Dispersion analysis and element-free Galerkin solutions of second- and fourth-order gradient-enhanced damage models

Gradient-dependent damage formulations incorporate higher-order derivatives of state variables in the constitutive equations. Different formulations h ave been derived for this gradient enhancement, comparison of which is diff icult in a finite element context due to higher-order continuity requiremen ts for certain formulations. On the other hand, the higher-order continuity requirements are met naturally by element-free Galerkin (EFG) shape functi ons. Thus, the EFG method provides a suitable tool for the assessment of gr adient enhanced continuum models. Dispersion analyses have been carried out to compare different gradient enhanced models with the non-local damage mo del. The formulation of the additional boundary conditions is addressed. Nu merical examples show the objectivity with respect to the discretization an d the differences between various gradient formulations with second- and fo urth-order derivatives. It is shown that with the same underlying internal length scale, very different results can be obtained. Copyright (C) 2000 Jo hn Wiley & Sons, Ltd.