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PhaseSchmidTensor.m
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function phase_schmid_tensors = PhaseSchmidTensor(nphases,crystal_type_all,covera_all,maxss)
%
% Calculates the Schmid tensor for either cubic (3) or hexagonal (6)
% symmetry
%
% return a 3x3 tensor for all ss of all grains, which is later convertedt
% to a 6x1 tensor
%
phase_schmid_tensors = zeros(maxss,3,3,nphases);
for iphase = 1:nphases
crystal_type = crystal_type_all(iphase);
%
% for cubics, covera is the flag for fcc or bcc type ss
% for hexagonals, covera is the c over a ratio
%
covera = covera_all(iphase);
num_ss = maxss;
m_ss = zeros(num_ss,3);
s_ss = zeros(num_ss,3);
if(crystal_type==3)
if(covera==1)
a= 1./sqrt(3.);
b= 1./sqrt(2.);
s_ss(1,1) = 0;
s_ss(1,2) = b;
s_ss(1,3) = -b;
m_ss(1,1) = a;
m_ss(1,2) = a;
m_ss(1,3) = a;
s_ss(2,1) = -b;
s_ss(2,2) = 0;
s_ss(2,3) = b;
m_ss(2,1) = a;
m_ss(2,2) = a;
m_ss(2,3) = a;
s_ss(3,1) = b;
s_ss(3,2) = -b;
s_ss(3,3) = 0;
m_ss(3,1) = a;
m_ss(3,2) = a;
m_ss(3,3) = a;
s_ss(4,1) = 0;
s_ss(4,2) = b;
s_ss(4,3) = -b;
m_ss(4,1) = -a;
m_ss(4,2) = a;
m_ss(4,3) = a;
s_ss(5,1) = b;
s_ss(5,2) = 0;
s_ss(5,3) = b;
m_ss(5,1) = -a;
m_ss(5,2) = a;
m_ss(5,3) = a;
s_ss(6,1) = b;
s_ss(6,2) = b;
s_ss(6,3) = 0;
m_ss(6,1) = -a;
m_ss(6,2) = a;
m_ss(6,3) = a;
s_ss(7,1) = 0;
s_ss(7,2) = b;
s_ss(7,3) = b;
m_ss(7,1) = -a;
m_ss(7,2) = -a;
m_ss(7,3) = a;
s_ss(8,1) = b;
s_ss(8,2) = 0;
s_ss(8,3) = b;
m_ss(8,1) = -a;
m_ss(8,2) = -a;
m_ss(8,3) = a;
s_ss(9,1) = -b;
s_ss(9,2) = b;
s_ss(9,3) = 0;
m_ss(9,1) = -a;
m_ss(9,2) = -a;
m_ss(9,3) = a;
s_ss(10,1) = 0;
s_ss(10,2) = b;
s_ss(10,3) = b;
m_ss(10,1) = a;
m_ss(10,2) = -a;
m_ss(10,3) = a;
s_ss(11,1) = b;
s_ss(11,2) = 0;
s_ss(11,3) = -b;
m_ss(11,1) = a;
m_ss(11,2) = -a;
m_ss(11,3) = a;
s_ss(12,1) = b;
s_ss(12,2) = b;
s_ss(12,3) = 0;
m_ss(12,1) = a;
m_ss(12,2) = -a;
m_ss(12,3) = a;
elseif(covera==2)
a= 1./sqrt(3.);
b= 1./sqrt(2.);
s_ss(1,1) = 0;
s_ss(1,2) = b;
s_ss(1,3) = -b;
m_ss(1,1) = a;
m_ss(1,2) = a;
m_ss(1,3) = a;
s_ss(2,1) = -b;
s_ss(2,2) = 0;
s_ss(2,3) = b;
m_ss(2,1) = a;
m_ss(2,2) = a;
m_ss(2,3) = a;
s_ss(3,1) = b;
s_ss(3,2) = -b;
s_ss(3,3) = 0;
m_ss(3,1) = a;
m_ss(3,2) = a;
m_ss(3,3) = a;
s_ss(4,1) = 0;
s_ss(4,2) = b;
s_ss(4,3) = -b;
m_ss(4,1) = -a;
m_ss(4,2) = a;
m_ss(4,3) = a;
s_ss(5,1) = b;
s_ss(5,2) = 0;
s_ss(5,3) = b;
m_ss(5,1) = -a;
m_ss(5,2) = a;
m_ss(5,3) = a;
s_ss(6,1) = b;
s_ss(6,2) = b;
s_ss(6,3) = 0;
m_ss(6,1) = -a;
m_ss(6,2) = a;
m_ss(6,3) = a;
s_ss(7,1) = 0;
s_ss(7,2) = b;
s_ss(7,3) = b;
m_ss(7,1) = -a;
m_ss(7,2) = -a;
m_ss(7,3) = a;
s_ss(8,1) = b;
s_ss(8,2) = 0;
s_ss(8,3) = b;
m_ss(8,1) = -a;
m_ss(8,2) = -a;
m_ss(8,3) = a;
s_ss(9,1) = -b;
s_ss(9,2) = b;
s_ss(9,3) = 0;
m_ss(9,1) = -a;
m_ss(9,2) = -a;
m_ss(9,3) = a;
s_ss(10,1) = 0;
s_ss(10,2) = b;
s_ss(10,3) = b;
m_ss(10,1) = a;
m_ss(10,2) = -a;
m_ss(10,3) = a;
s_ss(11,1) = b;
s_ss(11,2) = 0;
s_ss(11,3) = -b;
m_ss(11,1) = a;
m_ss(11,2) = -a;
m_ss(11,3) = a;
s_ss(12,1) = b;
s_ss(12,2) = b;
s_ss(12,3) = 0;
m_ss(12,1) = a;
m_ss(12,2) = -a;
m_ss(12,3) = a;
end
end
if(crystal_type==6)
num_ss_bp = 6;
num_ss_pyr = 12;
a= sqrt(3.)/2.;
b= 1./2.;
sqr3 = sqrt(3.);
m_ss(1,1) = 0.0;
m_ss(1,2) = 0.0;
m_ss(1,3) = 1.0;
m_ss(2,1) = 0.0;
m_ss(2,2) = 0.0;
m_ss(2,3) = 1.0;
m_ss(3,1) = 0.0;
m_ss(3,2) = 0.0;
m_ss(3,3) = 1.0;
m_ss(4,1) = 0.0;
m_ss(4,2) = 1.0;
m_ss(4,3) = 0.0;
m_ss(5,1) = -a;
m_ss(5,2) = -b;
m_ss(5,3) = 0.0;
m_ss(6,1) = a;
m_ss(6,2) = -b;
m_ss(6,3) = 0.0;
s_ss(1,1) = 1.0;
s_ss(1,2) = 0.0;
s_ss(1,3) = 0.0;
s_ss(2,1) = -b;
s_ss(2,2) = a;
s_ss(2,3) = 0.0;
s_ss(3,1) = -b;
s_ss(3,2) = -a;
s_ss(3,3) = 0.0;
s_ss(4,1) = 1.0;
s_ss(4,2) = 0.0;
s_ss(4,3) = 0.0;
s_ss(5,1) = -b;
s_ss(5,2) = a;
s_ss(5,3) = 0.0;
s_ss(6,1) = -b;
s_ss(6,2) = -a;
s_ss(6,3) = 0.0;
% pyramidal 11-22 -1-123
% c+a type 2
ann(1,1)=-2.;
ann(1,2)=1.;
ann(1,3)=1.;
ann(1,4)=2.;
abb(1,1)=2.;
abb(1,2)=-1.;
abb(1,3)=-1.;
abb(1,4)=3.;
ann(2,1)=1.;
ann(2,2)=-2.;
ann(2,3)=1.;
ann(2,4)=2.;
abb(2,1)=-1.;
abb(2,2)=2.;
abb(2,3)=-1.;
abb(2,4)=3.;
ann(3,1)=1.;
ann(3,2)=1.;
ann(3,3)=-2.;
ann(3,4)=2.;
abb(3,1)=-1.;
abb(3,2)=-1.;
abb(3,3)=2.;
abb(3,4)=3.;
abb(3,1)=-1.;
abb(3,2)=-1.;
abb(3,3)=2.;
abb(3,4)=3.;
ann(4,1)=2.;
ann(4,2)=-1.;
ann(4,3)=-1.;
ann(4,4)=2.;
abb(4,1)=-2.;
abb(4,2)=1.;
abb(4,3)=1.;
abb(4,4)=3.;
ann(5,1)=-1.;
ann(5,2)=2.;
ann(5,3)=-1.;
ann(5,4)=2.;
abb(5,1)=1.;
abb(5,2)=-2.;
abb(5,3)=1.;
abb(5,4)=3.;
ann(6,1)=-1.;
ann(6,2)=-1.;
ann(6,3)=2.;
ann(6,4)=2.;
abb(6,1)=1.;
abb(6,2)=1.;
abb(6,3)=-2.;
abb(6,4)=3.;
ann(7,1)=-1.;
ann(7,2)=0.;
ann(7,3)=1.;
ann(7,4)=1.;
abb(7,1)=2.;
abb(7,2)=-1.;
abb(7,3)=-1.;
abb(7,4)=3.;
ann(8,1)=-1.;
ann(8,2)=0.;
ann(8,3)=1.;
ann(8,4)=1.;
abb(8,1)=1.;
abb(8,2)=1.;
abb(8,3)=-2.;
abb(8,4)=3.;
ann(9,1)=0.;
ann(9,2)=-1.;
ann(9,3)=1.;
ann(9,4)=1.;
abb(9,1)=1.;
abb(9,2)=1.;
abb(9,3)=-2.;
abb(9,4)=3.;
ann(10,1)=0.;
ann(10,2)=-1.;
ann(10,3)=1.;
ann(10,4)=1.;
abb(10,1)=-1.;
abb(10,2)=2.;
abb(10,3)=-1.;
abb(10,4)=3.;
ann(11,1)=1.;
ann(11,2)=-1.;
ann(11,3)=0.;
ann(11,4)=1.;
abb(11,1)=-1.;
abb(11,2)=2.;
abb(11,3)=-1.;
abb(11,4)=3.;
ann(12,1)=1.;
ann(12,2)=-1.;
ann(12,3)=0.;
ann(12,4)=1.;
abb(12,1)=-2.;
abb(12,2)=1.;
abb(12,3)=1.;
abb(12,4)=3.;
nslips = num_ss_bp + 1;
num_ss_all = num_ss_bp+num_ss_pyr;
for i=nslips:num_ss_all
jcount = i - num_ss_bp;
m_ss(i,1) = ann(jcount,1);
m_ss(i,2) = (2.*ann(jcount,2)+ann(jcount,1))/sqr3;
m_ss(i,3) = ann(jcount,4)/covera;
xnrm = m_ss(i,1)^2 + m_ss(i,2)^2 + m_ss(i,3)^2;
xnrm = sqrt(xnrm);
m_ss(i,1) = m_ss(i,1) / xnrm;
m_ss(i,2) = m_ss(i,2) / xnrm;
m_ss(i,3) = m_ss(i,3) / xnrm;
s_ss(i,1) = 3.*abb(jcount,1)/2.;
s_ss(i,2) = (abb(jcount,1)/2. + abb(jcount,2))*sqr3;
s_ss(i,3) = abb(jcount,4) * covera;
xnrs = s_ss(i,1)^2 + s_ss(i,2)^2 + s_ss(i,3)^2;
xnrs = sqrt(xnrs);
s_ss(i,1) = s_ss(i,1) / xnrs;
s_ss(i,2) = s_ss(i,2) / xnrs;
s_ss(i,3) = s_ss(i,3) / xnrs;
end
end
ss_schmid=zeros(3,3);
for i=1:num_ss
for j=1:3
for k=1:3
ss_schmid(j,k) = s_ss(i,j)*m_ss(i,k);
end
end
sym_schmid = (ss_schmid+ss_schmid')/2;
for j=1:3
for k=1:3
phase_schmid_tensor(i,j,k) = sym_schmid(j,k);
end
end
end
phase_schmid_tensors(:,:,:,iphase) = phase_schmid_tensor(:,:,:);
end