On the use of a damage model based on non-local displacements in the Element-Free Galerkin method

One of the ingredients of Element-Free Galerkin (EFG) shape functions are the weight functions as employed in Moving Least Squares interpolations [

1

]. They are similar to the weight functions used in non-local damage [

2

]. Therefore, it seems a natural choice to use non-local damage as a localisation limiter within the EFG method.

This contribution investigates the need for regularisation techniques within the EFG method as meshfree approximations can be already considered to possess intrinsic non-local properties [

3

]. However, one must make a distinction between the

mathematical

non-local properties of the interpolation method (whether it be Finite Elements, EFG etc), and the

mechanical

non-local properties of the constitutive model.

The recently developed displacement based non-local damage model [

4

] is utilised here to regularise damage within the EFG framework and provide further computational efficiency over strain based nonlocal methods due to (typically) less nodes being employed than integration points and less components for the displacements compared to the strains.

The formulation of the displacement based non-local damage within the EFG framework is elucidated and examples of the new model’s regularisation capabilities is compared to a local damage formulation within the EFG method.