Interatomic force in systems with multibody interactions

The system of particles (atoms) interacting via multibody interatomic potential of general form is considered. Possible variants of partition for the total force acting on a single particle into pair contributions are discussed. Two definitions for the force acting between a pair of particles are compared. The forces coincide only if the particles interact via pair or embedded-atom potentials. However in literature both definitions are used in order to determine Cauchy stress tensor. A simplest example of pure shear for perfect square lattice is analyzed. Two methods for stress calculation are considered. It is observed that, at least in the particular case, stresses calculated using classical continuum mechanics definition do not depend on the way of partition for the total force. In contrast, Hardy’s definition gives different results depending on the radius of localization function. The differences strongly depend on the way of the partition.

Figure 1

Particle number 0 and its nearest neighbors.

Figure 2

Calculated elastic constant $C_{44}$ divided by the exact solution $C_{44}^{\ast }$. Squares, triangles and circles correspond to elastic constant calculated using expressions (17, 21, 23), respectively.