This model is another candidate to be used for loading histories involving loading and reverse loading. The model is calibrated using uniaxial stress-strain data as described next. The monotonic part of the response (o-a-b) is fitted with the Ramberg-Osgood fit as described in Appendix C. For the results in Figure F.1, o-a-b had the following Ramberg-Osgood parameters:

(a)

Figure F.1: Fit parameters of uniaxial monotonic and hysteresis stress-strain responses for the Tseng-Lee two-surface model.

where ? _om is the proportional limit stress.

The material parameters for the basic hysteresis curve (b-c-d-e), E _c, ? _oc and h are obtained as follows:

1. E _c is the elastic modulus of the hysteresis curve; i.e., it is the slope of section b-c of the unloading curve. Usually, but not always, E _c = E _m.

2. ? _oc is the radius of the yield surface, calculated as follows. Identify the elastic limit of the hysteresis curve (point c). Then

   (F.1)

   where ? _b and ? _c are the stresses corresponding to points b and c on the response.

3. h is a shape parameter representing the hardening characteristics of the hysteresis curve. It can be evaluated as follows:

   • Find the slope, E _m, of the monotonic curve at point b. The corresponding plastic modulus at point b is

     (F.2)

   • The stress at point b, ? _b, represents the current size of the memory surface.

   • Construct the memory line by drawing a...