TY - JOUR
T1 - Mapping the stochastic response of nanostructures
AU - Pattamatta, Subrahmanyam
AU - Elliott, Ryan S.
AU - Tadmor, Ellad B.
PY - 2014/4/29
Y1 - 2014/4/29
N2 - Nanostructures are technological devices constructed on a nanometer length scale more than a thousand times thinner than a human hair. Due to the unique properties of matter at this scale, such devices offer great potential for creating novel materials and behaviors that can be leveraged to benefit mankind. This paper addresses a particular challenge involved in the design of nanostructures- their stochastic or apparently random response to external loading. This is because fundamentally the function that relates the energy of a nanostructure to the arrangement of its atoms is extremely nonconvex, with each minimum corresponding to a possible equilibrium state that may be visited as the system responds to loading. Traditional atomistic simulation techniques are not capable of systematically addressing this complexity. Instead, we construct an equilibrium map (EM) for the nanostructure, analogous to a phase diagram for bulk materials, which fully characterizes its response. Using the EM, definitive predictions can be made in limiting cases and the spectrum of responses at any desired loading rate can be obtained. The latter is important because standard atomistic methods are fundamentally limited, by computational feasibility, to simulations of loading rates that are many orders of magnitude faster than reality. In contrast, the EMbased approach makes possible the direct simulation of nanostructure experiments. We demonstrate the method's capabilities and its surprisingly complex results for the case of a nanoslab of nickel under compression.
AB - Nanostructures are technological devices constructed on a nanometer length scale more than a thousand times thinner than a human hair. Due to the unique properties of matter at this scale, such devices offer great potential for creating novel materials and behaviors that can be leveraged to benefit mankind. This paper addresses a particular challenge involved in the design of nanostructures- their stochastic or apparently random response to external loading. This is because fundamentally the function that relates the energy of a nanostructure to the arrangement of its atoms is extremely nonconvex, with each minimum corresponding to a possible equilibrium state that may be visited as the system responds to loading. Traditional atomistic simulation techniques are not capable of systematically addressing this complexity. Instead, we construct an equilibrium map (EM) for the nanostructure, analogous to a phase diagram for bulk materials, which fully characterizes its response. Using the EM, definitive predictions can be made in limiting cases and the spectrum of responses at any desired loading rate can be obtained. The latter is important because standard atomistic methods are fundamentally limited, by computational feasibility, to simulations of loading rates that are many orders of magnitude faster than reality. In contrast, the EMbased approach makes possible the direct simulation of nanostructure experiments. We demonstrate the method's capabilities and its surprisingly complex results for the case of a nanoslab of nickel under compression.
KW - Bifurcation
KW - Continuation
KW - Lattice statics
KW - Nonconvexity
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=84899643133&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84899643133&partnerID=8YFLogxK
U2 - 10.1073/pnas.1402029111
DO - 10.1073/pnas.1402029111
M3 - Article
AN - SCOPUS:84899643133
SN - 0027-8424
VL - 111
SP - E1678-E1686
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
IS - 17
ER -