Asymmetric bilinear Takeda  curve - Takeda _asm

This is a model similar to the modified Takeda hysteresis loop described here, whereby different yield values may be specified for tension Fy(+) and compression Fy(-), so that to enable the modelling of asymmetric behaviour. Six parameters need to be defined in order to fully characterise its behaviour:

Yielding strength (Fy(+))
The default value is 500

Yielding strength (Fy(-))
The default value is 400

Initial stiffness (Ky)
The default value is 200000

Post-yielding to initial stiffness ratio ()
The default value is 0.1

Outer loop stiffness degradation factor (0)
The default value is 0.4

Inner loop stiffness degradation factor (1)
The default value is 0.9

Notes

1. The unloading stiffness from the post yielding curve in outer hysteresis loop is defined by:
   
   Ky: Initial stiffness
   Dy: Yielding displacement
   Dm: Previous maximum displacement
   0: Outer loop stiffness degradation factor (Krout), i.e. for unloading from the primary curve
2. The unloading stiffness in inner hysteresis loop is defined by:
   
   1: Inner loop stiffness degradation factor (Krin = 1 * Krout), i.e. for unloading and reloading in the inner cycles