cratepy.material.models.von_mises.get_available_hardening_types

get_available_hardening_types()[source]

Get available isotropic hardening laws.

The isotropic hardening law is specified in the input data file as a material property of the constitutive model.

Available isotropic hardening laws:

  • Piecewise linear hardening

    \[\{\bar{\varepsilon}^{p}_{i}, \, \sigma_{y, i}\}, \quad i = 1, \dots, n_{\text{points}}\]

    Input data file syntax:

    isotropic_hardening piecewise_linear < n_points >
        hp_1 < value > < value >
        hp_2 < value > < value >
        ...
    

    where

    • isotropic_hardening - Isotropic strain hardening type and number of parameters.

    • hp_i - Hardening point with coordinates (\(\bar{\varepsilon}^{p}\), \(\sigma_{y}\)).


  • Linear hardening

    \[\sigma_{y}(\bar{\varepsilon}^{p}) = \sigma_{y, 0} + a \bar{\varepsilon}^{p}\]

    Input data file syntax:

    isotropic_hardening linear 2
        s0 < value >
        a  < value >
    

    where

    • isotropic_hardening - Isotropic strain hardening type and number of parameters.

    • s0 - Initial yielding stress (\(\sigma_{y, 0}\)).

    • a - Hardening law parameter (\(a\)).


  • Nadai-Ludwik hardening:

    \[\sigma_{y}(\bar{\varepsilon}^{p}) = \sigma_{y, 0} + a (\bar{\varepsilon}^{p}_{0} + \bar{\varepsilon}^{p})^{b}\]

    Input data file syntax:

    isotropic_hardening nadai_ludwik 4
        s0  < value >
        a   < value >
        b   < value >
        ep0 < value >
    

    where

    • isotropic_hardening - Isotropic strain hardening type and number of parameters.

    • s0 - Initial yielding stress (\(\sigma_{y, 0}\)).

    • a - Hardening law parameter (\(a\)).

    • b - Hardening law parameter (\(b\)).

    • ep0 - Accumulated plastic strain corresponding to initial yielding stress (\(\bar{\varepsilon}^{p}_{0}\))


Returns:

available_hardening_types – List of available isotropic hardening laws (str).

Return type:

tuple[str]