The expressions should take one input argument, the damage variable, κ. The κ is different from the degradation denoted as d. The output should have a size of six.
The normalized energy should be provided, which is used to generate objective results. It is typically around the size of the area under the curve.
The output consists of six components, which are explained in the following.
The expression shall generate six numbers based on the input κ:
Index
Symbol
Description
1
damage degradation index
2
3
4
5
6
The κ ranges from 0 to 1.
The damage degradation index d shall satisfy: d(0)=0 and d(1)=1.
The f is the actual stress observed as the final output of the model.
By following these rules imposed, users can implement any custom backbone and damage evolution.
Example
For the purpose of illustration, we provide a simple example, which may not be applicable to real concrete behaviour.
Let's, say, for example, the damage degradation is a linear function of κ, that is
d(κ)=κ,
so that d(0)=0 and d(1)=1.
Assume the effective stess is a constant, say fˉ=10. The stress is then
f=fˉ(1−d)=10(1−κ).
One can define an expression as follows:
expression SimpleVector 1 x y|6 example
where x maps to κ and y maps to the six components of the output.