"""module containing the FatigueAnalysis class and
calc_kf for calculating dynamic stress concentration factor
"""
from math import log10
from sympy import sqrt
from me_toolbox.tools import NotInRangeError, print_atributes
from sympy import oo
from me_toolbox.fatigue import FailureCriteria


def calc_kf(q, Kt):
    """Kf - dynamic stress concentration factor

    :param float Kt: stress concentration theoretical factor
    :param float q: notch Sensitivity

    :returns: dynamic stress concentration factor
    :rtype: float
    """
    return 1 + q * (Kt - 1)


class FatigueAnalysis:
    """Perform fatigue analysis"""

    # TODO: make endurance_limit optional and add option to input Se, Stress_type and Kc directly
    # TODO: replace Kc as way to determine what to do in factors calculation

    def __init__(self, endurance_limit, ductile, Sy=None,
                 Kf_bending=0, Kf_normal=0, Kf_torsion=0,
                 alt_bending_stress=0, alt_normal_stress=0, alt_torsion_stress=0,
                 mean_bending_stress=0, mean_normal_stress=0, mean_torsion_stress=0):
        """ Instantiating fatigue object
        Note: all stresses are in [MPa]

        :param fatigue_analysis.EnduranceLimit endurance_limit: EnduranceLimit object containing
        the modified Se
        :param bool ductile: True if material is ductile
        :param float Sut: Ultimate tensile strength in [Mpa]
        :param float Sy: Yield strength in [Mpa]
        :param float Kf_bending: dynamic stress concentration factor for bending
        :param Kf_normal: dynamic stress concentration factor for normal
        :param Kf_torsion: dynamic stress concentration factor for torsion
        :param float alt_bending_stress: Alternating bending stress
        :param float alt_normal_stress: Alternating normal stress
        :param float alt_torsion_stress: Alternating torsion stress
        :param float mean_bending_stress: Mean bending stresses
        :param float mean_normal_stress: Mean normal stresses
        :param float mean_torsion_stress: Mean torsion stresses
        """

        self.Sy = Sy
        self.Se = endurance_limit.modified
        self.Kc = endurance_limit.Kc
        self.Sut = endurance_limit.Sut
        self.stress_type = endurance_limit.stress_type
        self.ductile = ductile
        self.Kf_bending, self.Kf_normal, self.Kf_torsion = Kf_bending, Kf_normal, Kf_torsion
        self.alt_bending_stress = alt_bending_stress
        self.alt_normal_stress = alt_normal_stress
        self.alt_torsion_stress = alt_torsion_stress
        self.mean_bending_stress = mean_bending_stress
        self.mean_normal_stress = mean_normal_stress
        self.mean_torsion_stress = mean_torsion_stress
        self.alt_eq_stress = self.calc_alt_eq_stress()
        self.mean_eq_stress = self.calc_mean_eq_stress()

    def calc_alt_eq_stress(self):
        """Returns the alternating equivalent stress according to the load type indicated by Kc

        :returns: Alternating equivalent stress
        :rtype: float
        """

        Kc = self.Kc
        if Kc == 1 and self.stress_type == 'multiple':
            corrected_bending = self.Kf_bending * self.alt_bending_stress
            corrected_normal = self.Kf_normal * (self.alt_normal_stress / 0.85)
            corrected_torsion = self.Kf_torsion * self.alt_torsion_stress
            return sqrt((corrected_bending + corrected_normal) ** 2 + 3 * corrected_torsion ** 2)

        elif Kc == 1:
            return self.Kf_bending * self.alt_bending_stress

        elif Kc == 0.85:
            return self.Kf_normal * self.alt_normal_stress

        elif Kc == 0.59:
            return self.Kf_torsion * self.alt_torsion_stress

    def calc_mean_eq_stress(self):
        """Returns the mean equivalent stress according to the load type indicated by Kc

        :returns: Mean equivalent stress
        :rtype: float
        """
        if self.ductile:
            # if the material is ductile no correction is needed
            Kf_bending, Kf_normal, Kf_torsion = 1, 1, 1
        else:
            Kf_bending, Kf_normal, Kf_torsion = self.Kf_bending, self.Kf_normal, self.Kf_torsion

        Kc = self.Kc
        if Kc == 1 and self.stress_type == 'multiple':
            corrected_bending = Kf_bending * self.mean_bending_stress
            corrected_normal = Kf_normal * self.mean_normal_stress
            corrected_torsion = Kf_torsion * self.mean_torsion_stress

            return sqrt((corrected_bending + corrected_normal) ** 2 + 3 * corrected_torsion ** 2)

        elif Kc == 1:
            return Kf_bending * self.mean_bending_stress

        elif Kc == 0.85:
            return Kf_normal * self.mean_normal_stress

        elif Kc == 0.59:
            return Kf_torsion * self.mean_torsion_stress

    @property
    def shear_ultimate_strength(self):
        """Returns shear_ultimate_strength which is the
        ultimate_tensile_strength correction for shear stress

        :returns: Sst - ultimate shear tensile strength
        :type: float
        """
        return 0.67 * self.Sut

    @property
    def shear_yield_stress(self):
        """Returns shear_yield_strength which is the Sy correction for shear stress

        :returns: shear_yield_strength - yield stress for shear
        :type: float
        """
        return self.Sy / sqrt(3).evalf()

    @property
    def modified_goodman(self):
        """Safety factor according to modified Goodman failure criterion
        (very common criterion)

        :returns: Safety factor
        :rtype: any

        :raises ValueError: if ultimate_tensile_strength is not in the fatigue call
        """

        if self.Sut is None:
            raise ValueError("ultimate_tensile_strength is None")

        ultimate_strength = self.Sut
        if self.Kc == 0.59:
            # ultimate_tensile_strength correction for shear stress
            ultimate_strength = self.shear_ultimate_strength

        return FailureCriteria.modified_goodman(ultimate_strength, self.Se,
                                                self.alt_eq_stress,
                                                self.mean_eq_stress)

    @property
    def soderberg(self):
        """Safety factor according to Soderberg failure criterion
        (the safest criterion)

        :returns: Safety factor
        :rtype: any

        :raises ValueError: if Sy is not in the fatigue call
        """

        if self.Sy is None:
            raise ValueError("Sy is None")

        yield_strength = self.Sy
        if self.Kc == 0.59:
            # ultimate_tensile_strength correction for shear stress
            yield_strength = self.shear_yield_stress

        return FailureCriteria.soderberg(yield_strength, self.Se,
                                         self.alt_eq_stress,
                                         self.mean_eq_stress)

    @property
    def gerber(self):
        """Safety factor according to Gerber failure criterion
        (the most lenient criterion)

        :returns: Safety factor
        :rtype: any
        :raises ValueError: if ultimate_tensile_strength is not in the fatigue call
        """

        if self.Sut is None:
            raise ValueError("ultimate_tensile_strength is None")

        ultimate_strength = self.Sut
        if self.Kc == 0.59:
            # ultimate_tensile_strength correction for shear stress
            ultimate_strength = self.shear_ultimate_strength

        return FailureCriteria.gerber(ultimate_strength, self.Se,
                                      self.alt_eq_stress,
                                      self.mean_eq_stress)

    @property
    def ASME_elliptic(self):
        """Safety factor according to ASME Failure criterion

        :returns: Safety factor
        :rtype: any

        :raises ValueError: if ultimate_tensile_strength is not in the fatigue call
        """

        if self.Sut is None:
            raise ValueError("ultimate_tensile_strength is None")

        yield_strength = self.Sut
        if self.Kc == 0.59:
            # ultimate_tensile_strength correction for shear stress
            yield_strength = self.shear_yield_stress

        return FailureCriteria.asme_elliptic(yield_strength, self.Se, self.alt_eq_stress,
                                             self.mean_eq_stress)

    @property
    def langer_static_yield(self):
        """ Static safety factor according to Langer Failure criterion
        it's customary to use Langer, as an assessment to yielding in the first cycle

        :returns: Safety factor
        :rtype: any

        :raises ValueError: if Sy is not in the fatigue call
        """

        if self.Sy is None:
            raise ValueError("Sy is None")

        yield_strength = self.Sy
        if self.Kc == 0.59:
            # yield_strength correction for shear stress
            Ssy = 0.67 * self.Sut
            yield_strength = Ssy

        return FailureCriteria.langer_static_yield(yield_strength,
                                                   self.alt_eq_stress,
                                                   self.mean_eq_stress)

    def get_safety_factor(self, criterion, verbose=False):
        """Returns dynamic and static safety factors
        according to the quadrant in the alternating-mean
        stress plain where the stresses are in

        Note: Should always be used instead of accessing the
        individual safety factors properties directly

        :param str criterion: The criterion to use
        :param bool verbose: Print the result

        :returns: dynamic and static safety factors
        :rtype: tuple[float, float]
        """

        if self.mean_eq_stress > 0:
            # stress is in the first quadrant of the alternating-mean stress plan
            safety_factors = {'modified goodman': self.modified_goodman,
                              'soderberg': self.soderberg,
                              'gerber': self.gerber, 'asme-elliptic': self.ASME_elliptic}

            nF = safety_factors.get(criterion.lower(), 'Error')

            if nF == 'Error':
                raise ValueError(f"Unknown criterion - {criterion}\n"
                                 f"Available criteria: 'Modified Goodman', 'Soderberg',"
                                 f"'Gerber', 'ASME-elliptic'")

            msg = f"the {criterion} safety factor is: {nF}\n"

        else:
            # stress is in the second quadrant of the alternating-mean stress plan
            nF = self.Se / self.alt_eq_stress
            msg = f"the dynamic safety factor is: {nF}\n"

        nl = self.langer_static_yield

        if verbose:
            print(msg + f"the Langer static safety factor is: {nl}")

        return nF, nl

    @property
    def Sm_stress(self):
        """Getter for the Sm_stress property

        :returns: Sm - stress at 1e3 cycles
        :rtype: float
        """
        return self.calc_Sm(self.Sut)

    @staticmethod
    def calc_Sm(Sut):
        """Calculate Sm_stress which is the stress at 1e3 cycles, the boundary
        dividing Low cycle fatigue and high cycle fatigue

        :param Sut: Ultimate tensile strength

        :returns: Sm_stress stress
        :rtype: float
        """

        def f(x):
            """ f - fatigue strength fraction
                function constructed from curve fitting to the f graph in Shigley's
                the range of the fit is ( 70[kPsi] < ultimate_tensile_strength < 200[kPsi] ) """
            return (-2.56710686e-16 * x ** 5 + 1.35729780e-12 * x ** 4 - 2.92474777e-09 * x ** 3 +
                    3.28990748e-06 * x ** 2 - 2.04929617e-03 * x + 1.38405394e+00)

        # TODO: add proper warning and solutions to ultimate_tensile_strength out of graph range
        if Sut < 482.633:  # 482.633[Mpa] = 70[kPsi]
            print(f"Note: ultimate_tensile_strength={Sut} < 482.633[Mpa] (70[kPsi]) so f~0.9")
            return 0.9 * Sut
        elif Sut > 1378.95:
            print(
                f"Note: ultimate_tensile_strength={Sut} > 1378.95[Mpa] (200[kPsi]) which is out of "
                f"the graph range, f={f(Sut)}")
        return f(Sut) * Sut

    def num_of_cycle(self, z=-3):
        """ calculate number of cycles until failure

        Note: zeta = log(N1) - log(N2), N1 - number of cycles at Sm_stress,
            N2 - Number of cycles at Se for steel N1=1e3 and N2 = 1e6

        :param float z: -3 for steel where N=1e6, -5 for metal where N=1e8,
            -5.69 for metal where N=5e8

        :returns: The Number of cycles and the fatigue stress at failure
        :rtype: tuple[float, float]
        """
        mean_stress = self.mean_eq_stress
        alternating_stress = self.alt_eq_stress
        Se = self.Se
        Sut, Sy, Sm = self.Sut, self.Sy, self.Sm_stress

        if mean_stress >= 0:
            reversible_stress = alternating_stress / (1 - (mean_stress / Sut))
        else:
            reversible_stress = alternating_stress

        if Sm < reversible_stress < Sy:
            # Low Cycle Fatigue
            if z != -3:
                raise ValueError(
                    "Number of cycles calculation for low cycle fatigue is only possible for "
                    "zeta=-3 ")

            a = Sut
            b = (1 / z) * log10(Sut / Sm)

        elif Se < reversible_stress < Sm:
            # High Cycle Fatigue
            a = Sm * (Sm / Se) ** (-3 / z)
            b = (1 / z) * log10(Sm / Se)

        elif reversible_stress < Se:
            print(
                f"reversible_stress = {reversible_stress} < Se = {Se}, Number of cycles is "
                f"infinite")
            return oo  # TODO: add to documentation the meaning of oo
        else:
            raise NotInRangeError("Reversible Stress", reversible_stress,
                                  (f'Sy={Sy}', f'Sm_stress={Sm}', f'Se={Se}'))
        N = (reversible_stress / a) ** (1 / b)
        return N, a * N ** b

    def miner_rule(self, stress_groups, Sut, Se, Sy=None, z=-3, verbose=False,
                   alt_mean=False, freq=False):
        """ Calculates total number of cycles for multiple periodic loads,
        the stress_groups format is as follows:
        [number_of_repetitions, maximum_stress, minimum_stress]

        Note: number_of_repetitions = frequency [Hz] * time

        Note: if the material don't have fatigue limit use the fatigue strength at Se=Sf(N=1e8)

        :param list stress_groups: list containing the pick stresses and number of repetition
        :param float Sut: Ultimate tensile strength [MPa]
        :param float Sy: yield strength [MPa], if None only HCF is checked
        :param float Se: endurance limit [MPa]
        :param float z: -3 for steel where N=1e6, -5 for metal where N=1e8, -5.69 for a metal
            where N=5e8
        :param bool verbose: printing the groups
            [number_of_repetitions,maximum_stress, minimum_stress, reversible_stress, Number of
            cycles]
        :param bool freq: if the input is frequency instead of number of repetition
        :param bool alt_mean: if True the stress_group structure contains
            alternating and mean stresses: [number_of_repetitions, alternating_stress, mean_stress]
            instead of the max and min stresses:
            [number_of_repetitions, maximum_stress, minimum_stress]

        :returns: Total number of cycles
        :rtype: float
        """

        Sm = self.calc_Sm(Sut)
        for group in stress_groups:

            # if the stress given are minimum and maximum instead of alternating and mean
            if not alt_mean:
                mean_stress = (group[1] + group[2]) / 2
                alternating_stress = abs(group[1] - group[2]) / 2
            else:
                alternating_stress = group[1]
                mean_stress = group[2]

            # calculate the reversible stress according to the mean stress sign
            if mean_stress >= 0:
                reversible_stress = alternating_stress / (1 - (mean_stress / Sut))
            else:
                reversible_stress = alternating_stress

            group.append(reversible_stress)

            if ((Sy is not None) and (Sm < reversible_stress < Sy)) or reversible_stress < Se:
                # infinite num of cycle - either the stress is less then
                # the endurance limit or its low cycle fatigue
                group.append(oo)

            elif Se < reversible_stress < Sm:
                # High Cycle Fatigue
                # TODO: this calculation is the same every
                #   iteration consider change to internal function and implement cash
                a = Sm * (Sm / Se) ** (-3 / z)
                b = (1 / z) * log10(Sm / Se)
                N = (reversible_stress / a) ** (1 / b)
                group.append(N)

            else:
                # print error but don't stop the loop
                print(
                    f"Reversible Stress = {reversible_stress} not in range,"
                    f"LCF-range=(Sm_stress={Sm},Sy={Sy}), "
                    f"HCF-range(Se={Se},Sm_stress={Sm})")

        result = 0
        for group in stress_groups:
            # summing n/N
            result += (group[0] / group[-1])
            if verbose:
                print(group)

        # casting the result to float - my be needed because the use of sympy's oo
        N_total = float(1 / result)

        if verbose:
            if freq:
                print(f"total time = {N_total:.2f} [s]")
            else:
                print(f"N_total = {N_total:.2f}")
        return N_total

    def get_info(self):
        """print object attributes"""
        print_atributes(self)

"""module containing the FatigueAnalysis class and
calc_kf for calculating dynamic stress concentration factor
"""
from math import log10
from sympy import sqrt
from me_toolbox.tools import NotInRangeError, print_atributes
from sympy import oo
from me_toolbox.fatigue import FailureCriteria


def calc_kf(q, Kt):
    """Kf - dynamic stress concentration factor

    :param float Kt: stress concentration theoretical factor
    :param float q: notch Sensitivity

    :returns: dynamic stress concentration factor
    :rtype: float
    """
    return 1 + q * (Kt - 1)


class FatigueAnalysis:
    """Perform fatigue analysis"""

    # TODO: make endurance_limit optional and add option to input Se, Stress_type and Kc directly
    # TODO: replace Kc as way to determine what to do in factors calculation

    def __init__(self, endurance_limit, ductile, Sy=None,
                 Kf_bending=0, Kf_normal=0, Kf_torsion=0,
                 alt_bending_stress=0, alt_normal_stress=0, alt_torsion_stress=0,
                 mean_bending_stress=0, mean_normal_stress=0, mean_torsion_stress=0):
        """ Instantiating fatigue object
        Note: all stresses are in [MPa]

        :param fatigue_analysis.EnduranceLimit endurance_limit: EnduranceLimit object containing
        the modified Se
        :param bool ductile: True if material is ductile
        :param float Sut: Ultimate tensile strength in [Mpa]
        :param float Sy: Yield strength in [Mpa]
        :param float Kf_bending: dynamic stress concentration factor for bending
        :param Kf_normal: dynamic stress concentration factor for normal
        :param Kf_torsion: dynamic stress concentration factor for torsion
        :param float alt_bending_stress: Alternating bending stress
        :param float alt_normal_stress: Alternating normal stress
        :param float alt_torsion_stress: Alternating torsion stress
        :param float mean_bending_stress: Mean bending stresses
        :param float mean_normal_stress: Mean normal stresses
        :param float mean_torsion_stress: Mean torsion stresses
        """

        self.Sy = Sy
        self.Se = endurance_limit.modified
        self.Kc = endurance_limit.Kc
        self.Sut = endurance_limit.Sut
        self.stress_type = endurance_limit.stress_type
        self.ductile = ductile
        self.Kf_bending, self.Kf_normal, self.Kf_torsion = Kf_bending, Kf_normal, Kf_torsion
        self.alt_bending_stress = alt_bending_stress
        self.alt_normal_stress = alt_normal_stress
        self.alt_torsion_stress = alt_torsion_stress
        self.mean_bending_stress = mean_bending_stress
        self.mean_normal_stress = mean_normal_stress
        self.mean_torsion_stress = mean_torsion_stress
        self.alt_eq_stress = self.calc_alt_eq_stress()
        self.mean_eq_stress = self.calc_mean_eq_stress()

    def calc_alt_eq_stress(self):
        """Returns the alternating equivalent stress according to the load type indicated by Kc

        :returns: Alternating equivalent stress
        :rtype: float
        """

        Kc = self.Kc
        if Kc == 1 and self.stress_type == 'multiple':
            corrected_bending = self.Kf_bending * self.alt_bending_stress
            corrected_normal = self.Kf_normal * (self.alt_normal_stress / 0.85)
            corrected_torsion = self.Kf_torsion * self.alt_torsion_stress
            return sqrt((corrected_bending + corrected_normal) ** 2 + 3 * corrected_torsion ** 2)

        elif Kc == 1:
            return self.Kf_bending * self.alt_bending_stress

        elif Kc == 0.85:
            return self.Kf_normal * self.alt_normal_stress

        elif Kc == 0.59:
            return self.Kf_torsion * self.alt_torsion_stress

    def calc_mean_eq_stress(self):
        """Returns the mean equivalent stress according to the load type indicated by Kc

        :returns: Mean equivalent stress
        :rtype: float
        """
        if self.ductile:
            # if the material is ductile no correction is needed
            Kf_bending, Kf_normal, Kf_torsion = 1, 1, 1
        else:
            Kf_bending, Kf_normal, Kf_torsion = self.Kf_bending, self.Kf_normal, self.Kf_torsion

        Kc = self.Kc
        if Kc == 1 and self.stress_type == 'multiple':
            corrected_bending = Kf_bending * self.mean_bending_stress
            corrected_normal = Kf_normal * self.mean_normal_stress
            corrected_torsion = Kf_torsion * self.mean_torsion_stress

            return sqrt((corrected_bending + corrected_normal) ** 2 + 3 * corrected_torsion ** 2)

        elif Kc == 1:
            return Kf_bending * self.mean_bending_stress

        elif Kc == 0.85:
            return Kf_normal * self.mean_normal_stress

        elif Kc == 0.59:
            return Kf_torsion * self.mean_torsion_stress

    @property
    def shear_ultimate_strength(self):
        """Returns shear_ultimate_strength which is the
        ultimate_tensile_strength correction for shear stress

        :returns: Sst - ultimate shear tensile strength
        :type: float
        """
        return 0.67 * self.Sut

    @property
    def shear_yield_stress(self):
        """Returns shear_yield_strength which is the Sy correction for shear stress

        :returns: shear_yield_strength - yield stress for shear
        :type: float
        """
        return self.Sy / sqrt(3).evalf()

    @property
    def modified_goodman(self):
        """Safety factor according to modified Goodman failure criterion
        (very common criterion)

        :returns: Safety factor
        :rtype: any

        :raises ValueError: if ultimate_tensile_strength is not in the fatigue call
        """

        if self.Sut is None:
            raise ValueError("ultimate_tensile_strength is None")

        ultimate_strength = self.Sut
        if self.Kc == 0.59:
            # ultimate_tensile_strength correction for shear stress
            ultimate_strength = self.shear_ultimate_strength

        return FailureCriteria.modified_goodman(ultimate_strength, self.Se,
                                                self.alt_eq_stress,
                                                self.mean_eq_stress)

    @property
    def soderberg(self):
        """Safety factor according to Soderberg failure criterion
        (the safest criterion)

        :returns: Safety factor
        :rtype: any

        :raises ValueError: if Sy is not in the fatigue call
        """

        if self.Sy is None:
            raise ValueError("Sy is None")

        yield_strength = self.Sy
        if self.Kc == 0.59:
            # ultimate_tensile_strength correction for shear stress
            yield_strength = self.shear_yield_stress

        return FailureCriteria.soderberg(yield_strength, self.Se,
                                         self.alt_eq_stress,
                                         self.mean_eq_stress)

    @property
    def gerber(self):
        """Safety factor according to Gerber failure criterion
        (the most lenient criterion)

        :returns: Safety factor
        :rtype: any
        :raises ValueError: if ultimate_tensile_strength is not in the fatigue call
        """

        if self.Sut is None:
            raise ValueError("ultimate_tensile_strength is None")

        ultimate_strength = self.Sut
        if self.Kc == 0.59:
            # ultimate_tensile_strength correction for shear stress
            ultimate_strength = self.shear_ultimate_strength

        return FailureCriteria.gerber(ultimate_strength, self.Se,
                                      self.alt_eq_stress,
                                      self.mean_eq_stress)

    @property
    def ASME_elliptic(self):
        """Safety factor according to ASME Failure criterion

        :returns: Safety factor
        :rtype: any

        :raises ValueError: if ultimate_tensile_strength is not in the fatigue call
        """

        if self.Sut is None:
            raise ValueError("ultimate_tensile_strength is None")

        yield_strength = self.Sut
        if self.Kc == 0.59:
            # ultimate_tensile_strength correction for shear stress
            yield_strength = self.shear_yield_stress

        return FailureCriteria.asme_elliptic(yield_strength, self.Se, self.alt_eq_stress,
                                             self.mean_eq_stress)

    @property
    def langer_static_yield(self):
        """ Static safety factor according to Langer Failure criterion
        it's customary to use Langer, as an assessment to yielding in the first cycle

        :returns: Safety factor
        :rtype: any

        :raises ValueError: if Sy is not in the fatigue call
        """

        if self.Sy is None:
            raise ValueError("Sy is None")

        yield_strength = self.Sy
        if self.Kc == 0.59:
            # yield_strength correction for shear stress
            Ssy = 0.67 * self.Sut
            yield_strength = Ssy

        return FailureCriteria.langer_static_yield(yield_strength,
                                                   self.alt_eq_stress,
                                                   self.mean_eq_stress)

    def get_safety_factor(self, criterion, verbose=False):
        """Returns dynamic and static safety factors
        according to the quadrant in the alternating-mean
        stress plain where the stresses are in

        Note: Should always be used instead of accessing the
        individual safety factors properties directly

        :param str criterion: The criterion to use
        :param bool verbose: Print the result

        :returns: dynamic and static safety factors
        :rtype: tuple[float, float]
        """

        if self.mean_eq_stress > 0:
            # stress is in the first quadrant of the alternating-mean stress plan
            safety_factors = {'modified goodman': self.modified_goodman,
                              'soderberg': self.soderberg,
                              'gerber': self.gerber, 'asme-elliptic': self.ASME_elliptic}

            nF = safety_factors.get(criterion.lower(), 'Error')

            if nF == 'Error':
                raise ValueError(f"Unknown criterion - {criterion}\n"
                                 f"Available criteria: 'Modified Goodman', 'Soderberg',"
                                 f"'Gerber', 'ASME-elliptic'")

            msg = f"the {criterion} safety factor is: {nF}\n"

        else:
            # stress is in the second quadrant of the alternating-mean stress plan
            nF = self.Se / self.alt_eq_stress
            msg = f"the dynamic safety factor is: {nF}\n"

        nl = self.langer_static_yield

        if verbose:
            print(msg + f"the Langer static safety factor is: {nl}")

        return nF, nl

    @property
    def Sm_stress(self):
        """Getter for the Sm_stress property

        :returns: Sm - stress at 1e3 cycles
        :rtype: float
        """
        return self.calc_Sm(self.Sut)

    @staticmethod
    def calc_Sm(Sut):
        """Calculate Sm_stress which is the stress at 1e3 cycles, the boundary
        dividing Low cycle fatigue and high cycle fatigue

        :param Sut: Ultimate tensile strength

        :returns: Sm_stress stress
        :rtype: float
        """

        def f(x):
            """ f - fatigue strength fraction
                function constructed from curve fitting to the f graph in Shigley's
                the range of the fit is ( 70[kPsi] < ultimate_tensile_strength < 200[kPsi] ) """
            return (-2.56710686e-16 * x ** 5 + 1.35729780e-12 * x ** 4 - 2.92474777e-09 * x ** 3 +
                    3.28990748e-06 * x ** 2 - 2.04929617e-03 * x + 1.38405394e+00)

        # TODO: add proper warning and solutions to ultimate_tensile_strength out of graph range
        if Sut < 482.633:  # 482.633[Mpa] = 70[kPsi]
            print(f"Note: ultimate_tensile_strength={Sut} < 482.633[Mpa] (70[kPsi]) so f~0.9")
            return 0.9 * Sut
        elif Sut > 1378.95:
            print(
                f"Note: ultimate_tensile_strength={Sut} > 1378.95[Mpa] (200[kPsi]) which is out of "
                f"the graph range, f={f(Sut)}")
        return f(Sut) * Sut

    def num_of_cycle(self, z=-3):
        """ calculate number of cycles until failure

        Note: zeta = log(N1) - log(N2), N1 - number of cycles at Sm_stress,
            N2 - Number of cycles at Se for steel N1=1e3 and N2 = 1e6

        :param float z: -3 for steel where N=1e6, -5 for metal where N=1e8,
            -5.69 for metal where N=5e8

        :returns: The Number of cycles and the fatigue stress at failure
        :rtype: tuple[float, float]
        """
        mean_stress = self.mean_eq_stress
        alternating_stress = self.alt_eq_stress
        Se = self.Se
        Sut, Sy, Sm = self.Sut, self.Sy, self.Sm_stress

        if mean_stress >= 0:
            reversible_stress = alternating_stress / (1 - (mean_stress / Sut))
        else:
            reversible_stress = alternating_stress

        if Sm < reversible_stress < Sy:
            # Low Cycle Fatigue
            if z != -3:
                raise ValueError(
                    "Number of cycles calculation for low cycle fatigue is only possible for "
                    "zeta=-3 ")

            a = Sut
            b = (1 / z) * log10(Sut / Sm)

        elif Se < reversible_stress < Sm:
            # High Cycle Fatigue
            a = Sm * (Sm / Se) ** (-3 / z)
            b = (1 / z) * log10(Sm / Se)

        elif reversible_stress < Se:
            print(
                f"reversible_stress = {reversible_stress} < Se = {Se}, Number of cycles is "
                f"infinite")
            return oo  # TODO: add to documentation the meaning of oo
        else:
            raise NotInRangeError("Reversible Stress", reversible_stress,
                                  (f'Sy={Sy}', f'Sm_stress={Sm}', f'Se={Se}'))
        N = (reversible_stress / a) ** (1 / b)
        return N, a * N ** b

    def miner_rule(self, stress_groups, Sut, Se, Sy=None, z=-3, verbose=False,
                   alt_mean=False, freq=False):
        """ Calculates total number of cycles for multiple periodic loads,
        the stress_groups format is as follows:
        [number_of_repetitions, maximum_stress, minimum_stress]

        Note: number_of_repetitions = frequency [Hz] * time

        Note: if the material don't have fatigue limit use the fatigue strength at Se=Sf(N=1e8)

        :param list stress_groups: list containing the pick stresses and number of repetition
        :param float Sut: Ultimate tensile strength [MPa]
        :param float Sy: yield strength [MPa], if None only HCF is checked
        :param float Se: endurance limit [MPa]
        :param float z: -3 for steel where N=1e6, -5 for metal where N=1e8, -5.69 for a metal
            where N=5e8
        :param bool verbose: printing the groups
            [number_of_repetitions,maximum_stress, minimum_stress, reversible_stress, Number of
            cycles]
        :param bool freq: if the input is frequency instead of number of repetition
        :param bool alt_mean: if True the stress_group structure contains
            alternating and mean stresses: [number_of_repetitions, alternating_stress, mean_stress]
            instead of the max and min stresses:
            [number_of_repetitions, maximum_stress, minimum_stress]

        :returns: Total number of cycles
        :rtype: float
        """

        Sm = self.calc_Sm(Sut)
        for group in stress_groups:

            # if the stress given are minimum and maximum instead of alternating and mean
            if not alt_mean:
                mean_stress = (group[1] + group[2]) / 2
                alternating_stress = abs(group[1] - group[2]) / 2
            else:
                alternating_stress = group[1]
                mean_stress = group[2]

            # calculate the reversible stress according to the mean stress sign
            if mean_stress >= 0:
                reversible_stress = alternating_stress / (1 - (mean_stress / Sut))
            else:
                reversible_stress = alternating_stress

            group.append(reversible_stress)

            if ((Sy is not None) and (Sm < reversible_stress < Sy)) or reversible_stress < Se:
                # infinite num of cycle - either the stress is less then
                # the endurance limit or its low cycle fatigue
                group.append(oo)

            elif Se < reversible_stress < Sm:
                # High Cycle Fatigue
                # TODO: this calculation is the same every
                #   iteration consider change to internal function and implement cash
                a = Sm * (Sm / Se) ** (-3 / z)
                b = (1 / z) * log10(Sm / Se)
                N = (reversible_stress / a) ** (1 / b)
                group.append(N)

            else:
                # print error but don't stop the loop
                print(
                    f"Reversible Stress = {reversible_stress} not in range,"
                    f"LCF-range=(Sm_stress={Sm},Sy={Sy}), "
                    f"HCF-range(Se={Se},Sm_stress={Sm})")

        result = 0
        for group in stress_groups:
            # summing n/N
            result += (group[0] / group[-1])
            if verbose:
                print(group)

        # casting the result to float - my be needed because the use of sympy's oo
        N_total = float(1 / result)

        if verbose:
            if freq:
                print(f"total time = {N_total:.2f} [s]")
            else:
                print(f"N_total = {N_total:.2f}")
        return N_total

    def get_info(self):
        """print object attributes"""
        print_atributes(self)

module containing the FatigueAnalysis class and calc_kf for calculating dynamic stress concentration factor Kf - dynamic stress concentration factor      :param float Kt: stress concentration theoretical factor     :param float q: notch Sensitivity      :returns: dynamic stress concentration factor     :rtype: float Perform fatigue analysis # TODO: make endurance_limit optional and add option to input Se, Stress_type and Kc directly # TODO: replace Kc as way to determine what to do in factors calculation Instantiating fatigue object         Note: all stresses are in [MPa]          :param fatigue_analysis.EnduranceLimit endurance_limit: EnduranceLimit object containing         the modified Se         :param bool ductile: True if material is ductile         :param float Sut: Ultimate tensile strength in [Mpa]         :param float Sy: Yield strength in [Mpa]         :param float Kf_bending: dynamic stress concentration factor for bending         :param Kf_normal: dynamic stress concentration factor for normal         :param Kf_torsion: dynamic stress concentration factor for torsion         :param float alt_bending_stress: Alternating bending stress         :param float alt_normal_stress: Alternating normal stress         :param float alt_torsion_stress: Alternating torsion stress         :param float mean_bending_stress: Mean bending stresses         :param float mean_normal_stress: Mean normal stresses         :param float mean_torsion_stress: Mean torsion stresses Returns the alternating equivalent stress according to the load type indicated by Kc          :returns: Alternating equivalent stress         :rtype: float Returns the mean equivalent stress according to the load type indicated by Kc          :returns: Mean equivalent stress         :rtype: float # if the material is ductile no correction is needed Returns shear_ultimate_strength which is the         ultimate_tensile_strength correction for shear stress          :returns: Sst - ultimate shear tensile strength         :type: float Returns shear_yield_strength which is the Sy correction for shear stress          :returns: shear_yield_strength - yield stress for shear         :type: float Safety factor according to modified Goodman failure criterion         (very common criterion)          :returns: Safety factor         :rtype: any          :raises ValueError: if ultimate_tensile_strength is not in the fatigue call # ultimate_tensile_strength correction for shear stress Safety factor according to Soderberg failure criterion         (the safest criterion)          :returns: Safety factor         :rtype: any          :raises ValueError: if Sy is not in the fatigue call # ultimate_tensile_strength correction for shear stress Safety factor according to Gerber failure criterion         (the most lenient criterion)          :returns: Safety factor         :rtype: any         :raises ValueError: if ultimate_tensile_strength is not in the fatigue call # ultimate_tensile_strength correction for shear stress Safety factor according to ASME Failure criterion          :returns: Safety factor         :rtype: any          :raises ValueError: if ultimate_tensile_strength is not in the fatigue call # ultimate_tensile_strength correction for shear stress Static safety factor according to Langer Failure criterion         it's customary to use Langer, as an assessment to yielding in the first cycle          :returns: Safety factor         :rtype: any          :raises ValueError: if Sy is not in the fatigue call # yield_strength correction for shear stress Returns dynamic and static safety factors         according to the quadrant in the alternating-mean         stress plain where the stresses are in          Note: Should always be used instead of accessing the         individual safety factors properties directly          :param str criterion: The criterion to use         :param bool verbose: Print the result          :returns: dynamic and static safety factors         :rtype: tuple[float, float] # stress is in the first quadrant of the alternating-mean stress plan # stress is in the second quadrant of the alternating-mean stress plan Getter for the Sm_stress property          :returns: Sm - stress at 1e3 cycles         :rtype: float Calculate Sm_stress which is the stress at 1e3 cycles, the boundary         dividing Low cycle fatigue and high cycle fatigue          :param Sut: Ultimate tensile strength          :returns: Sm_stress stress         :rtype: float f - fatigue strength fraction                 function constructed from curve fitting to the f graph in Shigley's                 the range of the fit is ( 70[kPsi] < ultimate_tensile_strength < 200[kPsi] ) # TODO: add proper warning and solutions to ultimate_tensile_strength out of graph range # 482.633[Mpa] = 70[kPsi] calculate number of cycles until failure          Note: zeta = log(N1) - log(N2), N1 - number of cycles at Sm_stress,             N2 - Number of cycles at Se for steel N1=1e3 and N2 = 1e6          :param float z: -3 for steel where N=1e6, -5 for metal where N=1e8,             -5.69 for metal where N=5e8          :returns: The Number of cycles and the fatigue stress at failure         :rtype: tuple[float, float] # Low Cycle Fatigue # High Cycle Fatigue # TODO: add to documentation the meaning of oo Calculates total number of cycles for multiple periodic loads,         the stress_groups format is as follows:         [number_of_repetitions, maximum_stress, minimum_stress]          Note: number_of_repetitions = frequency [Hz] * time          Note: if the material don't have fatigue limit use the fatigue strength at Se=Sf(N=1e8)          :param list stress_groups: list containing the pick stresses and number of repetition         :param float Sut: Ultimate tensile strength [MPa]         :param float Sy: yield strength [MPa], if None only HCF is checked         :param float Se: endurance limit [MPa]         :param float z: -3 for steel where N=1e6, -5 for metal where N=1e8, -5.69 for a metal             where N=5e8         :param bool verbose: printing the groups             [number_of_repetitions,maximum_stress, minimum_stress, reversible_stress, Number of             cycles]         :param bool freq: if the input is frequency instead of number of repetition         :param bool alt_mean: if True the stress_group structure contains             alternating and mean stresses: [number_of_repetitions, alternating_stress, mean_stress]             instead of the max and min stresses:             [number_of_repetitions, maximum_stress, minimum_stress]          :returns: Total number of cycles         :rtype: float # if the stress given are minimum and maximum instead of alternating and mean # calculate the reversible stress according to the mean stress sign # infinite num of cycle - either the stress is less then # the endurance limit or its low cycle fatigue # High Cycle Fatigue # TODO: this calculation is the same every #   iteration consider change to internal function and implement cash # print error but don't stop the loop # summing n/N # casting the result to float - my be needed because the use of sympy's oo print object attributes