Instead of averaging the equivalent strain, one can average the compliance variable , directly related to damage according to the formula .
The weight function contains a certain parameter with the dimension of length, which is in general called the characteristic length. Its specific meaning depends on the type of weight function. The following functions are currently supported:
The above functions depend only on the distance between the interacting points and are not normalized. If the normalizing condition
If the body of interest is finite (or even semiinfinite), the averaging integral can be performed only over the domain filled by the body, and the volume contributing to the nonlocal average at a point near the boundary is reduced as compared to points far from the boundary or in an infinite body. To make sure that the normalizing condition
In a recent paper [11], special techniques that modify the averaging procedure based on the distance from a physical boundary of the domain or on the stress state have been considered. The details are explained in [11]. These techniques can be invoked by setting the optional parameter nlVariation to 1, 2 or 3 and specifying additional parameters and for distancebased averaging, or for stressbased averaging.
The model parameters are summarized in Tabs. 24 and 25.

Borek Patzak