This work attempts to contribute further knowledge and understanding in the discipline of computational science in general and numerical modeling of discontinuity
problems in particular. Of particular interest is numerical simulation of dynamic strain localization and fracture problems. The distinguishing feature in this study is the employment of neural-networks-(RBF)-based meshfree
methods, which differentiates the present approach from many other computational approaches for numerical simulation of strain localization and fracture mechanics.
As a result, new meshfree methods based on RBF networks, namely moving RBF-based meshless methods, have been devised and developed for solving PDEs. Unlike the conventional RBF methods, the present moving RBF is locally supported and yields sparse, banded resultant matrices, and better condition numbers. The shape functions of the new method satisfy the Kroneckerdelta property, which facilitates the imposition of the essential boundary conditions.
In addition, the method is applicable to arbitrary domain and scattered nodes. To capture the characteristics of discontinuous problems, the method is further improved by special techniques including coordinate mapping and
local partition of unity enrichment. Results of simulation of strain localization and fracture, presented in the latter chapters of the thesis, indicate that the proposed meshless methods have been successfully applied to model such problems
