Tailored metamaterials based on carbon nanotube nanotrusses

The paper at hand deals with the optimal design of metamaterials. As a fundamental building block of such metamaterials, a nanotruss is used, preserving the benefits of classical macroscopic trusses. Each truss element is made of a single-walled carbon nanotube. Such a choice should ensure superior strength of this class of metamaterials. Due to the repetitive nature of the optimization process, a computationally efficient framework is required. On the other hand, molecular dynamics is considered to be the most accurate, albeit prohibitively slow for this purpose. To achieve this goal, machine learning is used. More specifically, a partially input convex neural network takes the role of a constitutive model for all single-walled carbon nanotube configurations of practical interest. This network also incorporates fundamental principles of physics. Convexity is included in the architecture of the neural network and addresses the issue of noise caused by temperature effects. It is important to emphasize that the neural network is trained on a dataset obtained by molecular dynamics, and thus retains the accuracy of molecular dynamics. The developed neural network is then coupled to the Abaqus finite element code, providing constitutive behavior to nonlinear finite element calculations. Finally, the framework is linked to the optimization code Indago. The performance of the framework is demonstrated on an example. It is concluded that the framework is computationally efficient, yet accurate. The strong nonlinear apparatus available in Abaqus ensures the versatility of the framework.