Multiscale Modeling of Thermo-Mechanical Coupling Between Atomistic and Continuum Domains

The motivation to study multiscale problems such as friction and crack propagation/nucleation has triggered the development of multiscale models. The state-of-the-art multiscale models that have been developed until today are successfully applied to a variety of physical problems. However, most of these applications are limited to zero Kelvin studies. Yet, the behavior of materials at finite temperatures is crucial in most of the mechanical and materials science problems. So, there is a tremendous need for multiscale models that are applicable to both isothermal and non-isothermal problems. In this thesis, we begin with the application of one of the existing multiscale model known as the Bridging Domain method to a normal contact problem at finite temperatures. The difficulty of using this method at finite temperatures is illustrated with the observation of the development of strong thermal gradients and related thermal expansion/contraction near the handshake/coupling region. To overcome this difficulty, a constant finite temperature coupling strategy is proposed and applied to simulate the normal loading of two rough surfaces. Results show that a linear dependence of real contact area on load is observed in accordance with experimental and theoretical results. However, the influence of the temperature on the slope of contact area versus load curve is not observed and the reason for this behavior is discussed in more details. Later on, we investigate the application of digital filters to split the energy spectrum of an atomistic model simulated with molecular dynamics into low and high energy components as the first step to develop a coupling formulation that is applicable for both isothermal and non-isothermal problems. A step-by-step procedure to design the filters with a cutoff frequency based on the dispersion relations of continuum and atomistic models is presented. Several parametric studies comparing the frequency response of time and spatial filters are conducted using a one-dimensional numerical model based on the generalized Langevin equation (GLE) to study their influence on the system dynamics. Both one-dimensional and two-dimensional examples are presented. The results demonstrate that spatial filters are better than time filters and thus we favor the usage of spatial filters in coupling molecular dynamics and finite elements to simulate finite temperature problems. Finally, we present a new multiscale model to couple molecular dynamics with finite elements at finite temperatures using spatial filters. The need of spatial filters is demonstrated by simulating a one-dimensional coupled atomistic-continuum model at constant finite temperature. The mismatch in the dispersion relations between continuum and atomistic models leads, at finite temperature, to unwanted mesh vibrations which are illustrated using a standard least square coupling formulation. We propose the use of spatial filters with the least square minimization to selectiv