**6.1. MAAD**

MAAD or "macroscopic, atomistic, ab initio dynamics" is a multiple- scale approach that incorporates tight binding (TB), molecular dynamics (MD), and finite elements (FE) concurrently to model a configuration of nano- and large- scale materials. In this method, the FE Mesh will be done until we approach the same size as much as atomic spacing; from here, the MD method is entered until we arrived in a physical phenomenon like a crack tip. At this point, we will use the TB approach. Thus, we will have two overlapping regions: FE/MD and MD/TB. Not only here but also in all multiple- scale methods, such overlap‐ ping areas are termed "handshake" regions. In this method, each handshake region provides a contribution to the total energy of the system. This contribution is done by linear law in each handshake region. Thus, the total energy that will be used to find equation of motion is as follows:

$$H\_{\rm FE} = H\_{\rm FE} + H\_{\rm FE/MD} + H\_{\rm MD} + H\_{\rm MD/TB} + H\_{\rm TB} \tag{10}$$

There are two problems in this method. First, having finite elements in the scale of atomic space prolongs the process of solving by increasing time steps. Second, that it seems unphysical that continuum relations can be evolved at the same timescales as the atomistic variables.
