4.1.1.6.1.11. pyfem.materials.MaxStrain module

Maximum strain failure criterion for composite materials.

This module implements the maximum strain failure criterion, which is commonly used for fiber-reinforced composite materials. Failure is predicted when any principal strain component exceeds its allowable limit.

class MaxStrain(props)

Bases: BaseFailure

Maximum strain failure criterion.

This criterion predicts failure when any strain component exceeds its corresponding allowable strain. It is one of the simplest failure criteria for orthotropic materials like fiber-reinforced composites.

The failure index is computed as: FI = max(ε₁/ε₁ᵗ, |ε₁|/ε₁ᶜ, ε₂/ε₂ᵗ, |ε₂|/ε₂ᶜ, |γ₁₂|/γ₁₂ᵘ)

where: - ε₁, ε₂: normal strains in principal material directions - γ₁₂: shear strain - Superscripts: t = tension, c = compression, u = ultimate

Failure occurs when FI ≥ 1.0

4.1.1.6.1.11. Required Properties

eps1tfloat

Maximum tensile strain in fiber direction (direction 1).

eps1cfloat

Maximum compressive strain in fiber direction (magnitude, positive).

eps2tfloat

Maximum tensile strain transverse to fibers (direction 2).

eps2cfloat

Maximum compressive strain transverse to fibers (magnitude, positive).

gamma12ufloat

Maximum shear strain (magnitude, positive).

Examples

Typical values for carbon fiber/epoxy composite:

<Failure>

type = “MaxStrain”; eps1t = 0.015; # 1.5% tensile strain in fiber direction eps1c = 0.012; # 1.2% compressive strain eps2t = 0.005; # 0.5% transverse tensile strain eps2c = 0.010; # 1.0% transverse compressive strain gamma12u = 0.020; # 2.0% shear strain

</Failure>

Notes

• This criterion does not account for interaction between strain components

• Conservative for combined loading conditions

• Simple to implement and computationally efficient

• Suitable for preliminary design and conservative estimates

check(stress: ndarray, deformation) → float

Evaluate the maximum strain failure criterion.

Parameters:

• stress (ndarray) – Stress tensor (not used in this criterion, but kept for interface consistency).

• deformation (object) – Deformation object containing strain information. Must have attribute ‘strain’ or ‘eps’.

Returns:

Failure index (FI). FI ≥ 1.0 indicates failure. FI < 1.0 indicates safe condition.

Return type:

float

Notes

The strain tensor should be in engineering notation: - For 2D: [ε₁, ε₂, γ₁₂] - For 3D: [ε₁, ε₂, ε₃, γ₂₃, γ₁₃, γ₁₂]

Shear strains are engineering shear strains (γ = 2ε₁₂).