Universal Design and Modeling of Symmetric Origami Structures
Abstract
Origami is capable of the large and coordinated shape-change increasingly sought in engineering. Armed with the right folding pattern, one can achieve rapid deployment across scales, from medical stents to reconfigurable antennas to solar sails. Origami is also useful as a mechanism for soft robotic motion, or as a way of manufacturing complex deployable electronics. At present, however, the applications of origami to engineering have been limited to well-known folding patterns (e.g., Miura-Ori) or perturbations thereof. Lacking is a general theoretical framework for origami design: one that catalogs all reasonably manufacturable folding patterns, and predicts their response to mechanical loads and stimuli. The proposed project addresses this gap in the modeling and design of origami-based structures. Objectives. Towards general design and modeling principles, the proposal s objectives are: 1. Identify all symmetric origami structures well-described as "repeated" unit cells, by linking the design of a rigidly foldable unit cell to the choice of an Abelian group. The group-theoretic approach will systematize the discovery of folding patterns. As opposed to other approaches that are either limited to examples or based on approximations, this approach will yield exact and easily implementable formulas for their design and rigid deformations. 2. Derive the effective continuum mechanical theories of symmetric origami structures in the limit of a very large number of folds. Most origami deformations are not rigid, and involve small yet non-negligible panel stresses which makes their deformations hard to predict. The proposed research will introduce a general approach based on rigorous asymptotic constitutive modeling (i.e., Gammaconvergence) to model the deformation of origami s aggregate mid-surface. Numerical methods will be developed to solve the models. Broader significance. Discrete mechanical systems, made of repeated but highly tunable building blocks, are at the forefront of materials science, advanced manufacturing and engineering design. As these systems easily undergo large and nonlinear elastic deformations, the choice of unit cell has a direct impact on the system s bulk mechanical properties. Traditional approaches to modeling (e.g., high-fidelity simulation) do not efficiently capture this impact. The proposed research will apply ideas from group theory, the calculus of variations, and homogenization (by Gamma-convergence) to symmetric origami, a key example in the field of discrete mechanical systems, with the goal of providing a direct and explicit link between the choice of the unit cell and the system s emergent mechanical properties. The long-term goal is to develop a modeling framework for informing design of discrete mechanical systems at the frontiers of engineering.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Apr 26, 2023
- Source ID
- W911NF2310137
Entities
People
- Paul Plucinsky
Organizations
- Army Contracting Command
- United States Army
- University of Southern California