Nonlinear mechanics of non-rigid origami: an efficient computational approach

• Published in: Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Vol. 473; no. 2206; p. 20170348
• Main Authors: Liu, K., Paulino, G. H.
• Format: Journal Article
• Language: English
• Published: England The Royal Society Publishing 01-10-2017
• Edition: Royal Society (Great Britain)
• Subjects: Bar-And-Hinge Model; Computer simulation; Deformation; Elastic Deformations; Formability; Geometric nonlinearity; Large Deformation; Large Displacement; Mathematical models; Mechanical properties; Mechanics (physics); Nonlinear Analysis; Nonlinear response; Origami; Panels; Robustness (mathematics); Structural engineering; large displacement; origami; bar-and-hinge model; nonlinear analysis; large deformation; elastic deformations
• ISSN: 1364-5021; 1471-2946
• DOI: 10.1098/rspa.2017.0348

Origami-inspired designs possess attractive applications to science and engineering (e.g. deployable, self-assembling, adaptable systems). The special geometric arrangement of panels and creases gives rise to unique mechanical properties of origami, such as reconfigurability, making origami designs well suited for tunable structures. Although often being ignored, origami structures exhibit additional soft modes beyond rigid folding due to the flexibility of thin sheets that further influence their behaviour. Actual behaviour of origami structures usually involves significant geometric nonlinearity, which amplifies the influence of additional soft modes. To investigate the nonlinear mechanics of origami structures with deformable panels, we present a structural engineering approach for simulating the nonlinear response of non-rigid origami structures. In this paper, we propose a fully nonlinear, displacement-based implicit formulation for performing static/quasi-static analyses of non-rigid origami structures based on ‘bar-and-hinge’ models. The formulation itself leads to an efficient and robust numerical implementation. Agreement between real models and numerical simulations demonstrates the ability of the proposed approach to capture key features of origami behaviour.