[IMPL] Implement stress-life prediction function based on the Gerber mean-stress correction

[MartinNesladek]

ℹ️ General Information

Component Name: Gerber

Component Location: core/stress_life/damage_params/uniaxial_stress_eq_amp/

Suggested Python Name: calc_stress_eq_amp_gerber

FABER WG Relation: 4.1

Brief Description: Uniaxial equivalent stress amplitude based on Gerber parabola

Priority: 2

Technical Complexity: 2

Estimated Effort: 2

Dependencies: -

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Implementation Details

📋 Specification

Using the Gerber mean stress correction, compute the value of equivalent stress amplitude, $\sigma_{aeq}$, in MPa for given stress values $\sigma_a$ and $\sigma_m$ representing a single load cycle.

Mathematical Formulation

$$ \displaystyle\sigma_{aeq}=\frac{\sigma_a}{1-\left(\frac{\sigma_m}{\sigma_{UTS}}\right)^2 } $$

$$  \displaystyle\sigma_{aeq}=\frac{\sigma_a}{1-\left(\frac{\sigma_m}{\sigma_{UTS}}\right)^2 } $$

Inputs

1. Static tensile parameters

Parameter	Symbol	Type	Description	Units	Constraints
ult_stress	$\sigma_{UTS}$	array of floats	Ultimate tensile strength	MPa	$>0$

2. Stress / Strain values

Parameter	Symbol	Type	Description	Units	Range
stress_amp	$\sigma_a$	array of floats	stress amplitude	MPa	$(0; \infty)$
mean_stress	$\sigma_m$	array of floats	mean stress	MPa	$(-\infty;\infty)$

Outputs

Parameter	Type	Description	Units	Range
$\sigma_{aeq}$	array of floats	Equivalent stress amplitude by Gerber	-	$(-\infty;\infty)$

Expected Behavior

🔧 Implementation Guidelines

Function Signature

# Suggested function signature
def calc_stress_eq_amp_gerber(
    stress_amp: ArrayLike,
    mean_stress: ArrayLike,
    ult_stress: ArrayLike,
) -> NDArray[np.float64]:

Code Structure

Error Handling

✅ Validation & Testing

Test Cases

Test Case	Inputs	Expected Outputs	Notes
Example 1	$\sigma_{UTS} = 700 MPa; \sigma_a = 180 MPa, \sigma_m = 100 MPa$	$\sigma_{aeq} = 183.8 MPa$

Validation Criteria

• Mathematical accuracy verified against literature
• Edge cases handled appropriately
• Output format matches specification

📚 References & Resources

S. Suresh: Fatigue of Materials, Cambridge University Press, 1998

📝 Technical Notes

Performance Considerations

Edge Cases to Handle

Issue a warning if $\left| \sigma_m \right| > \sigma_{UTS}$
An error handling should be implemented for $\left| \sigma_m \right| = \sigma_{UTS}$

Special Requirements