FredrickArmstrongPlasticHardening

Source: models/solid_mechanics/plasticity/FredrickArmstrongPlasticHardening.py

Map the flow rate (i.e., the consistency parameter in the KKT conditions) to the rate of internal variables. This object defines the non-associative Fredrick-Armstrong kinematic hardening. In the model, back stress is directly treated as an internal variable. Rate of back stress is given as \(\dot{\boldsymbol{X}} = \left( \frac{2}{3} C \frac{\partial f}{\partial \boldsymbol{M}} - g \boldsymbol{X} \right) \dot{\gamma}\).\(\frac{\partial f}{\partial \boldsymbol{M}}\) is the flow direction, \(\dot{\gamma}\) is the flow rate, and \(C\) and \(g\) are material parameters.

Inputs

flow_rate — input · Scalar · required

Flow rate

flow_direction — input · SR2 · required

Flow direction

back_stress — input · SR2 · required

Back stress

Outputs

back_stress_rate — output · SR2 · default back_stress_rate

Optional name for the derived output (defaults to ‘back_stress_rate’, i.e. the ‘back_stress’ variable name with the ‘_rate’ suffix).

Parameters

C — parameter · Scalar · required

Kinematic hardening coefficient

g — parameter · Scalar · required

Dynamic recovery coefficient