Crate russell_tensor

Expand description

Russell - Rust Scientific Library

russell_tensor: Tensor analysis, calculus, and functions for continuum mechanics

Important: This crate depends on external libraries (non-Rust). Thus, please check the Installation Instructions on the GitHub Repository.

This library implements structures and functions for tensor analysis and calculus. The library focuses on applications in engineering and [Continuum Mechanics](Continuum Mechanics). The essential functionality for the targeted applications includes second-order and fourth-order tensors, scalar “invariants,” and derivatives.

This library implements derivatives for scalar functions with respect to tensors, tensor functions with respect to tensors, and others. A convenient basis representation known as Mandel basis (similar to Voigt notation) is considered by this library internally. The user may also use the Mandel basis to perform simpler matrix-vector operations directly.

Structs§

AuxDeriv2InvariantJ3: Holds auxiliary data to compute the second derivative of the J3 invariant
AuxDeriv2InvariantLode: Holds auxiliary data to compute the second derivative of the Lode invariant
AuxDeriv2InvariantSigmaD: Holds auxiliary data to compute the second derivative of the deviatoric invariant
LinElasticity: Implements the linear elasticity equations for small-strain problems
SampleTensor2: Collects values related to a sample Tensor2
SamplesTensor2: Holds second-order tensor samples
SamplesTensor4: Holds fourth-order tensor samples
Spectral2: Holds the spectral representation of a symmetric second-order tensor
Tensor2: Implements a second-order tensor, symmetric or not
Tensor4: Implements a fourth order-tensor, minor-symmetric or not

Enums§

Mandel: Specifies the Mandel representation

Constants§

IDENTITY2: Second-order identity tensor in Mandel basis (I)
IDENTITY4: Fourth-order identity tensor in Mandel basis (II)
IJKL_TO_MN: Maps (i,j,k,l) of Tensor4 to the (m,n)-th position in the matrix representation
IJKL_TO_MN_SYM: Maps (i,j,k,l) of Tensor4 to the (m,n)-th position in the matrix representation (minor-symmetric version)
IJ_TO_M: Maps (i,j) of Tensor2 to the m-th position in the vector representation
IJ_TO_M_SYM: Maps (i,j) of Tensor2 to the m-th position in the vector representation (symmetric version)
MN_TO_IJKL: Maps the (m,n)-th position in the matrix representation to (i,j,k,l) of Tensor4
M_TO_IJ: Maps the m-th position in the vector representation to the index (i,j) of Tensor2
ONE_BY_3: 1/3
P_DEV: Fourth-order deviatoric making projector (Pdev)
P_ISO: Fourth-order isotropic making projector (Piso)
P_SKEW: Fourth-order skew making projector (Pskew)
P_SYM: Fourth-order symmetric making projector (Psym)
P_SYMDEV: Fourth-order symmetric-deviatoric projector in Mandel basis
SQRT_2: sqrt(2) https://oeis.org/A002193
SQRT_3: sqrt(3) https://oeis.org/A002194
SQRT_6: sqrt(6) https://oeis.org/A010464
SQRT_2_BY_3: sqrt(2/3) https://oeis.org/A157697
SQRT_3_BY_2: sqt(3/2) https://oeis.org/A115754
TOL_J2: Tolerance to avoid zero division with the J2 invariant
TRACE_PROJECTION: Fourth-order trace-projection tensor (JJ)
TRANSPOSITION: Fourth-order transposition tensor in Mandel basis (TT)
TWO_BY_3: 2/3

Traits§

AsMatrix3x3: Defines a trait to handle 3x3 matrices
AsMatrix9x9: Defines a trait to handle 9x9 matrices

Functions§

deriv1_invariant_jj2: Calculates the first derivative of the J2 invariant w.r.t. the stress tensor
deriv1_invariant_jj3: Calculates the first derivative of the J3 invariant w.r.t. the stress tensor
deriv1_invariant_lode: Calculates the first derivative of the Lode invariant w.r.t. the stress tensor
deriv1_invariant_sigma_d: Calculates the first derivative of the deviatoric stress invariant (von Mises) w.r.t. the stress tensor
deriv1_invariant_sigma_m: Calculates the first derivative of the mean stress invariant w.r.t. the stress tensor
deriv1_norm: Calculates the first derivative of the norm w.r.t. the defining Tensor2
deriv2_invariant_jj2: Calculates the second derivative of the J2 invariant w.r.t. the stress tensor
deriv2_invariant_jj3: Calculates the second derivative of the J3 invariant w.r.t. the stress tensor
deriv2_invariant_lode: Calculates the second derivative of the Lode invariant w.r.t. the stress tensor
deriv2_invariant_sigma_d: Calculates the second derivative of the deviatoric invariant (von Mises) w.r.t. the stress tensor
deriv_inverse_tensor: Calculates the derivative of the inverse tensor w.r.t. the defining Tensor2
deriv_inverse_tensor_sym: Calculates the derivative of the inverse tensor w.r.t. a symmetric Tensor2
deriv_squared_tensor: Calculates the derivative of the squared tensor w.r.t. a Tensor2
deriv_squared_tensor_sym: Calculates the derivative of the squared tensor w.r.t. a symmetric Tensor2
t2_add: Adds two second-order tensors
t2_ddot_t2: Performs the double-dot (ddot) operation between two Tensor2 (inner product)
t2_ddot_t4: Performs the double-dot (ddot) operation between a Tensor2 and a Tensor4
t2_ddot_t4_ddot_t2: Computes Tensor2 double-dot Tensor4 double-dot Tensor2
t2_dot_t2: Performs the single dot operation between two Tensor2 (matrix multiplication)
t2_dot_vec: Performs the single dot operation between a Tensor2 and a vector
t2_dyad_t2: Performs the dyadic product between two Tensor2 resulting a Tensor4
t2_dyad_t2_update: Performs the dyadic product between two Tensor2 resulting in a Tensor4 (with update)
t2_odyad_t2: Performs the overbar dyadic product between two Tensor2 resulting in a (general) Tensor4
t2_qsd_t2: Performs the quad-sum-dyadic (qsd) operation with two Tensor2 yielding a minor-symmetric Tensor4
t2_ssd: Performs the self-sum-dyadic (ssd) operation with a Tensor2 yielding a minor-symmetric Tensor4
t2_udyad_t2: Performs the underbar dyadic product between two Tensor2 resulting in a (general) Tensor4
t4_add: Adds two fourth-order tensors
t4_ddot_t2: Performs the double-dot (ddot) operation between a Tensor4 and a Tensor2
t4_ddot_t4: Performs the double-dot (ddot) operation between two Tensor4
t4_ddot_t2_dyad_t2_ddot_t4: Computes Tensor4 double-dot Tensor2 dyadic Tensor2 double-dot Tensor4
t4_ddot_t2_update: Performs the double-dot (ddot) operation between a Tensor4 and a Tensor2 with update
t4_ddot_t4_update: Performs the double-dot (ddot) operation between two Tensor4 with update
vec_dot_t2: Performs the single dot operation between a vector and a Tensor2
vec_dyad_vec: Performs the dyadic product between two vectors resulting in a second-order tensor

Type Aliases§

StrError: Defines the error output as a static string