Mechanics of Multistable Reprogrammable Structural Systems

Janav P Udani, Purdue University

Abstract

Natural systems are known to achieve remarkable functional performance by leveraging drastic adaptability, fine tunability and complete (re)programmability of global properties in response to external stimuli. In the mechanical domain, this programmability manifests in the form of shape morphing and associated changes in static and dynamic properties that allow for efficient operation in largely unstructured environments. Borrowing from these ideas, mechanical metamaterials offer an interesting avenue for introducing programmability in engineering systems. Nonlinearity and multistability in these architectures allow for encoding an adaptable property set which can be tuned for meeting a diverse set of functional requirements. However, the underlying functional advantages of multistable systems are accompanied by a unique set of design challenges that warrant a paradigm shift from the conventional system design philosophy tailored for linear systems. The primary feature necessary for enabling this new design approach is the ability to reliably model and understand the fundamental nonlinear mechanics and dynamics of such mechanical metamaterials. The present work contributes towards addressing this research gap. The investigation is tailored towards developing modelling tools and analysis frameworks to further the understanding of the underlying nonlinear mechanics of multistable structural systems. Particular emphasis is given to approaching this challenge from a property programmability standpoint, i.e., leveraging the multiple stable states as a mechanism for programming a diverse set of property characteristics in a single host structure. In addition, this investigation is also focused towards maturing the understanding of the nonlinear behavior of multistable systems, as a route to uncovering novel physical phenomena, and the ensuing unconventional functionalities that are supported by these architectures. In the first part of this thesis, an analytical modelling framework is developed to capture the intrinsic deformation mechanics and state-driven response characteristics of an individual bistable unit cell. The modelling framework is designed to account for different forms of boundary and elastic constraints imposed on the continuum unit, thus enabling a holistic analysis of the programmability characteristics when the unit is embedded as part of a larger reconfigurable structural system. Any property programmability afforded by multistable systems is conditional upon the ability to achieve on-demand access to the desired state, i.e., the desired property characteristics, in a fast, reversible manner. Consequently, the static property modelling framework is complemented with the design and implementation of a novel, dynamics-driven control algorithm for achieving fast, efficient switching between the stable states of a bistable unit. The actuation methodology is based on manipulating the system response by employing controlled external phase perturbations, in order to trigger the nonlinear resonant dynamics and subsequent transition to the desired stable state. As the strategy leverages the nonlinear dynamics of the system, particularly the snap-through instability, as a mechanical amplifier, it is compatible with solid-state actuators that can be monolithically integrated with the host system. Accordingly, the presented numerical and experimental results confirm the potential for realizing smart, programmable structural systems that can be triggered on-demand to exhibit the desired response characteristics. Building on the mechanics of individual bistable units, in the second part of this thesis, the design and analysis of a continuum metamaterial architecture is presented. The metamaterial features a microstructure consisting of a series of individually bistable domes connected together.

Degree

Ph.D.

Advisors

Arrieta, Purdue University.

Subject Area

Mechanics|Energy

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