Vibration Induced Spatial Ordering of Periodic Patterns in Multistable Metamaterials
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Abstract: Topological solitons are highly non-linear waves encountered in multi-stable systems. These waves have been found in nature in a wide variety of settings, such as ferro-electrics, chemical systems, ferromagnets etc wherein, they directly influence the properties and behaviour of the material. Consequently, these waves have been replicated in manufactured metamaterial lattices leading to applications in shape reconfiguration, stable signal propagation, impact mitigation etc. In the context of materials with multiple equilibrium states, the propagation of topological solitons is a model for, e.g., polarization switching in ferroelectric and ferromagnetic materials and structural phase transitions—transformation phenomena that impact material performance and under-pin multi-functionality in applications. Thus, command of transition wave dynamics promotes their utility in applications and there has been a growing interest from the community to explore and leverage the rich dynamics offered by topological solitons. Various strategies such as introducing graded potentials, spatio-temporal modulations have been proposed to dictate the soliton dynamics.
The highly localized nature of the topological soliton drives numerous non-linear phenomena such as wrinkles in soft systems, faults in earthquakes and phase changes in metamaterials. So, understanding the localized nature of the topological soliton can help us design desired patterns and interfaces in architected metamaterials. Previous studies have utilized the localized nature of solitons using long-range interactions, defects, geometric frustration etc. However, multiple-soliton pair localizations in defect free systems remains unexplored. Recently, Vinod et al. (2020), proposed a theoretical method to predict the soliton response by treating the soliton as a quasi-particle. Furthermore, we proposed spatio temporal modulations to the local elastic potential to control the soliton motion. We now try to extend this to controlling multiple pairs of solitons to produce periodic patterns.
In this presentation, we propose a metamaterial design which can be dynamically reconfigured to a pre-determined state using linear eigen mode analysis and modulations to elastic potentials. The desired final state is expanded out in terms of the eigen modes of the system and boundary excitations of the respective eigen mode frequencies are applied. Exciting the material for sufficient time produces standing waves close to the target pattern. At this stage, the local elastic potential is altered from a monostable to a bi-stable potential. This switches the phase around the anti-nodal regions of the vibration thus giving rise to a sequence of kink-antikink pairs which freeze the phase of the system according to the target pattern. Numerical simulations for 1D and 2D systems are performed and the results are presented.
Citation: V. Ramakrishnan and M.J.Frazier, “Vibration Induced Spatial Ordering of Periodic Patterns in Multistable Metamaterials”, at ASME IMECE 2021, Virtual, November 1 - 4, 2021.