4.1.1.6.1.22. pyfem.materials.TsaiWu module

Tsai-Wu failure criterion for composite materials.

This module implements the Tsai-Wu failure criterion, which is a tensor polynomial criterion that accounts for interaction between stress components. It is widely used for orthotropic materials such as fiber-reinforced composites.

class TsaiWu(props)

Bases: BaseFailure

Tsai-Wu failure criterion for orthotropic materials.

The Tsai-Wu criterion is a general tensor polynomial failure theory that accounts for interaction between stress components. It is expressed as:

FI = F₁σ₁ + F₂σ₂ + F₆τ₁₂ + F₁₁σ₁² + F₂₂σ₂² + F₆₆τ₁₂² + 2F₁₂σ₁σ₂

where the coefficients are defined in terms of strength values: - F₁ = 1/Xᵗ - 1/Xᶜ - F₂ = 1/Yᵗ - 1/Yᶜ - F₁₁ = 1/(Xᵗ·Xᶜ) - F₂₂ = 1/(Yᵗ·Yᶜ) - F₆₆ = 1/S² - F₁₂ = interaction coefficient (typically -0.5·sqrt(F₁₁·F₂₂))

Failure occurs when FI ≥ 1.0

4.1.1.6.1.22. Required Properties

Xtfloat

Tensile strength in fiber direction (direction 1).

Xcfloat

Compressive strength in fiber direction (positive value).

Ytfloat

Tensile strength transverse to fibers (direction 2).

Ycfloat

Compressive strength transverse to fibers (positive value).

Sfloat

Shear strength.

F12float, optional

Interaction coefficient F₁₂. If not provided, computed as: F₁₂ = -0.5 × sqrt(F₁₁ × F₂₂) This is a typical assumption when experimental data is unavailable.

Examples

Typical values for carbon fiber/epoxy composite:

<Failure>

type = “TsaiWu”; Xt = 1500.0; # MPa - fiber tensile strength Xc = 1200.0; # MPa - fiber compressive strength Yt = 50.0; # MPa - transverse tensile strength Yc = 200.0; # MPa - transverse compressive strength S = 100.0; # MPa - shear strength F12 = -0.5e-6; # Optional interaction coefficient (1/MPa²)

</Failure>

Notes

Advantages: - Accounts for interaction between stress components - Single equation for all loading conditions - Distinguishes between tension and compression - Widely validated for composite materials

Limitations: - Requires interaction coefficient F₁₂ (often unknown) - Does not predict failure mode - May be non-conservative for some loading cases

The criterion reduces to von Mises for isotropic materials with appropriate strength values.

check(stress: ndarray, deformation) → float

Evaluate the Tsai-Wu failure criterion.

Parameters:

• stress (ndarray) – Stress tensor in material principal directions. For 2D: [σ₁, σ₂, τ₁₂] For 3D: [σ₁, σ₂, σ₃, τ₂₃, τ₁₃, τ₁₂]

• deformation (object) – Deformation object (not used but kept for interface consistency).

Returns:

Failure index (FI). FI ≥ 1.0 indicates failure. The square root of FI gives the strength ratio.

Return type:

float

Notes

The Tsai-Wu criterion is evaluated in the material coordinate system, so stress components must be rotated to principal material directions before calling this function.

For plane stress problems (2D), only σ₁, σ₂, and τ₁₂ are considered.