Modal Folding: Discovering Smooth Folding Patterns for Sheet Materials using Strain-Space Modes

TL;DR

This paper introduces Modal Folding, an automated method that discovers smooth, energetically optimal folding patterns for sheet materials by utilizing nonlinear strain-space modes, enabling complex folding transformations with minimal mechanical work.

Contribution

The paper presents strain-space modes as a novel nonlinear extension of elastic eigenmodes, facilitating automated discovery of complex folding patterns for sheet materials.

Findings

Effective generation of complex folding motions via energy minimization.

Simulation results demonstrate versatility across various shapes and materials.

Physical prototypes validate the practical applicability of the method.

Abstract

Folding can transform mundane objects such as napkins into stunning works of art. However, finding new folding transformations for sheet materials is a challenging problem that requires expertise and real-world experimentation. In this paper, we present Modal Folding -- an automated approach for discovering energetically optimal folding transformations, i.e., large deformations that require little mechanical work. For small deformations, minimizing internal energy for fixed displacement magnitudes leads to the well-known elastic eigenmodes. While linear modes provide promising directions for bending, they cannot capture the rotational motion required for folding. To overcome this limitation, we introduce strain-space modes -- nonlinear analogues of elastic eigenmodes that operate on per-element curvatures instead of vertices. Using strain-space modes to determine target curvatures for bending elements, we can generate complex nonlinear folding motions by simply minimizing the sheet's internal energy. Our modal folding approach offers a systematic and automated way to create complex designs. We demonstrate the effectiveness of our method with simulation results for a range of shapes and materials, and validate our designs with physical prototypes.