Crate russell_tensor

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_2_BY_3
  sqrt(2/3) https://oeis.org/A157697
• SQRT_3
  sqrt(3) https://oeis.org/A002194
• SQRT_3_BY_2
  sqt(3/2) https://oeis.org/A115754
• SQRT_6
  sqrt(6) https://oeis.org/A010464
• 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 2D arrays

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. the defining Tensor2 (symmetric)
• deriv_squared_tensor
  Calculates the derivative of the squared tensor w.r.t. the defining Tensor2
• deriv_squared_tensor_sym
  Calculates the derivative of the squared tensor w.r.t. the defining Tensor2 (symmetric)
• 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_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 in a Tensor4
• 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_ddot_t2
  Performs the double-dot (ddot) operation between a Tensor4 and a Tensor2
• t4_ddot_t2_update
  Performs the double-dot (ddot) operation between a Tensor4 and a Tensor2 with update
• t4_ddot_t4
  Performs the double-dot (ddot) operation between two Tensor4
• 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