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 (\(\bar{\varepsilon}^{p}_{0}\))