Session: Rising Stars of Mechanical Engineering Celebration & Showcase

Paper Number: 148061

148061 - Geometry and Elasticity of Deployable Structures and Morphing Metamaterials 

Deployable structures are used in several areas pertaining to robotics (e.g., soft and continuum 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, shells 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 is being leveraged to increase public engagement with science and technology through outreach activities which particularly target K-12 and underrepresented minorities.

The main purpose of the research 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, we develop analysis methods marrying differential geometry, asymptotics and homogenization theory.

The presented poster samples some of the main results obtained thus far. Mainly, we report on a complete mathematical theory that characterizes the ways in which compliant shell mechanisms composed of repetitive patterns deform at low energy by pure bending without stretching (i.e., isometrically). The theory is versatile in that it invariably handles shells that are smoothly corrugated or creased with straight and/or curved creases (i.e., piecewise smooth surfaces). It uses high level tools from differential geometry and the theory of partial differential equations to circumvent low level computations (e.g., fomalism for discrete linkages, spherical trigonometry, etc.). Various examples of theoretical predictions are presented and assessed based on folded and 3D printed toy models and full finite element computations.

Presenting Author: Hussein Nassar University of Missouri - Columbia

Presenting Author Biography: Hussein Nassar is an Assistant Professor of Mechanical and Aerospace Engineering at the University of Missouri – Columbia (MU). He holds a double degree in Mathematics and Engineering from Sorbonne Université and École des Mines – PSL as well as a PhD in Mechanics from Université Gustave Eiffel. He joined the faculty at MU in 2018. His research investigates theoretical models of continuum mechanics applicable to architected solids and shells with emphasis on interactions between geometry and elasticity, both in static and dynamic regimes. His research has been supported by the NSF and the Army Research Office; he is a recipient of the NSF CAREER Award.

Authors:

Hussein Nassar University of Missouri - Columbia