Analytical velocity field and hessian for 2-body potentials

Fig 1: 'Velocity' is defined as the rate of change of positions of crystal atoms with respect to downward motion of the indenter. The above expression assumes that the system is in mechanical equilibrium so that the response is essentially linear.



Fig 2: Derivation of elements of the Hessian matrix for a 2-body potential in a Cartesian coordinate system.