On the Analysis of an EFG Method Under Large Deformations and Volumetric Locking

This work investigates a modified element-free Galerkin (MEFG) method when applied to large deformation processes. The proposed EFG method enables the direct imposition of the essential boundary conditions, as a result of the kronecker delta property of the special shape functions, constructed in the neighborhood of the essential boundary. The plasticity model assumes a multiplicative decomposition of the deformation gradient into an elastic and a plastic part and considers a J2 elasto-plastic constitutive relation that accounts for a nonlinear isotropic hardening. The constitutive model is written in terms of the rotated Kirchhoff stress and of the conjugate logarithmic strain measure. A total Lagrangian formulation is considered in order to improve the computational performance of the proposed algorithm. Here, aspects related to the volumetric locking are numerically investigated and an F-bar approach is considered. Some numerical results are presented, under axisymmetric and plane strain assumption, in order to attest the performance of the proposed method.