A lumped-parameter model for the mechanics of interlocked geometries: Ribbons, origami, and woven structures

Document Type

Article

Publication Date

11-1-2025

Abstract

This work develops a lumped-parameter mechanical simulation to investigate the mechanics of interlocking behaviors in thin membrane systems like origami, ribbons, and woven structures. Unlike traditional finite element models (FEM) that require fine meshes and long computation to obtain good results, lumped-parameter models use specially derived coarse mesh formulations for rapid computation. Traditional lumped-parameter models tend to use a truss-based formulation to represent membrane systems, which can produce less accurate computation of in-plane stiffness. Moreover, these models lack the ability to capture contact behaviors in interlocked geometries. To address the challenge, this work develops a new lumped-parameter simulation with three components: a four-node rotational spring element to capture out-of-plane bending and folding, a new large-deformation triangle element to capture in-plane stretching and shearing, and a new triangle-to-triangle contact element for interlocking behaviors. Using verification tests, this work shows that the proposed model can outperform other lumped-parameter models in predicting the mechanics of thin membranes with potential contact. In addition, practical examples are presented to demonstrate the effectiveness of the simulation framework. Our results show that the proposed model can be 25 times faster than a full FEM simulation implemented in Abaqus for a selected case study. Finally, an implementation software package is developed to execute the proposed simulation and is published with this article.

Publication Title

Computer Methods in Applied Mechanics and Engineering

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