Struct TensorRank2

pub struct TensorRank2<const D: usize, I, J, U = Dimensionless>(/* private fields */);

Expand description

A d-dimensional tensor of rank 2.

D is the dimension, I, J are the configurations.

Implementations§

Returns the invariants of the 3x3 symmetric tensor.

Returns the eigenvalues and (row-wise) eigenvectors of the 3x3 symmetric tensor.

Reuse this alongside TensorRank2::powm_from_eigen/TensorRank2::dpowm_from_eigen to evaluate several exponents against the same tensor while sharing one eigendecomposition, instead of paying for a fresh cubic solve on every TensorRank2::powm/TensorRank2::dpowm call.

Returns the determinant of the rank-2 tensor.

Returns the inverse of the rank-2 tensor.

Returns the inverse and determinant of the rank-2 tensor.

Returns the inverse transpose of the rank-2 tensor.

Returns the inverse transpose and determinant of the rank-2 tensor.

Returns the LU decomposition of the rank-2 tensor.

Returns the inverse of the LU decomposition of the rank-2 tensor.

Returns the matrix logarithm of the 3x3 symmetric tensor.

Returns the derivative of the matrix logarithm of the 3x3 symmetric tensor.

Returns the matrix power of the 3x3 symmetric tensor.

Returns the matrix power from an eigendecomposition obtained from Self::eigen.

Returns the derivative of the matrix power of the 3x3 symmetric tensor.

Returns the derivative of the matrix power from an eigendecomposition obtained from Self::eigen.

Asserts that the tensor carries the given unit.

Returns a raw pointer to the slice’s buffer.

Returns the rank-2 tensor reshaped as a rank-1 tensor.

Trait Implementations§

The resulting type after applying the + operator.

Performs the + operation. Read more

The resulting type after applying the + operator.

Performs the + operation. Read more

The resulting type after applying the + operator.

Performs the + operation. Read more

Performs the += operation. Read more

Performs the += operation. Read more

Returns a duplicate of the value. Read more

Performs copy-assignment from source. Read more

The quantity the contraction gives.

Returns the full contraction with the other tensor.

Formats the value using the given formatter. Read more

Returns the “default value” for a type. Read more

The derivative with respect to the variable of integration.

Formats the value using the given formatter. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

The resulting type after applying the / operator.

Performs the / operation. Read more

Performs the /= operation. Read more

Performs the /= operation. Read more

Calculates and returns the Cauchy stress.

\boldsymbol{\sigma} = \frac{1}{J_2}\,\boldsymbol{\sigma}_1

Calculates and returns the tangent stiffness associated with the Cauchy stress.

\boldsymbol{\mathcal{T}} = \frac{1}{J_2}\,\boldsymbol{\mathcal{T}}_1\cdot\mathbf{F}_2^{-T}

Calculates and returns the first Piola-Kirchhoff stress.

\mathbf{P} = \mathbf{P}_1\cdot\mathbf{F}_2^{-T}

Calculates and returns the second Piola-Kirchhoff stress.

\mathbf{S} = \mathbf{F}_2^{-1}\cdot\mathbf{S}_1\cdot\mathbf{F}_2^{-T}

Calculates and returns the residual associated with the second deformation gradient.

\mathbf{R} = \mathbf{P}_2 - \mathbf{M}_1\cdot\mathbf{F}_2^{-T}

Calculates and returns the tangents of the coupled system.

\mathcal{C}_{iJkL} = \frac{\partial P_{iJ}}{\partial F_{kL}}

\frac{\partial R_{IJ}}{\partial F_{kL}} = -F_{IL}^{2-T}P_{kJ} - F_{mI}^1\mathcal{C}_{mJkL}

\frac{\partial P_{iJ}}{\partial F_{KL}^2} = -P_{iL}F_{KJ}^{2-T} - \mathcal{C}_{iJmL}F_{mK}^1

\frac{\partial R_{IJ}}{\partial F_{KL}^2} = \mathcal{C}_{IJKL}^2 + F_{IM}^1P_{ML}{F_{KJ}^{2-T}} - \frac{\partial R_{IJ}}{\partial F_{mL}}\,F_{mK}^1

The second deformation gradient is lower triangular to fix rotational freedom.

The residual associated with the internal variables. the internal variables are in equilibrium over, typically a stress.

The tangent of the internal variables residual with the deformation gradient.

The tangent of the deformation gradient residual with the internal variables.

The tangent of the internal variables residual with the internal variables.

Returns the initial value for the internal variables.

Calculates and returns the tangent stiffness associated with the first Piola-Kirchhoff stress. Read more

Calculates and returns the tangent stiffness associated with the second Piola-Kirchhoff stress. Read more

The tensor with its configurations and unit discarded.

Views the tensor with its configurations and unit discarded.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Converts to this type from the input type.

Creates a value from an iterator. Read more

Creates a value from an iterator. Read more

Creates a value from an iterator. Read more

The entry at the given (row, column) position.

The quadratic form of the Hessian with a vector. Read more

Fills the Hessian into a square matrix.

Return only the retained indices.

Calculates and returns the Helmholtz free energy density.

a(\mathbf{F}) = a_1(\mathbf{F}_1) + a_2(\mathbf{F}_2)

The returned type after indexing.

Performs the indexing (container[index]) operation. Read more

Performs the mutable indexing (container[index]) operation. Read more

The type of the elements being iterated over.

Which kind of iterator are we turning this into?

Creates an iterator from a value. Read more

Fills the Jacobian into a vector.

Fills the Jacobian chained with a vector into another vector.

Return only the retained indices.

Zero out the specified indices.