Adaptive Modelling of Finite Strain Shear Band Localization Using the Element-Free Galerkin Method

Efficient computational modelling of problems with material and geometric nonlinearities is very challenging. These problems are often solved with the adaptive finite element method (FEM), which involves error estimation coupled with refinement strategies to automatically find regions for fine and coarse discretization. For these problems meshless methods offer a good alternative involving no remeshing, and only simple insertion or deletion of the nodes. An adaptive element-free Galerkin method (EFGM) is developed here for these types of problems, in which an existing error estimation procedure for linear elasto-static analysis is extended here to nonlinear problems. Maximum entropy (max-ent) shape functions are used instead of the conventional moving least squares (MLS) approximation in the EFGM, which allows implementation of the essential boundary conditions directly. A numerical example is given to demonstrate the implementation and performance of the current approach