Topic: Equilibrium Map Method
Team: Ryan Elliott, Ellad Tadmor
Description: Due to the extreme nonconvexity of the interatomic potential energy landscape the response of nanostructures to applied loading is inherently stochastic. This complexity is addressed head-on by the construction, using branch-following and bifurcation (BFB) methods, of an "Equilibrium Map" (EM) of the nanostructure. The EM describes all of the stable and unstable states of the structure at each value of applied loading and thereby enables a systematic procedure for identifying physically-meaningful response scenarios. These include the limiting cases of a quasistatic process (QP) and quenched dynamic (QD), as well as the rate-dependent case of driven dynamic (DD). The latter achived using a time-dependent Kinetic Monte Carlo (KMC) prochedure, which enables atomistic simulations at realistic loading rates. As a first test, the method was applied to the uniaxial compression of a nanoslab of nickel modeled using a classical interatomic potential. The set of possible equilibrium solutions for this simple problem is surprisingly complex thereby demonstrating the need for such an approach.