A neural network-based surrogate model for carbon nanotubes with geometric nonlinearities

This paper presents a neural network (NN)-based surrogate modeling approach suitable for the geometrically nonlinear analysis of carbon nanotubes (CNTs). In this work we propose an NN-based equivalent beam element (NN-EBE) which is capable of accurately predicting the high-order phenomena caused by size-effects that characterize the behavior of CNTs at the nano-scale and can only be predicted by micro-mechanical models. The basic idea is to approximate the residual forces of the Newton-Raphson incremental-iterative formulation of the classical Euler or Timoshenko beams of the EBE model by an NN prediction, which is based on the response of the detailed MSM model of a CNT portion. Several numerical examples are presented for straight and wavy CNTs under bending and compression, which demonstrate that the proposed methodology is possible to efficiently predict the nonlinear response of large-scale CNT structures in a fraction computing time compared to the full-scale problem.