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lammps/lib/atc/VoigtOperations.h
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VoigtOperations.h
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#ifndef VOIGT_OPERATIONS_H
#define VOIGT_OPERATIONS_H
#include "MatrixDef.h"
#include "MatrixLibrary.h"
// Voigt indexing puts a symmetric 3x3 matrix into a
// vector form: [0 1 2 3 4 5]
//
// matrix form: [[ 0 5 4 ]
// [ 5 1 3 ]
// [ 4 3 2 ]]
//
// unsymmetric version
// vector form: [0 1 2 3 4 5 6 7 8]
//
// matrix form: [[ 0 5 4 ]
// [ 8 1 3 ]
// [ 7 6 2 ]]
namespace voigt3 {
//const int voigt_idx1_symm[] = {0,1,2,1,0,0}; // first packed voigt index
//const int voigt_idx2_symm[] = {0,1,2,2,2,1}; // second packed voigt index
const int voigt_idx1[] = {0,1,2,1,0,0,2,2,1}; // first packed voigt index
const int voigt_idx2[] = {0,1,2,2,2,1,1,0,0}; // second packed voigt index
// const int voigt_idx1[] = {0,1,2,0,0,1,1,2,2}; // first packed voigt index
// const int voigt_idx2[] = {0,1,2,1,2,2,0,0,1}; // second packed voigt index
//* Computes a symmetric matrix-matrix product
//* Inputs 6-length vectors A, B
inline DENS_VEC dsymm(const DENS_VEC &A, const DENS_VEC &B)
{
DENS_VEC C(6,false);
C(0) = A(0)*B(0)+A(5)*B(5)+A(4)*B(4);
C(1) = A(5)*B(5)+A(1)*B(1)+A(3)*B(3);
C(2) = A(4)*B(4)+A(3)*B(3)+A(2)*B(2);
C(3) = A(5)*B(4)+A(1)*B(3)+A(3)*B(2);
C(4) = A(0)*B(4)+A(5)*B(3)+A(4)*B(2);
C(5) = A(0)*B(5)+A(5)*B(1)+A(4)*B(3);
return C;
}
//* Returns the trace of a 3x3 matrix in symmetric voigt form.
inline double tr(const DENS_VEC &A)
{
return A(0) + A(1) + A(2);
}
//* Computes the determinant of a 3x3 matrix in symmetric voigt form.
inline double det(const DENS_VEC &A)
{
return A(0) * (A(1)*A(2)-A(3)*A(3))
-A(5) * (A(5)*A(2)-A(3)*A(4))
+A(4) * (A(5)*A(3)-A(1)*A(4));
}
//* Returns the derivative of C*C in voigt notation.
inline DENS_MAT derivative_of_square(const DENS_VEC &C)
{
DENS_MAT D(6,6);
D(0,0)=2.0*C(0); D(0,1)=0.0; D(0,2)=0.0;
D(1,0)=0.0; D(1,1)=2.0*C(1); D(1,2)=0.0;
D(2,0)=0.0; D(2,1)=0.0; D(2,2)=2.0*C(2);
D(0,3)=0.0; D(0,4)=2.0*C(4); D(0,5)=2.0*C(5);
D(1,3)=2.0*C(3); D(1,4)=0.0; D(1,5)=2.0*C(5);
D(2,3)=2.0*C(3); D(2,4)=2.0*C(4); D(2,5)=0.0;
D(3,0)=0.0; D(3,1)=C(3); D(3,2)=C(3);
D(4,0)=C(4); D(4,1)=0.0; D(4,2)=C(4);
D(5,0)=C(5); D(5,1)=C(5); D(5,2)=0.0;
D(3,3)=C(1)+C(2); D(3,4)=C(5); D(3,5)=C(4);
D(4,3)=C(5); D(4,4)=C(0)+C(2); D(4,5)=C(3);
D(5,3)=C(4); D(5,4)=C(3); D(5,5)=C(0)+C(1);
return D;
}
//* Computes the inverse of a 3x3 matrix in symmetric voigt form.
inline DENS_VEC inv(const DENS_VEC &A)
{
DENS_VEC B(6,false);
const double inv_det = 1.0/det(A);
B(0) = (A(1)*A(2)-A(3)*A(3))*inv_det;
B(1) = (A(0)*A(2)-A(4)*A(4))*inv_det;
B(2) = (A(0)*A(1)-A(5)*A(5))*inv_det;
B(3) = (A(4)*A(5)-A(0)*A(3))*inv_det;
B(4) = (A(5)*A(3)-A(4)*A(1))*inv_det;
B(5) = (A(4)*A(3)-A(5)*A(2))*inv_det;
return B;
}
//* Returns the identify matrix in voigt form, optionally scaled by a factor.
inline DENS_VEC eye(INDEX N=3, double scale=1.0)
{
const double dij[] = {0.0, scale};
const INDEX voigt_size = N*N-((N*N-N)>>1); // total - symmetric elements
DENS_VEC I(voigt_size,false);
for (INDEX i=0; i<voigt_size; i++) I(i) = dij[i<N];
return I;
}
//* Returns the voigt form of a symmetric matrix.
// consistent with voigt_idx1,2
inline DENS_VEC to_voigt(const DENS_MAT &C)
{
DENS_VEC B(6,false);
B(0)=C(0,0);
B(1)=C(1,1);
B(2)=C(2,2);
B(3)=C(1,2); // take upper triangle entries
B(4)=C(0,2);
B(5)=C(0,1);
return B;
}
//* Returns a symmetric matrix form a voigt form.
// consistent with voigt_idx1,2
inline DENS_MAT from_voigt(const DENS_VEC &B)
{
DENS_MAT C(3,3,false);
C(0,0)=B(0); C(0,1)=B(5); C(0,2)=B(4);
C(1,0)=B(5); C(1,1)=B(1); C(1,2)=B(3);
C(2,0)=B(4); C(2,1)=B(3); C(2,2)=B(2);
return C;
}
//* Returns the voigt form of an unsymmetric matrix.
// consistent with voigt_idx1,2
inline DENS_VEC to_voigt_unsymmetric(const DENS_MAT &C)
{
DENS_VEC B(9,false);
B(0)=C(0,0);
B(1)=C(1,1);
B(2)=C(2,2);
B(3)=C(1,2); // upper triangle entries
B(4)=C(0,2);
B(5)=C(0,1);
B(6)=C(2,1); // lower triangle entries
B(7)=C(2,0);
B(8)=C(1,0);
return B;
}
//* Returns a symmetric matrix form a voigt form.
// consistent with voigt_idx1,2
inline DENS_MAT from_voigt_unsymmetric(const DENS_VEC &B)
{
DENS_MAT C(3,3,false);
C(0,0)=B(0); C(0,1)=B(5); C(0,2)=B(4);
C(1,0)=B(8); C(1,1)=B(1); C(1,2)=B(3);
C(2,0)=B(7); C(2,1)=B(6); C(2,2)=B(2);
return C;
}
//* adds the identity to an unsymmetric matrix form
inline void add_identity_voigt_unsymmetric(DENS_VEC &B)
{
B(0) +=1;
B(1) +=1;
B(2) +=1;
}
//* Converts voigt vector form to 3x3 matrix for non-symmetric tensor at specified node.
inline void vector_to_matrix(const int i, const DENS_MAT & IN, DENS_MAT & OUT)
{
OUT.reset(3,3);
OUT(0,0)=IN(i,0); OUT(0,1)=IN(i,1); OUT(0,2)=IN(i,2);
OUT(1,0)=IN(i,3); OUT(1,1)=IN(i,4); OUT(1,2)=IN(i,5);
OUT(2,0)=IN(i,6); OUT(2,1)=IN(i,7); OUT(2,2)=IN(i,8);
return;
}
//* Converts 3x3 matrix to voigt vector form for non-symmetric tensor at specified node.
inline void matrix_to_vector(const int i, const DENS_MAT & IN, DENS_MAT & OUT)
{
OUT(i,0) = IN(0,0);
OUT(i,1) = IN(0,1);
OUT(i,2) = IN(0,2);
OUT(i,3) = IN(1,0);
OUT(i,4) = IN(1,1);
OUT(i,5) = IN(1,2);
OUT(i,6) = IN(2,0);
OUT(i,7) = IN(2,1);
OUT(i,8) = IN(2,2);
return;
}
//* Converts voigt vector form to 3x3 matrix for symmetric tensor at specified node.
inline void vector_to_symm_matrix(const int i, const DENS_MAT & IN, DENS_MAT & OUT)
{
OUT.reset(3,3);
OUT(0,0)=IN(i,0); OUT(0,1)=IN(i,5); OUT(0,2)=IN(i,4);
OUT(1,0)=IN(i,5); OUT(1,1)=IN(i,1); OUT(1,2)=IN(i,3);
OUT(2,0)=IN(i,4); OUT(2,1)=IN(i,3); OUT(2,2)=IN(i,2);
return;
}
//* Converts 3x3 matrix to voigt vector form for symmetric tensor at specified node.
inline void symm_matrix_to_vector(const int i, const DENS_MAT & IN, DENS_MAT & OUT)
{
OUT(i,0) = IN(0,0);
OUT(i,1) = IN(1,1);
OUT(i,2) = IN(1,2);
OUT(i,3) = IN(1,2);
OUT(i,4) = IN(0,2);
OUT(i,5) = IN(0,1);
return;
}
//* Converts voigt vector form to vector at specified node.
inline DENS_VEC global_vector_to_vector(const int i, const DENS_MAT & IN)
{
DENS_VEC OUT(9);
OUT(0)=IN(i,0); OUT(5)=IN(i,1); OUT(4)=IN(i,2);
OUT(8)=IN(i,3); OUT(1)=IN(i,4); OUT(3)=IN(i,5);
OUT(7)=IN(i,6); OUT(6)=IN(i,7); OUT(2)=IN(i,8);
return OUT;
}
inline void vector_to_global_vector(const int i, const DENS_VEC & IN, DENS_MAT & OUT)
{
OUT(i,0) = IN(0);
OUT(i,1) = IN(5);
OUT(i,2) = IN(4);
OUT(i,3) = IN(8);
OUT(i,4) = IN(1);
OUT(i,5) = IN(3);
OUT(i,6) = IN(7);
OUT(i,7) = IN(6);
OUT(i,8) = IN(2);
return;
}
//* Converts vector to DENS_MAT_VEC
inline void vector_to_dens_mat_vec(const DENS_MAT & IN, DENS_MAT_VEC & OUT)
{
for (int i=0; i<IN.nRows(); i++) {
for (int j=0; j<3; j++) {
for (DENS_MAT_VEC::size_type k=0; k<3; k++) {
OUT[k](i,j) = IN(i,3*j+k);
}
}
}
return;
}
//* Converts DENS_MAT_VEC to vector
inline void symm_dens_mat_vec_to_vector(const DENS_MAT_VEC & IN, DENS_MAT & OUT)
{
for (int i=0; i<IN.front().nRows(); i++) {
for (int v=0; v<6; v++) {
OUT(i,v) = IN[voigt_idx1[v]](i,voigt_idx2[v]);
}
}
return;
}
}
#endif
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