CAREER: Effective Continuum Modeling of Mechanism-Based Metamaterials

This Faculty Early Career Development (CAREER) award will support fundamental research on the mechanical response of a wide range of morphing metamaterials that take inspiration from popular artforms like origami and kirigami. Morphing metamaterials are cell-based patterns of stiff panels, connected at flexible hinges or folds, designed to achieve large overall shape-change at little overall stress. They are promising materials for many applications, including for locomotion in soft robotics and for deployment of medical devices and satellites. However, their mechanical behavior arises from a multiscale coupling that is challenging to model: collective cellwise elastic interactions, large panel rotations, and localized distortion at the hinges or folds. This study aims to develop modeling tools capable of efficiently navigating the design space of these materials and predicting their response under a broad range of loads and stimuli. The award also integrates research into educational and outreach efforts that embrace the diversity of the Los Angeles community. The outreach effort includes summer research opportunities for undergraduate students from Cal State LA, a minority serving regional university, and for local high school students through USC Viterbi’s Summer High School Intensive in Next Generation Engineering (SHINE) program. This research project seeks to lay a theoretical foundation to effective continuum modeling of mechanism-based morphing metamaterials. The key objective is to replace the complex micro-motions of the metamaterials building blocks by an effective (cell-averaged) continuum deformation and auxiliary fields, with the goal of coarse graining the material’s collective elastic interactions at the engineering scale. Far from being a constitutive choice, this study will employ rigorous asymptotic analysis methods, calculus of variations, and geometric rigidity to demonstrate that effective continuum theories underlie the mechanics of a host of morphing metamaterials. This theoretical development will enable practical continuum constitutive models that link the geometric design of the metamaterial directly to models of generalized elastic continua that are efficient to simulate and predictive. The knowledge gained will lead to broadly applicable tools to explore the design-property relationship of morphing metamaterials, as well as novel insight into their behavior under loads. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.