Dynamic Response of Some Noncarbon Nanomaterials Using Multiscale Modeling Involving Material and Geometric Nonlinearities

Abstract

Nonlinear dynamic response of some noncarbon nanomaterials, involving material and geometric nonlinearities under different types of dynamic loads, is investigated using computationally efficient multiscale modeling. Multiscale-based finite element model is developed in the framework of the Cauchy–Born rule, which couples the deformation at the atomic scale to deformation at the continuum scale. The Tersoff–Brenner type interatomic potential is employed to model the atomic interactions. The governing finite elemental equations are derived through Hamilton's principle for a dynamic system. The linearization of nonlinear discrete equations is done using Newton–Raphson method and are solved using Newmark's time integration technique. The effects of material and geometric nonlinearities, inherent damping, different types of dynamic loads, and initial strain on the transient response of noncarbon nanosheets with clamped boundary conditions are reported in detail. The present results obtained from the multiscale-based finite element method are compared with those obtained from molecular dynamics (MD) simulation for the free vibration analysis, and the results are found to be in good agreement. The present results are also compared with the results of those obtained from Kirchhoff plate model for some cases.