Tensors Namespace Reference


Classes

class  TijTensor
 Prof. Nakai's modified stress tensor tij. More...

Typedefs

typedef blitz::TinyVector<
REAL, 6 > 		Tensor2
 Second Order Tensor (Mandel representation) {{{.
typedef blitz::TinyMatrix<
REAL, 6, 6 > 		Tensor4
 Fourth Order Tensor (Mandel representation) {{{.
typedef blitz::TinyVector<
REAL, 3 > 		Tensor1

Functions

void Mult (Tensor2 const &S, Tensor2 const &T, Tensor2 &R)
 Tensor multiplication $ \TeSe{R} \gets \TeSe{S}\bullet\TeSe{T} $.
REAL Norm (Tensor2 const &T)
 Euclidian norm of a symmetric 2nd order tensor.
REAL Det (Tensor2 const &T)
 Determinant of T.
bool Inv (Tensor2 const &T, Tensor2 &R)
 Inverse of a tensor T $ \TeSe{R} \gets \TeSe{T}^{-1} $.
bool Eigenvals (Tensor2 const &T, REAL L[3])
 Eigenvalues (L) of a tensor T $ L_{i=1\cdots3} \gets eigenvalues(\TeSe{T}) $.
bool Eigenvp (Tensor2 const &T, REAL L[3], Tensor2 P[3])
 Eigenvalues (L) and Eigenprojectors (P) of a tensor T $ L_{i=1\cdots3} \gets eigenvalues(\TeSe{T}) \quad \TeSe{P}_{i=1\cdots3} \gets eigenprojectors(\TeSe{T}) $.
bool Sqrt (Tensor2 const &T, Tensor2 &R)
 Square root of a tensor T $ \TeSe{R} \gets \sqrt{\TeSe{T}} $.
void CharInvs (Tensor2 const &T, REAL I[3])
 Characteristic invariants of a symmetric second order tensor.
void Strain_Ev_Ed (Tensor2 const &Eps, REAL &Ev, REAL &Ed)
 Strain Invariants.
void Stress_p_q (Tensor2 const &Sig, REAL &p, REAL &q)
 Stress Invariants (Cambridge).
REAL Stress_q (Tensor2 const &Sig)
 Cambridge's q deviatoric stress invariant.
REAL Sin3ThDev (Tensor2 const &S)
 Sin3Th given deviator (S) of the stress tensor.
void Stress_p_q_S_sin3th (Tensor2 const &Sig, REAL &p, REAL &q, Tensor2 &S, REAL &sin3th)
 Stress Invariants (Cambridge) + deviator of Sigma.
bool Stress_tn_ts (Tensor2 const &Sig, REAL &tn, REAL &ts)
 Stress Invariants (Professor Nakai's invariants).
void Stress_P_Q (Tensor2 const &Sig, REAL &P, REAL &Q)
 Stress Invariants (Professor Brannon's isomorphic invariants).
void Stress_P_Q_S_sin3th (Tensor2 const &Sig, REAL &P, REAL &Q, Tensor2 &S, REAL &sin3th)
 Stress Invariants (Professor Brannon's isomorphic invariants) + deviator of Sigma.
REAL Sin3Th (REAL SI, REAL SII, REAL SIII)
 Returns Sin3Th, given three principal values, which are not necessary sorted.
void Hid2Sig (REAL const &p, REAL const &q, REAL const &th, REAL &Sig1, REAL &Sig2, REAL &Sig3)
 Converts hidrostatic coordinates to sigma (principal) coord (T in radians).
void Hid2Sig (REAL const *P, REAL const *Q, REAL const *T, REAL *SI, REAL *SII, REAL *SIII, int Size)
 Converts hidrostatic coordinates to sigma (principal) coord (T in radians).
void Hid2Sig_ (REAL const &SX, REAL const &SY, REAL const &p, REAL &SI, REAL &SII, REAL &SIII)
 Converts hidrostatic coordinates (Sx, Sy, Sz) to sigma (principal) coord (T in radians).
int JacobiRot (Tensor2 const &T, REAL V0[3], REAL V1[3], REAL V2[3], REAL L[3])
 Jacobi Transformation of a Symmetric Matrix (given as a Tensor2) Out: Eigenvalues (array with 3 values).
int JacobiRot (Tensor2 const &T, REAL L[3])
 Jacobi Transformation of a Symmetric Matrix (given as a Tensor2) Out: Eigenvalues (array with 3 values).
void Dot (Tensor2 const &A, Tensor1 const &u, Tensor1 &v)
REAL Dot (Tensor2 const &x, Tensor2 const &y)
 $ sc\gets\{x\}\bullet\{y\} \quad\equiv\quad sc\gets\TeSe{x}:\TeSe{y} $
void Dot (Tensor2 const &x, Tensor4 const &A, Tensor2 &y)
 $ \{y\}\gets\{x\}\bullet[A] \quad\equiv\quad \TeSe{y}\gets\TeSe{x}:\TeFo{A} $
void Dot (Tensor4 const &A, Tensor2 const &x, Tensor2 &y)
 $ \{y\}\gets[A]\bullet\{x\} \quad\equiv\quad \TeSe{y}\gets\TeFo{A}:\TeSe{x} $
void Dot (Tensor4 const &A, Tensor4 const &B, Tensor4 &C)
 $ [C]\gets[A]\bullet[B] \quad\equiv\quad \TeFo{C}\gets\TeFo{A}:\TeFo{B} $
void Dyad (Tensor2 const &x, Tensor2 const &y, Tensor4 &A)
 $ [A]=\{x\}\otimes\{y\} \quad\equiv\quad \TeFo{A}\gets\TeSe{x}\otimes\TeSe{y} $
void AddScaled (REAL const &a, Tensor4 const &X, REAL const &b, Tensor4 const &Y, Tensor4 &Z)
 Add scaled tensors: $ [Z] \gets a[X]+b[Y] \quad\equiv\quad \TeFo{Z}\gets a\TeFo{X}+b\TeFo{Y} $.
void Ger (REAL const &a, Tensor2 const &x, Tensor2 const &y, Tensor4 &A)
 $ [A]=\alpha\{x\}\otimes\{y\}+[A] \quad\equiv\quad \TeFo{A}\gets\alpha\TeSe{x}\otimes\TeSe{y}+\TeFo{A} $
void GerX (REAL const &a, Tensor4 const &A, Tensor2 const &x, Tensor2 const &y, Tensor4 const &B, Tensor4 const &C, Tensor4 &D)
 $ [D]=\alpha([A]\bullet\{x\})\otimes(\{y\}\bullet[B])+[C] \quad\equiv\quad \TeFo{D}\gets\alpha(\TeFo{A}:\TeSe{x})\otimes(\TeSe{y}:\TeFo{B})+\TeFo{C} $
void Scale (REAL const &a, Tensor4 &B)
 $ [B]=\alpha([B]) \quad\equiv\quad \TeFo{B}\gets\alpha\TeFo{B} $
void CopyScale (REAL const &a, Tensor4 const &A, Tensor4 &B)
 $ [B]=\alpha([A]) \quad\equiv\quad \TeFo{B}\gets\alpha\TeFo{A} $
REAL Reduce (Tensor2 const &x, Tensor4 const &A, Tensor2 const &y)
 $ s=\{x\}^T[A]\{y\} \quad\equiv\quad s=\Dc{\Dc{\TeSe{x}}{\TeFo{A}}}{\TeSe{y}} $
int __initialize_the_I (Tensor2 &theI)
int __initialize_the_IIsym (Tensor4 &theIIsym)
int __initialize_the_IdyI (Tensor4 &theIdyI)
int __initialize_the_Psd (Tensor4 &thePsd)
int __initialize_the_Piso (Tensor4 &thePiso)

Variables

Tensor2 I
 Second order identity (symmetric/Mandel's basis) $ \TeSe{I} $.
Tensor4 IIsym
 Forth order identity (symmetric/Mandel's basis) $ \Dc{\TeFo{I}^{sym}}{\TeSe{a}}=\TeSe{a} $.
Tensor4 IdyI
 Forth order tensor given by I dyadic I, in which I is the second order identity (symmetric/Mandel's basis) $ \TeFo{I}^{sym}=\Dy{\TeSe{I}}{\TeSe{I}} $.
Tensor4 Psd
 Forth order "symmetric-deviatoric" tensor $ \TeFo{P}^{symdev}=\TeFo{I}^{sym}-\frac{I\otimes I}{3} $.
Tensor4 Piso
 Forth order "isotropic" tensor $ \TeFo{P}^{iso}=\frac{I\otimes I}{3} $.
int __dummy1 = __initialize_the_I(I)
int __dummy2 = __initialize_the_IIsym(IIsym)
int __dummy3 = __initialize_the_IdyI(IdyI)
int __dummy4 = __initialize_the_Psd(Psd)
int __dummy5 = __initialize_the_Piso(Piso)

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