Mechanical instabilities in molecular, self-similar structures of higher order

Many hierarchically structured materials found in nature are based on the principle of self-similarity. The imitation of this principle for the development of new molecular structures is becoming increasingly realistic thanks to modern synthesis processes. The use of self-similar structures in nanotechnological applications requires that their complex mechanical behavior be understood, mapped in mathematical models and reliably predicted with the help of computer-aided simulations.

The aim of the project is to gain fundamental insights into the cause and effect of mechanical instabilities in higher-order self-similar structures - using the example of the 'super' carbon nanotubes recently presented to the scientific community. Mechanical instabilities, such as the initiation and propagation of defects or rod-like buckling and shell-like buckling, can lead to the failure of the overall structure. The interaction of such phenomena across several hierarchical levels will be investigated in detail here. Since the atomistic models usually used at the molecular level are inefficient for higher-order structures, novel cross-scale models are developed by exploiting self-similarity. In the course of numerical implementation, these models are then embedded in the formalism of the finite element method.

The knowledge gained in the project will make important contributions to the development of novel bottom-up materials with hierarchical structures.