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

Author (s): Huerta, A. and Fernández-Méndez, S.
Journal: International Journal for Numerical Methods in Engineering

Volume: 51, Issue 11
Pages: 1361 – 1383
Date: 2001

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-physical locking modes is independent of the dilation parameter (support of the interpolation functions).
Thus increasing the dilation parameter does not suppress locking. Nevertheless, an increase in the dilation parameter does reduce the energy associated to the non-physical locking modes; thus, in part, it alleviates the locking phenomena.
This is shown for linear and quadratic orders of consistency. Moreover, the biquadratic order of consistency, as in finite elements, improves the locking behavior. Although more locking modes are present in the Element Free Galerkin method with quadratic
consistency than with the standard biquadratic finite element method. Finally numerical examples are shown.



  Author   = {A. Huerta and S. Fernandez-Mendez},
  Title    = {Locking in the incompressible limit for the Element Free Galerkin method},
  Fjournal = {International Journal for Numerical Methods in Engineering},
  Journal  = {Int. J. Numer. Methods Eng.},
  Volume   = {51},
  Number   = {11},
  Pages    = {1361--1383},
  Year     = {2001}}
  Doi      = {10.1002/nme.213}