Interplay of Performance and Robustness in Architected and Naturally Evolved Structures

Abstract

Humans have long drawn inspiration from nature, drawing on its intricate and efficient designs for solving complex engineering challenges. One such feature is the aperiodicity observed in biological systems, which exhibit remarkable robustness and functionality. These systems offer valuable insights for design of advanced engineering structures. Performance and robustness are essential yet often competing attributes in both engineering and biological systems. Structures optimized for peak performance tend to be sensitive to uncertainties such as material or geometric variations. On the other hand, robust systems may compromise performance to ensure reliability under variable conditions. The novelty of this thesis lies in investigating the fundamental interplay between these two attributes, and demonstrating how structural configurations can be designed or evolved to balance this trade-off. This conceptual link is established across two apparently contrasting domains: architected acoustic metamaterials and foraging webs of social spiders.

Metamaterials are architected materials, meticulously designed to possess extraordinary properties, offering a typically unattainable range of effects and characteristics, beyond those found in naturally occurring substances. A subclass of metamaterials of particular relevance to structural engineers is acoustic metamaterials (AMMs), which are utilized in vibration and noise control. Vibration propagation in AMMs can be manipulated through creation of frequency bandgaps, also known as stopbands or attenuation bands. While conventional periodic arrangements perform well under ideal conditions, they are highly susceptible to manufacturing imperfections, resulting in degraded bandgap performance. This thesis addresses this challenge by proposing a novel robustness index, and subsequently developing a multi-objective optimization framework to explore whether introducing designed aperiodicity can enhance the performance and robustness of attenuation bands in presence of geometric variability. The framework incorporates this robustness index as an additional design objective. The optimization methodology is implemented numerically and validated through laboratory-scale experiments on metamaterial beam (metabeam) and metamaterial plate (metaplate) configurations. Results show that aperiodic AMMs can exhibit improved robustness and wider attenuation bands compared to the periodic structure. Additionally, to address certain observed computational challenges in the multi-objective design framework, two novel formulations are developed: a sensitivity-based robustness index, and an energy-based stopband performance metric. These formulations are more efficient than traditional design strategies and significantly reduce computational cost by avoiding the double-loop problem during constrained optimization.

Building on the understanding of performance-robustness interplay in metamaterials, the thesis further examines whether nature employs similar structural principles in biological systems. In particular, it investigates the complex, disordered networks formed by the webs of Indian social spiders Stegodyphus sarasinorum, seeking to reveal the mechanics of vibration propagation that underlies their collective behavior. Using both synthetically generated web topologies and digitized models derived from real images, the dynamic performance of these structures is analyzed in terms of vibration transmission without significant attenuation. Results indicate the existence of optimality in pretension and damping characteristics of the web to transmit vibrations efficiently. Secondly, despite the absence of regularity, certain topological biases enhance signal transmission towards spiders' retreat, suggesting a naturally evolved structural robustness. The findings provide useful quantitative inputs for biologists to design new behavioral or sensory experiments on social spiders.

Together, these investigations highlight how structural configuration, whether designed through engineering optimization or shaped through natural evolution, can facilitate the trade-off between performance and robustness. The thesis contributes to a broader understanding of design under uncertainty, relevant to potential applications in materials science, structural engineering, and biomechanics.