Project: s41467-024-51491-7 | Function: CriteriaEvaluator.fracture_toughness_envelope (python)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow Python best practices and maintain consistent code style.
Return **only** the complete Python function code.

user: Complete this Python function:

**DESCRIPTION:** Evaluates the mixed-mode fracture toughness interaction law using power-law criterion. Implements Equation 1 from the paper: (G_I/G_Ic)^(1/n) + (G_II/G_IIc)^(1/m) = 1, which defines the fracture envelope for mixed-mode anticrack propagation.

**KEY TERMS:** {
  "G_I": "Mode I energy release rate",
  "G_II": "Mode II energy release rate",
  "G_Ic": "Mode I fracture toughness",
  "G_IIc": "Mode II fracture toughness",
  "gn": "power-law exponent n",
  "gm": "power-law exponent m"
}

**CONTEXT CODE:** @dataclass
class FindMinimumForceResult:
    """
    Holds the results of the find_minimum_force evaluation.

    Attributes:
    -----------
    success : bool
        Whether the algorithm converged.
    critical_skier_weight : float
        The critical skier weight.
    new_segments : List[Segment]
        The new segments.
    old_segments : List[Segment]
        The old segments.
    iterations : int
        The number of iterations.
    max_dist_stress : float
        The maximum distance to failure.
    min_dist_stress : float
        The minimum distance to failure.
    """

    success: bool
    critical_skier_weight: float
    new_segments: List[Segment]
    old_segments: List[Segment]
    iterations: Optional[int]
    max_dist_stress: float
    min_dist_stress: float


class CriteriaEvaluator:
    """
    Provides methods for stability analysis of layered slabs on compliant
    elastic foundations, based on the logic from criterion_check.py.
    """

    criteria_config: CriteriaConfig

    def __init__(self, criteria_config: CriteriaConfig):
        """
        Initializes the evaluator with global simulation and criteria configurations.

        Parameters:
        ----------
        criteria_config (CriteriaConfig): The configuration for failure criteria.
        """
        self.criteria_config = criteria_config

    def fracture_toughness_envelope(
        self, G_I: float | np.ndarray, G_II: float | np.ndarray, weak_layer: WeakLayer
    ) -> float | np.ndarray:
        """
        Evaluates the fracture toughness criterion for a given combination of
        Mode I (G_I) and Mode II (G_II) energy release rates.

        The criterion is defined as:
            g_delta = (|G_I| / G_Ic)^gn + (|G_II| / G_IIc)^gm

        A value of 1 indicates the boundary of the fracture toughness envelope is reached.

        Parameters:
        -----------
        G_I : float
            Mode I energy release rate (ERR) in J/m².
        G_II : float
            Mode II energy release rate (ERR) in J/m².
        weak_layer : WeakLayer
            The weak layer object containing G_Ic and G_IIc.

        Returns:
        -------
        g_delta : float
            Evaluation of the fracture toughness envelope.
        """
        # MASKED: Evaluates the mixed-mode fracture toughness interaction law using power-law criterion. Implements Equation 1 from the paper: (G_I/G_Ic)^(1/n) + (G_II/G_IIc)^(1/m) = 1, which defines the fracture envelope for mixed-mode anticrack propagation.
        raise NotImplementedError("Function has been masked for testing purposes")

    def stress_envelope(
        self,
        sigma: Union[float, np.ndarray],
        tau: Union[float, np.ndarray],
        weak_layer: WeakLayer,
        method: Optional[str] = None,
    ) -> np.ndarray:
        """
        Evaluate the stress envelope for given stress components.
        Weak Layer failure is defined as the stress envelope crossing 1.

        Parameters
        ----------
        sigma: ndarray
            Normal stress components (kPa).
        tau: ndarray
            Shear stress components (kPa).
        weak_layer: WeakLayer
            The weak layer object, used to get density.
        method: str, optional
            Method to use for the stress envelope. Defaults to None.

        Returns
        -------
        stress_envelope: ndarray
            Stress envelope evaluation values in [0, inf].
            Values > 1 indicate failure.

        Notes
        -----
        - Mede's envelopes ('mede_s-RG1', 'mede_s-RG2', 'mede_s-FCDH') are derived
            from the work of Mede et al. (2018), "Snow Failure Modes Under Mixed
            Loading," published in Geophysical Research Letters.
        - Schöttner's envelope ('schottner') is based on the preprint by Schöttner
            et al. (2025), "On the Compressive Strength of Weak Snow Layers of
            Depth Hoar".
        - The 'adam_unpublished' envelope scales with weak layer density linearly
            (compared to density baseline) by a 'scaling_factor'
            (weak layer density / density baseline), unless modified by
            'order_of_magnitude'.
        - Mede's criteria ('mede_s-RG1', 'mede_s-RG2', 'mede_s-FCDH') define
            failure based on a piecewise function of stress ranges.
        """
        sigma = np.abs(np.asarray(sigma))
        tau = np.abs(np.asarray(tau))
        results = np.zeros_like(sigma)

        envelope_method = (
            method
            if method is not None
            else self.criteria_config.stress_envelope_method
        )
        density = weak_layer.rho
        sigma_c = weak_layer.sigma_c
        tau_c = weak_layer.tau_c
        fn = self.criteria_config.fn
        fm = self.criteria_config.fm
        order_of_magnitude = self.criteria_config.order_of_magnitude
        scaling_factor = self.criteria_config.scaling_factor

        def mede_common_calculations(sigma, tau, p0, tau_T, p_T):
            results_local = np.zeros_like(sigma)
            in_first_range = (sigma >= (p_T - p0)) & (sigma <= p_T)
            in_second_range = sigma > p_T
            results_local[in_first_range] = (
                -tau[in_first_range] * (p0 / (tau_T * p_T))
                + sigma[in_first_range] * (1 / p_T)
                + p0 / p_T
            )
            results_local[in_second_range] = (tau[in_second_range] ** 2) + (
                (tau_T / p0) ** 2


Complete the function implementation replacing "raise NotImplementedError".