LinearDamage

Linear Damage Degradation With Cut-offs

Syntax

material LinearDamage (1) (2) (3) (4) [5]
# (1) int, unique material tag
# (2) int, associated material tag
# (3) double, start strain
# (4) double, end strain
# [5] double, end damage value, default: 0.0

Theory

In this model, the equivalent total strain is used to characterize the damage development, namely, $d=f({\epsilon }_{eq})$. Then the final response is defined as

$$\sigma =d\overline{\sigma },$$

where $\overline{\sigma }$ is the intact stress response of the associated material model.

The final stiffness can be derived as

$$\mathbf{K}={\displaystyle \frac{\mathrm{d}\sigma }{\mathrm{d}\epsilon }}={\displaystyle \frac{\mathrm{d}\overline{\sigma }}{\mathrm{d}\epsilon }}d+\overline{\sigma }\otimes {\displaystyle \frac{\mathrm{d}d}{\mathrm{d}\epsilon }}=\overline{\mathbf{K}}d+\overline{\sigma }\otimes {\displaystyle \frac{\mathrm{d}d}{\mathrm{d}\epsilon }}.$$