Locking in the incompressible limit for the element-free Galerkin method

Volumetric locking (locking in the incompressible limit) for linear elastic isotropic materials is studied in the context of the element-free Galerkin method. The modal analysis developed here shows that the number of non-phy sical locking modes is independent of the dilation parameter (support of th e interpolation functions). Thus increasing the dilation parameter does not suppress locking. Nevertheless, an increase in the dilation parameter does reduce the energy associated with the non-physical locking modes; thus, in part, it alleviates the locking phenomena. This is shown for linear and qu adratic orders of consistency. Moreover, the biquadratic order of consisten cy, as in finite elements, improves the locking behaviour. Although more lo cking modes are present in the element-free Galerkin method with quadratic consistency than with standard biquadratic finite elements. Finally, numeri cal examples are shown to validate the modal analysis. In particular, the c onclusions of the modal analysis are also confirmed in an elastoplastic exa mple. Copyright (C) 2001 John Wiley & Sons, Ltd.