|Position Title||Parallel Quasicontinuum Branch-Following and Bifurcation (BFB) Researcher|
|Summary||Perform large scale computations to study the BFB behavior of quasicontinuum simulations of nano-indentation into thin metalic films. (Project Leaders: Ryan S. Elliott & Ellad B. Tadmor)|
|Job Description||Static multiscale quasicontinuum (QC) simulations aim to obtain a stable equilibrium configuration (local energy minimum) of a body composed of discrete atomistic and finite element regions subjected to external loads such as forces and/or displacements. Often a system of "proportional loading" is considered and the evolution of the system's equilibrium configuration is determined in an incremental fashion as the scalar "loading parameter" is varied. At each step, a minimization procedure, such as the conjugate gradient method, is employed using the previous relaxed configuration as an initial guess.|
A practical problem with such simulations is that due to their highly nonlinear nature, many equilibrium configurations should be expected. Therefore, the real possibility of multiple competing physical processes is encountered. Unfortunately, the above described simulation procedure provides only one of the possible equilibrium evolutions. Even more troubling is the fact that this one equilibrium evolution will, generally, depend on the numerical energy minimization method employed and the particular values used for its parameters.
This work takes a different approach to the exploration of the equilibrium behavior of atomistic systems. It performs a Branch-Following and Bifurcation (BFB) investigation in order to map out a large number of equilibrium configurations over a wide range of the problem's loading parameter. Once a reasonably complete picture of the system's --possible behaviors-- is in hand, one can then interpret these results to draw conclusions about the most likely behavior of the system.
The project involves the novel application of BFB methods to multiscale problems, by studying a quasicontinuum simulation of nano-indentation into a Ni thin film. The set of possible equilibrium states will be explored. Based on preliminary work on atomistic systems we expect to obtain a highly complex network of possible equilibrium pathways. Such a network will shed a great deal of light on the possible deformation mechanisms that can be encountered in nano-indentation experiments.
The application of BFB techniques to the QC method is ideal for parallelization. The creation of the BFB network involves a large number of independent calculations which can be performed most efficiently with a large scale computational system such as BlueWaters. A specialized parallel algorithm will be developed to automatically detect new paths in the BFB network and spawn the corresponding QC/BFB computation on an available processor.
The intern will develop and implement the algorithm and use it to study the nano-indentation problem. Further, he/she will analyze the results.