by Wing Kam Liu, Eduard G. Karpov, Harold S. Park Nano Mechanics and Materials: Theory, Multiscale Methods and Applications by Wing Kam Liu, Eduard G. Karpov, Harold S. Park

8. Non-Nearest Neighbor MD Boundary Condition

Motivation to Non-Nearest Neighbor Interaction Modeling Atomic interactions inherently non-local Some potentials have angular dependence Usage of nearest neighbor potentials leads to different physics being displayed (Holian, Physical Review A 1991), particularly at large deformations/high strain rates Need to account for non-nearest neighbor interactions in impedance force Impedance Force

Pairwise vs. Many-body Potential Morse pair potential EAM many-body potential Both images taken from Holian et al., Physical Review A 1991; 43: 2655-2661

MD Impedance Boundary Condition There are 4 ’s for second-nearest neighbor interactions instead of 1 for nearest neighbor interactions 1 2 3 Eliminated Atoms Boundary atoms

Numerical Examples – 1D Wave Propagation Problem Description: Non-nearest neighbor harmonic potential of form: Initial MD displacements like previous 1D examples 10 atoms per finite element MD energy transfer if MD impedance force applied correctly

1D MD Wave Propagation Problem Description: Harmonic potential of form: Gaussian wave initial displacements Second neighbor interactions Initial MD displacements

1D MD Wave Propagation MD region energy transfer