An iterative bar & hinge formulation to model the nonlinear dynamics of origami structures

Deployable structures are essential in aerospace, biomedical devices, architecture, robotics, and metamaterials. Accurately predicting their motion demands fast and reliable modeling tools. In this study we present and validate a dynamic bar-and-hinge modeling framework, capable of simulating origami-inspired deployable structures accurately and with low computational cost. Built in MATLAB, the novelty of our dynamic model, with respect to the others in the literature, is its iterative nature and the capability of adopting different time integration algorithms (Forward Euler, Newmark-β, and HHT-α) with mass distributed evenly among the nodes. We first introduce details of our formulation and then analyse four case studies, from a simple fold to a full Miura pattern and a snap-through Waterbomb unit, to benchmark the method against Finite-Element (FE) simulation in a commercial software. Results show good agreement with the FE reference models while significantly reducing computational effort. The paper briefly presents the evolution of bar-and-hinge theory and the mathematical formulations behind it, successively detailing the case studies’ results; finally it discusses the results of the framework and the time-integration approaches, as well as the limitations of the current model and the direction of future research, towards experimental validation.