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.

在 Cauchy-Born 规则框架下开发的基于多尺度的有限元模型用于研究一些考虑几何和材料非线性的非碳纳米片的非线性响应。采用具有新校准经验参数的 Tersoff-Brenner 型原子间势来模拟原子相互作用。二次型 Cauchy-Born 规则用于在连续尺度上将原子实体与实体耦合。四节点基尔霍夫型有限元用于不同纳米片的连续近似。通过最小势能原理推导出控制有限元方程，并使用Newton-Raphson方法对非线性代数方程进行线性化。非碳纳米片的非线性弯曲响应，具有夹紧边界条件，详细报告了受均匀分布和中心集中载荷的影响。在某些情况下，分子静态模拟也支持从基于多尺度有限元方法获得的当前结果。还报告了纳米片在单轴面内压缩时的后屈曲响应。还详细研究了初始应变对分布和中心点载荷下纳米片中心偏转的影响，并揭示了一些有趣的发现。