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