Research Topic

[Equilibrium Map] Topic: Equilibrium Map Method

Team: Subrahmanyam Pattamatta, Ryan Elliott, Ellad Tadmor

Collaboration: Timothy Germann, Director of the DOE Exascale Co-Design Center for Materials in Extreme Environments (ExMatEx)

Funding: Pending

Figure: A schematic of the possible behaviors of a compressed nickel nanoslab. As the compression increases with time, the initially perfect structure (bottom) develops defects associated with minima on its evolving potential energy surface. The sequence of states observed in repeated experiments on nominally identical nanostructures is highly stochastic and rate dependent. Each colored line in the figure represents one such realization obtained using the equilibrium map methodology.

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.