arXiv subjects

Zhixuan Wen

Publications and source records attributed to Zhixuan Wen.

3 recordsLinked to original sources

arXiv2026

An exact dimension-reduced dynamic theory for developable surfaces and curve-fold origami

Curve-fold origami, composed of developable panels joined along a curved crease, exhibits rich dynamic behaviors relevant to metamaterials and soft robotic systems. Despite multiple approximated models, a comprehensive and exact dynamical theory for curve-fold origami remains absent, limiting the precise predictions of its dynamics, especially for those with wide panels. In this work, we develop an exact dimension-reduced theory that focuses on the dynamics of curve-fold origami, utilizing the intrinsic one-dimensional nature of developable surfaces. Starting from a single developable surface, we investigate the kinematics and kinetic energy of a moving developable surface. By overcoming the difficulty of describing the motion of local frames, we derive the exact velocity field of wide surfaces solely described by the motion of the reference curve, which leads to the kinetic energy of the entire surface. Owing to the one-dimensional feature, the Lagrangian of the system, composed of both kinetic and elastic energy, is a functional of the reference curve. Thus, we may variate the Lagrangian and derive a nonlinear dynamical theory for the reference curve, which comprises governing equations similar to the rod model but can precisely describe the motion of developable surfaces. The theory is validated consistently in both Lagrangian and Eulerian frameworks and is further extended to curved-fold origami modeled as a coupled bi-rod system. Utilizing our exact 1D model, we theoretically analyze the dynamical behaviors of various developable structures, revealing that the coupling of curvature and torsion along with the motion of local frames in our theory leads to the accurate modeling of arbitrarily deformed developable surfaces, which are validated by finite element analysis quantitatively.

cond-mat.soft↗

arXiv2025

Geometry and Mechanics of Non-Euclidean Curved-Crease Origami

Recently there have been extensive theoretical, numerical and experimental works on curved-fold origami. However, we notice that a unified and complete geometric framework for describing the geometry and mechanics of curved-fold origami, especially those with nontrivial Gaussian curvature at the crease (non-Euclidean crease), is still absent. Herein we provide a unified geometric framework that describes the shape of a generic curved-fold origami composed of two general strips. The explicit description indicates that four configurations emerge, determined by its spatial crease and configuration branch. Within this geometric framework, we derive the equilibrium equations and study the mechanical response of the curved-crease origami, focusing on Euler's buckling behavior. Both linear stability analysis and finite element simulation indicate that the overlaid configuration exhibits a lower buckling threshold. To further capture the large deformation behavior efficiently, we develop a bistrip model based on the anisotropic Kirchhoff rod theory, which predicts the main features successfully. This work bridges the geometry and mechanics of curved-crease origami, offering insights for applications in robotics, actuators, and deployable space structures.

cond-mat.soft↗

arXiv2024

A generalized geometric mechanics theory for multi-curve-fold origami: vertex constrained universal configurations

Folding paper along curves leads to spatial structures that have curved surfaces meeting at spatial creases, defined as curve-fold origami. In this work, we provide an Eulerian framework focusing on the mechanics of arbitrary curve-fold origami, especially for multi-curve-fold origami with vertices. We start with single-curve-fold origami that has wide panels. Wide panel leads to different domains of mechanical responses induced by various generator distributions of the curved surface. The theories are then extended to multi-curve-fold origami, involving additional geometric correlations between creases. As an illustrative example, the deformation and equilibrium configuration of origami with annular creases are studied both theoretically and numerically. Afterward, single-vertex curved origami theory is studied as a special type of multi-curve-fold origami. We find that the extra periodicity at the vertex strongly constrains the configuration space, leading to a region near the vertex that has a striking universal equilibrium configuration regardless of the mechanical properties. Both theories and numerics confirm the existence of the universality in the near-field region. In addition, the far-field deformation is obtained via energy minimization and validated by finite element analysis. Our generalized multi-curve-fold origami theory, including the vertex-contained universality, is anticipated to provide a new understanding and framework for the shape programming of the curved fold origami system.

cond-mat.soft↗