Elaine Gorom: Nonlocal-to-Local Coupling: a Study in Statics and Dynamics

Computational materials science plays a crucial role in advancing new and improved materials. To leverage the advantages of local and nonlocal methods and aid in the advancement of predictive capabilities for materials, multiscale models have been introduced. Many such methods have been proposed to overcome computational challenges in accuracy and efficiency. 

I discuss two different multiscale models. First, we delve into the creation and stability of an Atomistic-to-Continuum blended scheme for a 1D atomistic chain. This scheme blends local and nonlocal descriptions of force through a blending function to smoothly transition between the two. The second project describes a Peridynamics-to-Peridynamics scheme to model a bimaterial bar in 1D. We focus on preserving conservation laws while reducing spurious reflection from the model itself due to its nonlocality. These models aim to ensure stability and accuracy of the proposed models which remains an issue in multiscale modeling.