def eeff(e_1, nu_1, e_2, nu_2):
    """

    Calculate the effective (Young's) modulus of two contact bodies according
    to Hertzian contact theory.

    Parameters
    ----------
    e_1: ndarray, scalar
        The Young's modulus of contact body 1.
    nu_1: ndarray, scalar
        The Poisson ratio of contact body 1.
    e_2: ndarray, scalar
        The Young's modulus of contact body 2.
    nu_2: ndarray, scalar
        The Poisson ratio of contact body 1.

    Returns
    -------
    e_eff: scalar
        The effective modulus.

    """
    e_eff = 1 / ((1 - nu_1 ** 2) / (2 * e_1) + (1 - nu_2 ** 2) / (2 * e_2))
    return e_eff