# Flag

Symmetric/Asymmetric Flag

Some self-centering and rocking systems show flag shaped hysteresis behavior. The `Flag01` model defines a symmetric flag shaped hysteresis rule. The `Flag02` model is an extension of the `Flag01` model and defines an asymmetric flag shaped hysteresis rule.

More flexible flag shaped hysteresis behavior can be achieved by combining multilinear elastic model with for example bilinear hardening model.

## Syntax

```
material Flag01 (1) (2) (3) (4) (5)
# (1) int, unique material tag
# (2) double, elastic modulus
# (3) double, yield stress, positive
# (4) double, residual stress, can be either positive or negative
# (5) double, hardening ratio

material Flag02 (1) (2) (3) (4) (5) (6) (7) (8)
# (1) int, unique material tag
# (2) double, elastic modulus
# (3) double, tension yield stress, positive
# (4) double, tension residual stress, can be either positive or negative
# (5) double, tension hardening ratio
# (6) double, compression yield stress, negative
# (7) double, compression residual stress, can be either positive or negative
# (8) double, compression hardening ratio
```

## History Variable Layout

| location             | value                             |
| -------------------- | --------------------------------- |
| `initial_history(0)` | tension\_reverse\_strain          |
| `initial_history(1)` | tension\_reverse\_low\_strain     |
| `initial_history(2)` | compression\_reverse\_strain      |
| `initial_history(3)` | compression\_reverse\_low\_strain |

## Remarks

1. `Flag01` is a wrapper of `Flag02`.
2. If `Flag01` is used, the compression yield stress and residual stress would be `-(3)` and `-(4)` so that the response would be symmetric.

## Usage

```
material Flag01 1 1000 10 3 .1
materialTest1D 1 1E-3 20 2 7 5 10 20 10 50 10 5 20 10 12 25 40
exit
```

![example one](https://4006314410-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MQ5rMqEBbzA9NgGETGX%2Fuploads%2Fgit-blob-6c500557b89b56da9339b919441e59669b960e94%2FFlag01.EX1.svg?alt=media)

```
material Flag02 1 1000 10 3 .1 -20 -5 -.1
materialTest1D 1 1E-3 20 2 7 5 10 20 10 50 10 5 20 10 12 25 40
exit
```

![example two](https://4006314410-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-MQ5rMqEBbzA9NgGETGX%2Fuploads%2Fgit-blob-7b7115d0b929736ebf504f09d5debb426b301802%2FFlag02.EX1.svg?alt=media)