Multiple scale meshfree methods for damage fracture and localization

The Reproducing Kernel Particle Method (RKPM), which utilizes the fundament al notions of the convolution theorem, multiresolution analysis and meshfre e properties, is reviewed. The multiple-scale RKPMs are then proposed as an alternative to commonly used numerical methods such as the finite element method. The elimination of a mesh, combined with the filtering properties o f window functions, makes a particle method suitable for problems with larg e deformations, high gradients, and localization problems. This class of me thods has been applied to shear band problems, and large deformation fractu re and damage problems. (C) 1999 Elsevier Science B.V. All rights reserved.