Temperature-dependent homogenization technique and nanoscale meshfree particle methods

Abstract

In this thesis, we develop a temperature-dependent homogenization technique and implement it into the meshfree particle method for nanoscale continuum simulations. As a hierarchical multiscale method, the nanoscale meshfree particle method is employed to model and simulate nanostructured materials and devices. Recently developed multiscale methods can overcome the limitations of both length and time scales that molecular dynamics has. However, multiscale methods have difficulties in investigating temperature-dependent physical phenomena since most homogenization techniques employed in continuum models have an assumption of zero temperature. A new homogenization technique, the temperature-related Cauchy-Born (TCB) rule, is proposed with the consideration of the free energy instead of the potential energy in this thesis. This technique is verified via stress analyses of several crystalline solids. The studies of material stability demonstrate the significance of temperature effects on nanostructured material stability. Since meshfree particle methods have advantages on simulating the problems involving extremely large deformations and moving boundaries, they become attractive options to be used in the hierarchical multiscale modeling to approximate a large number of atoms. In this thesis, a nanoscale meshfree particle method with the implementation of the developed homogenization technique, i.e. the TCB rule, is proposed. It is shown that numerical simulations in nanotechnology can be beneficial from this technique by saving a great amount of computer time. The nanoscale meshfree particle method is employed to investigate the crack propagation in a nanoplate with the development of cohesive zone model and a thermal-mechanical coupling model. In addition, the nanoscale meshfree