The quasicontinuum method provides an efficient way to simulate the mechanical response of relatively large crystallinematerials at zero temperature by combining continuum and atomistic approaches. Unconstrained optimization constitutes thekey computational kernel of this method. The efficiency of the techniques for minimization depends on both the time needed toevaluate the energy expression and the number of iterations needed to converge to the minimum. In this research, we report theeffectiveness of the truncated Newton-Raphson method and quasi-Newton method with low-rank Hessian update strategy thatare evaluated against the full Newton-Raphson and preconditioned nonlinear conjugate gradient implementation available atqcmethod.com. Results of illustrative examples mainly focus on the number of minimization iterations to converge and CPUtime for the two-dimensional nanoindentation and shearing grain boundary problems.
展开▼
