# Foldable Cones as a Framework for Nonrigid Origami

## TL;DR

This paper investigates the elastic behavior of foldable cones (f-cones) in origami, incorporating nonlinear effects, crease mechanics, and testing inextensibility, offering a new numerical modeling approach for realistic origami structures.

## Contribution

It introduces a comprehensive nonlinear elastic model for f-cones, including crease mechanics and deformation effects, advancing beyond previous linear models.

## Key findings

- Nonlinear corrections significantly affect f-cone behavior.
- The phase field-like model effectively simulates realistic origami deformations.
- Inextensibility hypothesis is validated through numerical testing.

## Abstract

The study of origami-based mechanical metamaterials usually focuses on the kinematics of deployable structures made of an assembly of rigid flat plates connected by hinges. When the elastic response of each panel is taken into account, novel behaviors take place, as in the case of foldable cones (f-cones): circular sheets decorated by radial creases around which they can fold. These structures exhibit bistability, in the sense that they can snap-through from one metastable configuration to another. In this work, we study the elastic behavior of isometric f-cones for any deflection and crease mechanics, which introduce nonlinear corrections to a linear model studied previously. Furthermore, we test the inextensibility hypothesis by means of a continuous numerical model that includes both the extended nature of the creases, stretching and bending deformations of the panels. The results show that this phase field-like model could become an efficient numerical tool for the study of realistic origami structures.