CAREER: Finite Elasticity of Morphing Metamaterials. Theory and Applications

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This Faculty Early Career Development (CAREER) grant will investigate the elastic behavior of structures that can unfold and deploy from compact configurations into useful 3D geometries. Deployable structures are used in several areas pertaining to robotics (e.g., soft robots used in minimally invasive surgeries and in search-and-rescue), to aeronautics and astronautics (e.g., smart airfoils, deployable mirrors and solar panels and sails in space missions) and to smart structures (e.g., deployable shelters and rooftops). The relationships that exist between the global behavior of a deployable structure and the local behavior of its elementary constituents (bars, plates and membranes) are governed by a mixture of geometrical and mechanical laws. The research aims to establish a fundamental understanding of such local-to-global relationships and of the way they dictate how a deployable structure changes shape under external loads so as to improve current modeling, design and control paradigms. The theme of geometry provides aesthetic and appealing connections with several areas of artistic and fashion design and will be leveraged to increase public engagement with science and technology through outreach activities which, with the help of an institutional center, will particularly target K-12 and underrepresented minorities.The main purpose of the project is to initiate a theory of the finite, geometrically non-linear, elastic deformations of deployable structures that are tailored on small space scales as in architected materials and metamaterials. The technical objectives of the research efforts are to (i) characterize the macroscopic deformation paths compatible with the small-scale kinematics of a deployable structure composed of rigid or inextensible elements; to (ii) compute the generalized, strain-gradient or enriched, elasticity functionals that govern the equilibrium geometries of a deployable structure and particularly so in cases where standard Strength of Materials theories break down; (iii) formulate conceptual control problems and solve them for actuation parameters understood as the boundary data that deform the deployable structure into a target shape; and (iv) establish inverse design paradigms that allow us to find deployable structures with pre-programmed deformation paths. To do so, the project will develop analysis methods marrying differential geometry, asymptotics and homogenization theory. This project will allow the PI to advance the knowledge base in solid mechanics and to support his long-term career within that field.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.