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This class of methods has been applied to shear band problems, and large deformation fracture and damage problems.ĪB - The Reproducing Kernel Particle Method (RKPM), which utilizes the fundamental notions of the convolution theorem, multiresolution analysis and meshfree properties, is reviewed. The elimination of a mesh, combined with the filtering properties of window functions, makes a particle method suitable for problems with large deformations, high gradients, and localization problems. The multiple-scale RKPMs are then proposed as an alternative to commonly used numerical methods such as the finite element method. N2 - The Reproducing Kernel Particle Method (RKPM), which utilizes the fundamental notions of the convolution theorem, multiresolution analysis and meshfree properties, is reviewed. The content does not necessarily reflect the position or the policy of the government, and no official endorsement should be inferred. Sponsored in part by the Army High Performance Computing Research Center (AHPCRC) under the auspices of the Department of the Army Research Laboratory. The support of this research by Air Force Office of Scientific Research (AFOSR), Army Research Office (ARO), National Science Foundation (NSF) and Office of Naval Research (ONR) to Northwestern University is gratefully acknowledged. T1 - Multiple scale meshfree methods for damage fracture and localization