On the use of element-free Galerkin Method for problems involving incompressibility

The improvement of the performance of numerical methods, namely in the presence of incompressible deformations, have been, in the recent years, an important issue of discussion. However, incompressible or near incompressible behaviour has been a source of problems for numerical analysis of solid mechanics as the methods tend to present a locking response, or alternatively, spurious modes of deformation. The element-free Galerkin method (EFGM) is one of these methods, which exhibits some problems, namely, the so-called volumetric locking and hourglass. The first one is related with an inability to deform in some conditions. The hourglass is related with the apparition of non-physical eigenvectors. In this publication a new vision based in vector spaces theory is presented which can explain why these problems appear in the EFGM context.