Abstract

We propose to model thick multiwalled carbon nanotubes as beams with non-convex curvature energy. Such models develop stressed phase mixtures composed of smoothly bent sections and rippled sections. This model is motivated by experimental observations and large-scale atomistic-based simulations. The model is analyzed, validated against large-scale simulations, and exercised in examples of interest. It is shown that modelling MWCNTs as linear elastic beams can result in poor approximations that overestimate the elastic restoring force considerably, particularly for thick tubes. In contrast, the proposed model produces very accurate predictions both of the restoring force and of the phase pattern. The size effect in the bending response of MWCNTs is also discussed.

Abstract

Abstract

The properties of shape memory alloys (SMA) are mainly influenced by phase transformations between austenite and martensite. The complex material behavior is described by a variational method which describes the evolution of the phase fractions. We combined the method with a microstructural analysis based on fast Fourier transformations. Such a highly resolved microstructural analysis comes along with a high computational effort.To reduce the later one, we propose a model order reduction technique that uses just a reduced set of Fourier modes, which is adapted to the underlying microstructure. The presentation of the theoretical background as well as of the implemented algorithm is followed by numerical results that underline the performance of our method.