local coord
alfa=atan2(adv(2),adv(1));
% transpose of the rotation matrix
QT=[cos(alfa) sin(alfa); -sin(alfa) cos(alfa)];
% local coordinates
xp=QT*(x-xTip');            
% local polar coordinates
[r,theta]=cart2pol(xp(1),xp(2)); 

sigma=sigmato;
KI=sigmato*sqrt(pi*cracklength);   % exact KI


mu=E/(2*(1+nu));

if ( strcmp(stressState,'PLANE_STRAIN') )
    ux = 2*(1+nu)*KI/E*sqrt(r/2/pi)*cos(theta/2)*(2-2*nu-cos(theta/2)^2);
    uy = 2*(1+nu)*KI/E*sqrt(r/2/pi)*sin(theta/2)*(2-2*nu-cos(theta/2)^2);
end