"""Materials: elastic constants, the loss factor of internal friction, and the
thermal constants from which the thermoelastic damping follows."""

from __future__ import annotations

import math
from dataclasses import dataclass

from .constants import SPEED_OF_SOUND


@dataclass(frozen=True)
class Thermal:
    """Thermal constants of a metal. All three are needed for Zener's thermoelastic damping."""

    alpha: float
    """Linear thermal expansion [1/K]."""
    cp: float
    """Specific heat [J/(kg K)]."""
    k: float
    """Thermal conductivity [W/(m K)]."""

    def __post_init__(self) -> None:
        if not (self.alpha >= 0 and self.cp >= 1 and self.k >= 1e-3):
            raise ValueError("thermal constants must be positive (alpha >= 0, cp >= 1, k >= 1e-3)")


@dataclass(frozen=True)
class Material:
    """A homogeneous isotropic metal.

    The decay of the sound is not prescribed but derived from ``loss_factor``
    (the hysteretic loss factor of the metal's internal friction, of order
    1e-4 for bronze, steel and aluminum), from ``thermal`` (Zener's
    thermoelastic damping; ``None`` leaves it out) and from the radiation of
    the plate into the air, which the models compute from the geometry.
    """

    E: float
    """Young's modulus [Pa]."""
    nu: float
    """Poisson ratio."""
    rho: float
    """Density [kg/m^3]."""
    loss_factor: float = 0.0
    """Loss factor eta of internal friction: a mode decays at the rate eta omega / 2."""
    thermal: Thermal | None = None
    """Thermal constants for the thermoelastic damping, or None for none."""

    def __post_init__(self) -> None:
        if not self.E >= 1e6:
            raise ValueError("E must be at least 1e6 Pa")
        if not 0 <= self.nu < 0.5:
            raise ValueError("nu must lie in [0, 0.5)")
        if not self.rho >= 1:
            raise ValueError("rho must be at least 1 kg/m^3")
        if not 0 <= self.loss_factor < 0.1:
            raise ValueError("loss_factor must be small (metals have 1e-4 to 1e-3)")

    def bending_stiffness(self, h):
        """D = E h^3 / (12 (1 - nu^2)) [N m]; ``h`` may be an array."""
        return self.E * h**3 / (12 * (1 - self.nu**2))

    def membrane_stiffness(self, h):
        """C = E h / (1 - nu^2) [N/m]."""
        return self.E * h / (1 - self.nu**2)

    def shear_stiffness(self, h):
        """G = E h / (2 (1 + nu)) [N/m]."""
        return self.E * h / (2 * (1 + self.nu))

    @property
    def in_plane_speed(self) -> float:
        """Speed of in-plane waves, sqrt(E / (rho (1 - nu^2))) [m/s]; it sets the time step of the full model."""
        return math.sqrt(self.E / (self.rho * (1 - self.nu**2)))

    def bending_constant(self, h):
        """kappa = sqrt(D / (rho h)) [m^2/s], so that omega = kappa k^2 for a bending wave."""
        return (self.bending_stiffness(h) / (self.rho * h)) ** 0.5

    def coincidence_frequency(self, h):
        """Frequency at which the bending wavelength equals the wavelength of sound, c^2 / (2 pi kappa) [Hz]."""
        return SPEED_OF_SOUND**2 / (2 * math.pi * self.bending_constant(h))


STAINLESS_STEEL = Material(E=170e9, nu=0.29, rho=7900, loss_factor=3e-4, thermal=Thermal(17e-6, 500, 16))
"""Stainless steel sheet."""

MILD_STEEL = Material(E=200e9, nu=0.3, rho=7850, loss_factor=3e-4, thermal=Thermal(12e-6, 460, 50))
"""Carbon steel sheet."""

BRONZE = Material(E=110e9, nu=0.34, rho=8800, loss_factor=2e-4, thermal=Thermal(18e-6, 370, 40))
"""Bell bronze, as used for cymbals."""

ALUMINUM = Material(E=68.9e9, nu=0.33, rho=2700, loss_factor=1e-4, thermal=Thermal(23.6e-6, 896, 167))
"""6061-T6 aluminum."""