DEFORMATION MANIFOLD LEARNING MODEL FOR MULTI WALLED CARBON NANOTUBES

Two-Dimensional (2D) materials are being studied widely by researchers due to their superior material properties over the bulk materials. Since the isolation of graphene in 2004, graphene has gained popularity amongst the 2D materials community. Graphene when rolled into sheets form Carbon Nanotubes (CNTs) which possess excellent mechanical and electrical properties. Concentric stacks of CNTs yield Multi-walled Carbon Nanotubes (MWCNTs) which are superior to CNTs in certain aspects. It has been well established that the deformation of CNTs and MWCNTs change their mechanical and electrical properties significantly. This has opened doors for CNTs into numerous applications and also piqued the need of studying the deformation characteristics of CNTs. Efforts have been made by researchers to develop models that approximate the geometry of CNTs and simulate them under given loading conditions. Atomistic models, Continuum models, and atomistic-continuum models have been used to simulate the deformation of CNTs. These models have been accurate in generating the deformed CNTs and are in good agreement with the experimental results. The models have also been proven to work well for MWCNTs having millions of atoms. Despite being accurate these models require high computation power which is a bottleneck in the wide use of these models. In this work, we present a data-driven model to predict the deformation of MWCNTs under torsional and bending loads. Million atom MWCNTs are discretized and represented through a proposed dimensionality reduction technique described as constrained-Functional Principal Component Analysis. Further, learning is performed using Deep Neural Networks (DNNs) in the dimensionally reduced space. The proposed framework accurately predicts the deformation of MWCNTs and is in good agreement with the atomistic-physics simulations. The proposed model has an edge over traditional models in regards to the computational time and computational power required. The model yields dominant patterns of deformation which explain the prediction capability of the model. This makes our model comprehensible. The model is currently developed for MWCNTs and is presented here, but the model can be extended to other 2D materials and can form a basis towards the use of data-driven approaches for exploring the mechanics and physics of 2D materials