Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering

Committee Chair/Advisor

Suyi Li

Committee Member

Ahmed A. Shabana

Committee Member

Gang Li

Committee Member

Lonny Thompson


Origami, the ancient art of paper folding, has recently evolved into a design and fabrication framework for various engineering systems at vastly different scales: from large-scale deployable airframes to mesoscale biomedical devices to small-scale DNA machines. The increasingly diverse applications of origami require a better understanding of the fundamental mechanics and dynamics induced by folding. Therefore, formulating a high-fidelity simulation model for origami is crucial, especially when large amplitude deformation/rotation exists during folding.

The currently available origami simulation models can be categorized into three branches: rigid-facet models, bar-hinge models, and finite element models. The first branch of models assumes that the origami facets are rigid panels and creases behaving like hinges. It is a powerful tool for kinematics analysis without unnecessary complexities. On the other hand, the bar-hinge models have become widely used for simulating nonrigid-foldable origamis. The basic idea of these models is to place stretchable bar elements along the creases and across facet diagonals, discretizing the continuous origami into a pin-jointed truss frame system. Therefore, one can analyze facet deformations, including in-plane shearing, out-of-plane bending, and twisting. Moreover, more complex crease deformations can also be captured by adding appropriate components to the bar-hinge models. Because of their simplicity and modeling capability, the bar-hinge models have been utilized with many successes in analyzing the global deformation of non-rigid origami and uncovering its mechanical principles. However, one can only achieve qualitatively accurate predictions of the bar-hinge models compared to the physical experiments, especially when complex deformation exists during origami folding. The third branch, finite element models, does not impose explicit simplification on the facet deformation using shell elements. It can accurately analyze the deformation modes of origami structures; however, their disadvantages are also evident. On the one hand, it requires a time-consuming cycle for both modeling and computing, including pre-processing and post-processing. On the other hand, the traditional shell element might experience convergence issues when large and dynamic rotations occur, as commonly observed in origami systems.

This thesis investigates the mechanics modeling of non-rigid origami and proposes a new dynamic model based on Absolute Nodal Coordinate Formulation (ANCF hereafter). Firstly, we discuss the accuracy of the widely used bar-hinge model through a case study on the multi-stability behavior in a non-rigid stacked Miura-origami structure. The model successfully investigates the underpinning principles of the multi-stability behavior in non-rigid origami and finds the existence of asymmetric energy barriers for extension and compression by tailoring its crease stiffness and facet bending stiffness. This interesting phenomenon can be exploited to create a mechanical diode. Experiment results confirm the existence of asymmetric multi-stability; however, the model's prediction is only qualitatively verified due to its assumption of discrete lattices.

In the next part, we develop a new origami mechanics model based on ANCF, a powerful modeling tool for the nonlinear dynamic simulation of multibody systems with large rotation and deformation. The new model treats origami as ANCF thin plate elements rotating around compliant creases, and the so-called torsional spring damper connectors are developed and utilized to simulate crease folding. Finally, its modeling accuracy is experimentally validated through two case studies, including motion analysis of simple fold mechanism and dynamic deployment of Miura-ori structures. The new origami simulation model can be used to quantitatively predict the dynamic responses of non-rigid origami with complex deformations. It can help deepen our knowledge of folding-induced mechanics and dynamics and broaden the application of origami in science and engineering.

Author ORCID Identifier




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