Simulation of instabilities in thin nanostructures by a perturbation approach

摘要: A new numerical method is proposed to simulate instabilities in thin atomistic structures quasi-static regime. In contrast with previous approaches based on energy minimization or Newton---Raphson methods, the present technique uses a series expansion of displacements respect loading path parameter, truncated at high orders. The nonlinear set equations defined by minimizing potential discrete system nuclei positions then transformed into sequence linear sets equations, which can be solved efficiently. solution described along very large steps without correction, resulting significant reduction matrices inverted. Finally, treatment limit points and snap-back/snap-through arising when occur simplified due continuous description parameter. applied analysis single carbon atom layers nanostructures like graphene sheets nanotubes traction compression regimes. Accuracy efficiency demonstrated comparisons iterative Newton procedures.