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. 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
AuxDeriv2InvariantSigmaT: Holds auxiliary data to compute the second derivative of σt (or q)
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_p: Calculates the first derivative of p w.r.t. the stress tensor
deriv1_invariant_q: Calculates the first derivative of q (von Mises) w.r.t. the stress tensor
deriv1_invariant_sigma_s: Calculates the first derivative of σs w.r.t. the stress tensor
deriv1_invariant_sigma_t: Calculates the first derivative of σt 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_q: Calculates the second derivative of the deviatoric invariant (von Mises) w.r.t. the stress tensor
deriv2_invariant_sigma_t: Calculates the second derivative of the σt 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