MDS-D is based on the generalized mathematical homogenization (GMH) theory where the unit cell is modeled using molecular dynamics, whereas the coarse-scale model is based on the thermo-mecahnical continuum formulation.

Figure 1 (right) depicts phenolic resin reinforced with randomly dispersed nanotubes. The volume fraction of the nanotubes considered in the simulation was 0.6%. The diameter and length of the nanotubes was 24 and 1000 nanometers, respectively. MDS-D results are compared to the molecular dynamics simulation results in Figure 1 (left).

In Figure 2 MDS-D is used to study failure properties of a silicon nanowire. The nanowire depicted in Figure 2 (upper left) is 1.08*nm* X 1.08*nm *X 10.8*nm*. One end of the nanowire is held fixed, the other side is pulled uniformly with an applied displacement increasing with time. Temperature is kept fixed at 20K. For the atomistic unit cell, the atoms on the two surfaces normal to the axial direction have been constrained in the deformed configuration; the atoms on the lateral surfaces are free, which allows for relaxation at these free surfaces. Continuum is modeled using 8-node coupled temperature-displacement brick elements with eight quadrature points. It can be seen that the ultimate stress obtained by molecular dynamics is in good agreement with those obtained by MDS-D.