Locking in the incompressible limit: pseudo-divergence-free element free Galerkin

Abstract

Locking in finite elements has been a major concern since its early developments and has been extensively studied. However, locking in mesh-free methods is still an open topic. Until now the remedies proposed in the literature are extensions of already developed methods for finite elements. Here a new approach is explored and an improved formulation that asymptotically suppresses volumetric locking for the EFG method is proposed. The diffuse divergence converges to the exact divergence. Since the diffuse divergence-free condition can be imposed a priori, new interpolation functions are defined that asymptotically verify the incompressibility condition. Modal analysis and numerical results for classical benchmark tests in solids and fluids corroborate this issue.