An Adaptive Multi - Scale Computational Method for Modeling

In this dissertation a coupled multi-scale computational model for simulating nonlinear deformation processes in crystalline metals at finite temperatures is developed. The computational model uses the finite element method to model the coarse scale response of the material. The constitutive response in the finite element will be modeled through interatomic potentials acting on the underlying homogeneous crystal lattice that characterizes its nanostructure. An adaptive remeshing technique is proposed to automatically delineate regions of severe deformation where homogeneity of the microstructure/deformation is violated. In these regions the finite element will be replaced by a set of deformed atoms which interact with each other through the interatomic potential. The resulting coupled multi-scale model will be used to study defect generation and growth, through a computational nanoindentation experiment, in practical 2D and 3D problems.