Meshfree Technique with Adaptive Refinement Strategy for Crack Propagation Analysis

Abstract

MeshFree Technique with Adaptive Refinement Strategy for Crack Propagation Analysis” is an investigation that has aimed to develop an adaptive refinement scheme for EFG based MeshFree method for modeling and simulating high stress gradients in plate structures. Modelling high stress gradients like crack propagation are still a challenge to numerical methods and this has been addressed to a certain extent using MeshFree. Crack path follows the edge of the element in case of Finite Element Method (FEM) and getting the true path even with remeshing is complicated. Use of special functions to model discontinuity within the element (Extended Finite Element Method) has made modelling much simpler by reducing remeshing to a certain extent, but fails to arrive at smoother stress distribution. MeshFree method can offer solutions to the problems discussed and many researchers have thrown light in this direction. This work has focused on development of a MeshFree method that can be of help in crack propagation studies. On the Element-Free Galerkin (EFG) platform with Moving Least Square (MLS) technique for shape function construction, Lagrangian multipliers for imposition of constraints and satisfaction of Kronecker delta property has been attempted successfully. With strain energy release rate as basis, crack formation-propagation analysis formulation has been done and strategies for adaptive refinement have been suggested. The mathematical formulations have been verified and validated. Comparison with traditional FEM to highlight the superiority of MeshFree methods in handling high stress gradient problem have been detailed with illustrations.