Multiscale based finite element modeling for the nonlinear bending and postbuckling analyses of some noncarbon nanomaterials

Abstract

Multiscale based finite element model developed in the framework of the Cauchy–Born rule is employed to investigate the nonlinear response of some noncarbon nanosheets considering geometric and material nonlinearities. The Tersoff–Brenner type interatomic potentials with newly calibrated empirical parameters are employed to model the atomic interactions. The quadratic-type Cauchy–Born rule is used to couple atomic entities with entities at the continuum scale. A four-node Kirchhoff-type finite element is used for the continuum approximation of the different nanosheets. The governing finite elemental equations are derived through the principle of minimum potential energy and Newton–Raphson method is used to linearize the nonlinear algebraic equations. The nonlinear bending response of the noncarbon nanosheets, with clamped boundary conditions, subjected to uniformly distributed and central concentrated load is reported in detail. The present results obtained from the multiscale based finite element method are also supported with molecular static simulations for some cases. The postbuckling response of the nanosheets subjected to uniaxial in-plane compression is also reported. The effect of initial strain on the central deflection of nanosheets under distributed and central point load is also investigated in detail and few interesting findings are revealed.