Mapping the Stochastic Response of Nanostructures
Ellad Tadmor (University of Minnesota), Ryan Elliott (University of Minnesota), Subrahmanyam Pattamatta (University of Minnesota)
Instability in Solids and Structures
Tue 10:45 - 12:15
Barus-Holley 190
Due to the exponential complexity of the equilibrium set associated with the potential energy landscape of atomic interactions, 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 provides 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 method is 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 and therefore demonstrates the need for such an approach.