Surveying the Energy Landscapes of Multistable Elastic Structures

Abstract

Energy landscapes analysis is a versatile approach to study multistable systems by identifying the network of stable states and reconfiguration pathways. Thus far, it has primarily been used in microscale systems, such as studying chemical reaction rates and to characterise the behaviour of how protein fold. Here, however, we aim to utilise energy landscape techniques to study multistable elastic structures, in particular, complex 3D structures that have been buckled from 2D patterns, which are of interest for applications such as flexible electronics and microelectromechanical systems.

To this end we have developed new energy landscape methods and software that are well suited to continuous, macroscale systems with many degrees of freedom. The first is the binary image transition state search method (BITSS), which offers greater efficiency for large scale systems compared to traditional transition state search methods, and it is well suited to complex, non-linear pathways. Next, a new software library is introduced that contains a variety of energy landscape methods and potentials which are parallelised to study large-scale continuous systems. This library can be flexibly used for any chosen application, and has been designed to be easily extensible for new methods and potentials.

Furthermore, we exploit energy landscape analysis to tailor the stable states and reconfiguration paths of various reconfigurable buckled mesostructures. We establish stability phase diagrams and identify the corresponding available reconfiguration pathways by varying essential structural parameters. Furthermore, we identify how the introduction of creases affects the multistability of the structures, finding that a small number can increase the number of distinct states, but more creases can lead to a loss of multistability. Taken together, these results and methodology can be used to influence the design of new structures for a variety of different applications.