GP and GP-FEA Multiscale Modeling: Model Size Effects and Applications

Abstract

Multiscale analysis is the study that bridges the gap between theory and experiment via numerical simulation and works to couple material behavior across disparate length and time scales. There is a growing need for techniques that operate within this regime as progressing technology requires ever more accurate and fundamental understanding of their materials. Multiscale analysis seeks to offer atomistically-based informed solutions to the leading technological problems in materials science. In this thesis the Generalized Particle (GP) method is validated with elasticity solutions and coupled to a Finite Element Mesh capable of efficiently modelling in the micro-scale with atomistic detail at local regions such as crack tips. This coupling method (GP-FEA) is used to investigate model size effects on local atomistic phenomena. Size effects were found for both elastic and inelastic (crack propagation) pre-cracked crystalline Iron samples. For these examples it was seen that models 500nm and larger were consistent with Linear Elastic Fracture Mechanics predictions for the displacement filed around a crack tip for a given load, however models smaller than 500nm underestimated the amount of deformation and had smaller zones of crack-tip phase transformation causing a lower toughness. These results show that the model size used in simulation and modelling must be large enough for the interesting atomistic phenomena to be accurate. This work sets the stage for further model size research based on atomistic analyses in hopes of proving a useful model size guideline for future work to be more accurate. In addition to this research the multiscale program and numerous tools and utilities developed to acquire this data are explained and examples given. Those scientists interested in particle based dynamic simulation methods and analyses are encouraged to peruse the latter chapters and appendices for detailed information regarding the specific algorithms used and the structure of the programs. This additional rich information is appended to encourage further work and development in the field of multiscale analysis.