Predict Material Failure Before It Happens

# Engineering Failure Prediction Theorems
# ProximaED • Python 3.11+ • NumPy, SciPy, Matplotlib

import numpy as np
from dataclasses import dataclass
from typing import Optional

@dataclass
class MaterialProperties:
    elastic_modulus: float # GPa
    surface_energy: float # J/m²
    fracture_toughness: float # MPa√m
    yield_strength: float # MPa

class GriffithTheory:
    @staticmethod
    def breaking_strength(gamma_s: float, E: float, a: float) -> float:
        """Calculate critical stress for brittle fracture"""
        return np.sqrt((2 * gamma_s * E * 1e9) / (np.pi * a * 1e-3)) / 1e6 # MPa

class IrwinStressIntensity:
    @staticmethod
    def stress_intensity_factor(sigma: float, a: float) -> float:
        """Mode I stress intensity factor K₁"""
        return sigma * np.sqrt(np.pi * a * 1e-3) # MPa√m
    
    @staticmethod
    def critical_load(K_IC: float, a: float, area: float) -> float:
        """Maximum load before fracture"""
        sigma_crit = K_IC / np.sqrt(np.pi * a * 1e-3)
        return sigma_crit * area * 1e6 # Newtons
# ... 4 more theorem classes with full implementations