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posted on 17.02.2021, 18:01 by Janav Parag Udani
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. \\
\indent 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. The resulting dome-patterned metastructures exhibit extreme load-response programmability as inversion (state switching) of any microscale unit leads to a distinct macroscale property set. Numerical and experimental results indicate that state switching of individual microscale units leads to a transformation of the global response characteristics from plate- to shell-type behavior. This unique characteristic enables multi-directional linear and nonlinear response programmability and renders these metastructures particularly well-suited for soft robotic and morphing aerospace applications.
More fundamentally, the dome-patterned metamaterial architecture exhibits rich, nonlinear response characteristics with profound implications beyond structural programmability. The metasheet exhibits geometric frustration, a phenomenon found in water ice, self-folding biological structures, and condensed matter systems. Geometric frustration is characterized as the inability of a lattice system to minimize all of its interaction energies, thus leading to a degenerate manifold of disordered ground configurations. In the dome metasheet, geometric frustration manifests when a sufficient number of interacting domes are inverted, and uniquely leads to ordered 3D configurations of the metasheet. In particular, geometric frustration manifests in the form of hierarchical multistability, or the emergence of multiple stable global configurations for the same unit inversion pattern in the microstructure. A combination of analytical modelling tools, numerical simulations and experimental tests are developed in order to uncover the nonlinear mechanics governing this rich phenomenon, with particular emphasis on understanding the interactions between structural elasticity and deformation-driven geometric frustration that lead to ordered global frustrated states. The modelling and analysis framework leads to the detection of a unique class of higher-order frustrated states, that emerge when an (already) frustrated system is trapped between degenerate ground states, with equal propensity to go to either ground state. Additionally, a unique control strategy enabling on-demand access to any desired global frustrated state by controlling the sequence in which the units are inverted is presented. This control strategy offers a window to observe geometric frustration unfolding as the microstructural features evolve due to energy minimization of the constitutive units’ interactions. More broadly, the developed modelling and analysis framework serves as a blueprint for ``taming” macroscale geometric frustration, thereby facilitating the study of mechanisms governing this rich phenomenon. This in turn, opens avenues for employing geometric frustration for novel applications such as path-driven computation in structural systems.
Building on this idea, an abstraction of the geometrically frustrated metasheet architecture is presented as a mechanical computation platform for enabling deformation driven computing and information processing. Specifically, the computation platform parses spatiotemporal deformation fields and enables the mechanical abstraction of an AND logic gate.
The modelling and analysis tools and frameworks for understanding the mechanics of nonlinear multistable structural systems developed as part of this thesis can be leveraged for realizing targeted applications in reconfigurable structures, soft robotics, actuation and sensing systems, energy harvesting systems, and mechanical computation platforms. In essence, the developments and findings of this dissertation are directed towards the larger goal of understanding the interplay between “property, form and function” for nonlinear mechanical metamaterials and leveraging this interplay for augmenting functionality in engineering systems.


CAREER: The Mechanics of Hierachically Multistable Metastructures

Directorate for Engineering

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On-demand Stiffness Selectivity for Morphing Systems

United States Air Force

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DARPA NAC HR00112090010


Degree Type

Doctor of Philosophy


Mechanical Engineering

Campus location

West Lafayette

Advisor/Supervisor/Committee Chair

Andres F. Arrieta

Additional Committee Member 2

James M. Gibert

Additional Committee Member 3

Jeffrey F. Rhoads

Additional Committee Member 4

Shirley J. Dyke