MgO

MgO Class

Methods

class MgO(gamma_eff: float = 1.1, initial_density: float = 3.58, is_stochastic: bool = False, released: bool = True)

Initializer of the MgO class.

Parameters:

  • gamma_eff – \(\Gamma_{eff}\) is the updated Mie-Grüneisen (MG) parameter \(\Gamma\) for the linear reference of the Mie-Grüneisen (MGLR) model, that assumes the release path can be accurately reproduced with constant \(\Gamma\) along nearly its entirety. More details on the process of calculating the \(\Gamma_{eff}\) given experimental data can be found in [1]. Default value for MgO \(\Gamma_{eff}=1.1\).

  • initial_density – Density of MgO material at ambient environment conditions found here. Default Value \(3.58\). Units: \(g/cm^3\).

  • is_stochastic –

    Boolean that defines if the Hugoniot used for this material is the deterministic one or multiple Hugoniots that are produced as a result of the Bayesian Inference framework will be used.

    • If True, then samples of the Bayesian Inference will be used to generate the hugoniots_list attributed.

    • If False, only the nominal Hugoniot populates the list, and is derived from the least-square fitting of its analytical equation to the experimental data.

    Default value: False.

  • released –

    released: Boolean parameter indicating whether the reflected shock produced at the interface of the current material with the next is a rarefaction or a reshock.

    • If True, then the algorithms assumes that the material undergoes release and compute the release part of the isentrope.

    • If False, then the algorithm assumes the material will be reshocked and computed the respective part of the isentrope.

    Default value: True.

analytical_shock_velocity_equation(parameters: list, hugoniot_particle_velocity: ndarray)

Analytical Hugoniot equation for MgO, given by the following second order polynomial. \(U_s = a_0+a_1 \cdot u_p + a_2 \cdot u_p^2\)

Parameters:

  • parameters – A list containing the parameters \([a_0, a_1, a_2]\).

  • hugoniot_particle_velocity – The particle velocity \((u_p)\) domain where the values of the shock velocities \(U_s\) of the MgO will be calculated.

Attributes

MgO.nominal_hugoniot: Hugoniot

This attribute represents the deterministic value all possible shocked states of the MgO material. It is derived from the least-square fitting of its analytical equation to the experimental data. The fit of the data to a quadratic polynomial yields the following coefficients. \(\{a_0, a_1, a_2\} = \{6.6161, 1.4111, -0.016277\}\)

MgO.hugoniots_list

A list of the possible material Hugoniots. If the initialization parameter is_stochastic is False, then the nominal Hugoniot will be a member of the list. Otherwise, uncertain Hugoniots are generated using samples produced by the Bayesian Inference and are contained in the samplesMgO.p pickle file, inside the data folder of the materials_database module.