Implement stress to strain and strain to stress transformation according to Hooke's law

[JiriKuzelka]

ℹ️ General Information

Component Name: Hooke's Law
Component Location: material_laws/hookes_law
Suggested Python Name: hookes_law
FABER WG Relation: -
Brief Description: Elastic stress to strain and back conversion for linear elastic and isotropic material.
Priority: 3
Technical Complexity: 2
Estimated Effort: 2
Dependencies: -

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Implementation Details

📋 Specification

A function allowing compute stresses ($\sigma$) in MPa form given strains ($\epsilon$) and vice versa according to Hooke's law. Considering two material parameters Young's modulus ($E$) and Poisson's ratio ($\nu$).

Mathematical Formulation

Inputs

1. Material parameters

Parameter	Symbol	Type	Description	Units	Range
elastic_modulus	$E$	array of floats	Young's modulus	MPa	$(0;\infty)$
poisson_ratio	$\nu$	array of floats	Poisson's ratio	-	$(-\infty;0.5)$

2. Stress / Strain values

Parameter	Symbol	Type	Description	Units	Range
stress	$\sigma$	array of floats	stress	MPa	$(-\infty;\infty)$
strain	$\epsilon$	array of floats	strain	-	$(-\infty;\infty)$

Outputs

Parameter	Symbol	Type	Description	Units	Range
stress	$\sigma$	array of floats	stress	MPa	$(-\infty;\infty)$
strain	$\epsilon$	array of floats	strain	-	$(-\infty;\infty)$

Expected Behavior

🔧 Implementation Guidelines

Function Signature

# Suggested function signature
def calc_stress(
strain: ArrayLike,
) -> NDArray[np.float64]:

def calc_strain(
stress: ArrayLike,
) -> NDArray[np.float64]:

Code Structure

Error Handling

✅ Validation & Testing

Test Cases

Validation Criteria

• Edge cases handled appropriately
• Output format matches specification

📚 References & Resources

https://en.wikipedia.org/wiki/Hooke%27s_law

📝 Technical Notes

Performance Considerations

Edge Cases to Handle