Atomistically-informed Finite Element Simulations of Phase Transformations and Fracture in Materials

Abstract

Multiscale material modeling is a powerful computational method to investigate materials at disparate length and/or time scales, and has been widely employed to study a large variety of problems in science and engineering. In this dissertation, an atomistically-informed finite element method (AFEM) is introduced, which involves two scales of calculations: the finite element method (FEM) and atomistic simulation. The FEM as a powerful tool to simulate material response in the continuum scale is widely used in solid mechanics field. However, phenomenological model is usually employed as constitutive law, which lacks the fundamental insights of material. Atomistic simulation can provide us with thermomechanical properties of material based on the interactions between atoms, but is limited to small model size due to the computational efficiency. In the AFEM presented in this dissertation, the material properties are calculated from the atomistic scale simulations, and are employed in the continuum scale FEM simulations as material parameters. Using such a modeling method, we can predict the large scale mechanical response of a system without losing atomistic insights of materials. The AFEM is implemented in an \emph{in situ} simulation of a diamond anvil cell to predict the phase transformation of silicon under pressure, and a cohesive element simulation of epoxy--graphene composite to study the fracture mechanism at small graphene loading.