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

2 Separate versions should be implemented for both stress to strain and strain to stress conversion:

1. 1D Hooke's law for uniaxial stress and strain
2. 2D Hooke's law for plane stress and plane strain conditions

Additional requirements:

1. Voigt notation should be utilized for 2D and 3D cases, i.e. stress and strain tensors should be represented as 6-component vectors.

2. Isotropic material behavior is assumed. This should be clearly stated in the documentation.

Mathematical Formulation

3D Hooke's Law (Strain-Stress Relationship):

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3D Hooke's Law (Stress-Strain Relationship):

2D Hooke's Law (Strain-Stress Relationship):

2D Hooke's Law (Stress-Strain Relationship):

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	-	$(-\infty;\infty)$

🔧 Implementation Guidelines

Code Structure

Create separate file hookes_law.py in the material_laws directory for better namespace organization.

Function Signature

# import numpy as np
# from numpy.typing import ArrayLike, NDArray

def calc_stress_xD(
    elastic_modulus: float,
    poisson_ratio: float,
    strain: ArrayLike,
) -> NDArray[np.float64]:
    # x should be repalaced with 2 or 3
    pass

def calc_strain_xD(
    elastic_modulus: float,
    poisson_ratio: float,
    stress: ArrayLike,
) -> NDArray[np.float64]:
    # x should be repalaced with 2 or 3
    pass

Error Handling

No error handling is required.

Testing

Test cases are not provided, but should be straightforward to implement.

📚 References & Resources

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

[pavkukula]

3D case and 2D plane stress implemented;
for 2D case a temp func to check_shape was coded --> should be moved to voigt
issues with einsum (a numpy stub limitation) result typing (mypy) overcomed by wrap the return in a cast
unconsistency in names: poissons_ratio vs poisson_ration, hookes_law vs hooke_law --> without "s" prefered.