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PP_ShearAccum.m
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PP_ShearAccum.m
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% POST-PROCESSING %
% SHEAR ACCUMULATION FOR PARTICLES %
% %
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%
% %
% Giuseppe Di Labbio %
% Department of Mechanical, Industrial & Aerospace Engineering %
% Concordia University Montréal, Canada %
% %
% Last Update: October 3rd, 2018 by Giuseppe Di Labbio %
% %
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%
% %
% Copyright (C) 2018 Giuseppe Di Labbio %
% %
% This program is free software: you can redistribute it and/or modify it %
% under the terms of the GNU General Public License as published by the %
% Free Software Foundation, either version 3 of the License, or (at your %
% option) any later version. %
% %
% This program is distributed in the hope that it will be useful, but %
% WITHOUT ANY WARRANTY; without even the implied warranty of %
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU %
% General Public License for more details. %
% %
% You should have received a copy of the GNU General Public License along %
% with this program. If not, see <https://www.gnu.org/licenses/>. %
% %
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%
% %
% SYNTAX %
% %
% ShAcc = PP_ShearAccum(P, VEC, VGT, mu, dt); %
% %
% DESCRIPTION: %
% %
% N/A %
% %
% %
% References: %
% N/A %
% %
% ----------------------------------------------------------------------- %
% Variables: %
% ----------------------------------------------------------------------- %
% N/A %
% ----------------------------------------------------------------------- %
% %
% EXAMPLE %
% %
% N/A %
% %
% DEPENDENCIES %
% %
% Requires: %
% PP_AdvectPoints %
% PP_NewtStressTensor %
% %
% Called in: %
% N/A %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% PP_ShearAccum
function [ShAcc] = PP_ShearAccum(P, VEC, VGT, mu, dt)
n = length(VEC);
p = length(P.X);
A = PP_AdvectPoints(P, VEC, dt, 'singlestep');
NST = cell(n,1);
VMS = cell(n,1);
for k = 1:n
NST{k} = PP_NewtStressTensor(VGT{k},mu);
VMS{k} = sqrt(NST{k}.xx.^2 - NST{k}.xx.*NST{k}.yy + NST{k}.yy.^2 + ...
3*NST{k}.xy.^2)/sqrt(3);
end
ShAcc = zeros(n, p);
for k = 2:n
ShAcc(k,:) = dt*interp2(VEC{k}.X, VEC{k}.Y, VMS{k}, A.X(k,:), ...
A.Y(k,:));
end
ShAcc = cumsum(ShAcc);
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%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% NOTES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%