OVERVIEW

This model is usually used for loading histories involving loading and reverse loading. For this reason, the initial monotonic stress-strain response and the subsequent stable hysteresis are fitted separately. First convert the two responses into stress-plastic strain responses by using

(E.1)

Now follow the fitting steps below.

A. FIT OF MONOTONIC STRESS-STRAIN RESPONSE

The monotonic part of the response (o-a-b-c in Figure E.1 (a)) is fitted as follows:

1. E _m is Young's modulus of o-a.

2. ? _om is the elastic limit of o-a-b-c.

3. The bounding line is constructed by drawing the tangent to a-b-c at the maximum value of strain available.

4. is the slope of the bound.

5. ? _bm is the stress value at the point of intersection of the bound and the stress axis ( ? ^P = 0). ? _bm will be the radius of the bounding surface during monotonic loading.

6. Calculate the variable ? _in as follows

   (E.2)

7. Select a point along a-b-c (point b in Figure E.1(a)) and measure the stress difference ?. between it and its image on the bound. Point b is chosen such that

   (E.3)

8. Evaluate the plastic strain at point b,

9. h is evaluated by substituting the values of ? and ? ^P at point b into (E.4)

   (E.4)

Figure E.1: Stress-plastic strain responses with definitions of Dafalias-Popov model parameters (a) monotonic response and (b) Fit of Stable Hysteresis Response.

B. STABLE HYSTERESIS STRESS-STRAIN RESPONSE

The stable hysteresis loop c-d-e-f in...