# ExpMises1D

Exponential Isotropic Hardening Model

The kinematic hardening is not defined in this model.

## Theory

The isotropic hardening backbone function is defined as

$$
\sigma=\sigma\_y+a-ae^{-b\varepsilon\_p}+cE\varepsilon\_p,
$$

where $$a$$, $$b$$ and $$c$$ are three constants that control the shape of the backbone. The stiffness at the beginning of yielding is $$\sigma'|\_{\varepsilon\_p=0}=ab+cE$$.

It can be identified that

1. $$a$$ represents the saturation stress.
2. $$b$$ controls the rate of saturation.
3. $$c$$ represents the linear hardening ratio (w\.r.t. plastic strain).

## Syntax

```
material ExpMises1D (1) (2) (3) (4) (5) (6) [7]
# (1) int, unique tag
# (2) double, elastic modulus
# (3) double, yield stress
# (4) double, a, saturation stress
# (5) double, b, saturation rate
# (6) double, c, linear hardening ratio
# [7] double, density, default: 0
```
