Keywords: buckling, nanoparticles, nanofilms, finite element method, Monte Carlo simulations, ab initio.

In structural mechanics, instabilities, such as buckling under loads, are typically considered as failure modes. In contrast to this, the present review deals with modelling and computational simulation of instability phenomena with the objective of explaining and interpreting experimental observations at the micro and nano level. Different modelling techniques and simulation methods at different length scales are presented and discussed in terms of multi-scale/multi-method approaches. The presentation of problem solutions and comparisons with experimental results accompany the theoretical considerations.

A typical example treated is finding a reason for the growth limit of carbon onions, which are nanoparticles consisting of many concentrically arranged spherical graphene layers. Another example discussed in this review is shedding light onto the question of why carbon fibres, built by nanocrystallites consisting of graphene layers, show different axial stiffness in tension and in compression. In both of these examples the appearance of instabilities are possible explanations for the observed phenomena.

Computational simulations in combination with experiments are frequently used for determining material parameters of nano-structured systems which cannot be measured directly. An example of this approach is modelling and simulation of the behaviour of just a few nanometres thick films, which buckle locally under global tensile loading and lift up from the substrate to which they are bonded. The combination of experimental observations and computational considerations of this process provides a possible way of determining parameters for assessing the strength of the interface between film and substrate in terms of solving an inverse problem.

Atomistic as well as continuum mechanics modelling techniques for the computational simulation of such stability problems are presented. At the meso-level, the nanostructures considered here can be modelled as thin plates or shells in the framework of continuum mechanics. However, for using this approach, for instance for nanoparticles built by several stacked graphene layers, an effective thickness and effective elastic properties of graphene must be determined, and the van der Waals interaction must be modelled appropriately. Different approaches for solving these problems are presented, too.

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