Modeling and analysis of origami structures with smooth folds

• A model for origami with smooth folds including kinematics and kinetics is proposed.
• A model implementation for analysis of arbitrary fold patterns is presented.
• Arbitrarily complex fold patterns considering real materials can be modeled.
• The results obtained with the model are in good agreement with experiments and FEA.

Origami has the potential to impact numerous areas of design and manufacturing. Modeling and analysis of origami structures allow for the understanding of their behavior and the development of computational tools for their design. Most available origami models are limited to the idealization of folds as creases of zeroth-order geometric continuity, which is not proper for origami structures having non-negligible fold thickness or with maximum curvature at the folds restricted by material limitations. Structural analysis of origami sheets having creased folds requires further idealizations of the fold mechanical response such as the representation of the folds as torsional springs. In view of this, a novel model analogous to that for rigid origami is presented in this work for origami structures having folds of non-zero surface area that exhibit higher-order geometric continuity (termed smooth folds). This origami model allows for a proper structural analysis of origami sheets using plate or shell representations for the folds. The shape formulation of the smooth folds and the kinematic constraints on their associated shape variables are presented. Modeling of origami structures with smooth folds exhibiting elastic behavior is performed by determining the configuration of the structure that minimizes its total potential energy subject to the derived kinematic constraints. The presented results show that the structural response determined using the proposed model is in good agreement with both experiments and higher-fidelity finite element analyses.