Struct Tensor2 

pub struct Tensor2 {
    pub data: [[f64; 3]; 3],
}

Second-order tensor (3×3 matrix) stored as row-major [[f64; 3]; 3].

Fields

data: [[f64; 3]; 3]

Row-major 3×3 component array: data[i][j] is the (i,j) component.

Implementations

impl Tensor2

pub fn new(data: [[f64; 3]; 3]) -> Self

Create a new Tensor2 from a 3×3 array.

pub fn zero() -> Self

Zero tensor.

pub fn identity() -> Self

Second-order identity tensor.

pub fn add(&self, other: &Tensor2) -> Tensor2

Component-wise addition.

pub fn sub(&self, other: &Tensor2) -> Tensor2

Component-wise subtraction.

pub fn scale(&self, s: f64) -> Tensor2

Scalar multiplication.

pub fn dot(&self, other: &Tensor2) -> Tensor2

Matrix–matrix product (A · B).

pub fn transpose(&self) -> Tensor2

Transpose A^T.

pub fn trace(&self) -> f64

Trace: sum of diagonal components.

pub fn det(&self) -> f64

Determinant of the 3×3 matrix.

pub fn inverse(&self) -> Option<Tensor2>

Inverse via cofactor expansion; returns None if |det| < 1e-14.

pub fn sym(&self) -> Tensor2

Symmetric part: (A + A^T) / 2.

pub fn skew(&self) -> Tensor2

Skew-symmetric part: (A − A^T) / 2.

pub fn double_contract(&self, other: &Tensor2) -> f64

Double contraction A:B = Σ_ij A_ij B_ij.

pub fn norm(&self) -> f64

Frobenius norm √(A:A).

pub fn deviatoric(&self) -> Tensor2

Deviatoric part: A − (tr(A)/3) · I.

pub fn hydrostatic(&self) -> f64

Hydrostatic (mean normal) stress: tr(A) / 3.

pub fn von_mises(&self) -> f64

von Mises equivalent: √(3/2 · s:s) where s = deviatoric part.

pub fn eigenvalues_symmetric(&self) -> [f64; 3]

Eigenvalues of a symmetric 3×3 tensor via Cardano’s analytical formula.

The tensor is assumed symmetric; only the lower-triangular part is used. Returns eigenvalues sorted in ascending order.

pub fn outer_product(a: [f64; 3], b: [f64; 3]) -> Tensor2

Outer (dyadic) product a ⊗ b: result_ij = a_i * b_j.

pub fn apply(&self, v: [f64; 3]) -> [f64; 3]

Matrix–vector product: result_i = Σ_j A_ij v_j.

impl Tensor2

pub fn contract_vec(&self, v: [f64; 3]) -> [f64; 3]

Single contraction: c_i = A_ij * v_j (same as apply, alias).

pub fn dyadic(a: [f64; 3], b: [f64; 3]) -> Tensor2

Tensor outer (dyadic) product from two vectors (static method alias).

pub fn rotate(&self, r: &Tensor2) -> Tensor2

Rotate a tensor by a rotation matrix R: R * A * R^T.

pub fn invariant_i1(&self) -> f64

First invariant I1 = trace(A).

pub fn invariant_i2(&self) -> f64

Second invariant I2 = 0.5 * (trace(A)^2 - trace(A^2)).

pub fn invariant_i3(&self) -> f64

Third invariant I3 = det(A).

pub fn principal_invariants(&self) -> [f64; 3]

Principal invariants as an array [I1, I2, I3].

pub fn decompose_dev_hydro(&self) -> (Tensor2, f64)

Deviatoric and hydrostatic decomposition.

Returns (deviatoric, hydrostatic_scalar).

pub fn from_voigt(v: [f64; 6]) -> Tensor2

Create a tensor from Voigt notation [xx, yy, zz, xy, yz, xz].

pub fn to_voigt(&self) -> [f64; 6]

Convert to Voigt notation.

pub fn effective_strain(&self) -> f64

Effective strain (von Mises strain equivalent).

For a strain tensor: eps_eff = sqrt(2/3 * e_ij * e_ij) where e is the deviatoric strain.

pub fn diagonal(d: [f64; 3]) -> Tensor2

Create a diagonal tensor with given diagonal values.

pub fn is_symmetric(&self, tol: f64) -> bool

Check if the tensor is symmetric within tolerance.

pub fn matrix_exp_approx(&self) -> Tensor2

Matrix exponential approximation using Taylor series (for small tensors).

exp(A) ≈ I + A + A²/2! + A³/3! + … Uses 10 terms by default.