The Bilinear Model exhibits a linear behavior up to the yield force limit, after which the stiffness is reduced, resulting in a softer post-yield response.

The following model properties can be defined:

• Stiffness K, the gross stiffness [Kips/in]
• Positive Yield Ypos [Kips]
• Negative Yield Yneg [Kips]
• Positive hardening ratio (Khpos/K), where Khpos is the hardening stiffness in the positive direction
• Negative hardening ratio (Khneg/K), where Khneg is the hardening stiffness in the negative direction

Note that the hardening ratio can be positive (hardening) or negative (softening).

The yield strength and post-yield hardening ratio can be defined independently for the positive and negative directions directly. This also applies to the other bilinear models including Clough, Modified-Clough, Origin-Oriented, Peak-Oriented, Bilinear Elastic, Bilinear Flag, and Bilinear Slip element models.

Different properties can be specified for bidirectional analysis for orthogonal directions 1 and 2. While it is possible to specify different yield strength and stiffness values in the 1 and 2 directions, and the positive and negative directions of each of the 1 and 2 directions, strength and stiffness ratios can be specified that determine:

1. K2/K1 ratio, where K1 and K2 are the elastic stiffnesses in directions 1 and 2 respectively
2. Y2/Y1 ratio, where Y stands for Yield Strength (positive and negative)
3. Yneg/Ypos ratio, where Yneg and Ypos are the positive and negative yield strengths respectively

Figures 23 and 24 illustrate the bilinear model (symmetric and unsymmetric) and the resulting hysteresis under a simple displacement history (follow steps 1 through 6).

Figure 23: Hysteresis Behavior for a Symmetric Bilinear Model with Hardening

Figure 24: Hysteresis Behavior for an Unsymmetric Bilinear Model with Hardening