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Lookup NU author(s): Dr Weicheng Huang
This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).
© 2026 The Authors. The mechanics of growing slender filaments under geometric confinement is a fundamental problem in biological and engineering systems. While extensive studies have examined growth-induced instabilities in unconfined settings, the nonlinear interplay between elasticity, growth, and confinement remains poorly understood. Existing theoretical frameworks, which typically enforce strict rod-surface coupling via surface parameterization, cannot capture complex interactions such as partial contact, detachment, and contact-induced buckling. To address this limitation, we develop a simulation framework for surface-confined growing rods based on the discrete elastic rod model, incorporating explicit non-smooth contact mechanics. This approach naturally accommodates intermittent contact and elastic constraints, enabling the investigation of nonlinear deformation modes inaccessible to classical surface-based formulations. We apply the framework to analyze the growth of an elastic ring confined within three surfaces of distinct Gaussian curvature: a sphere, a cylinder, and a torus. Results show that the dimensionless confinement radius acts as a bifurcation parameter controlling the buckling modes for a torus-confined growing rod. The framework provides a versatile tool for studying the mechanics of slender structures under realistic constraints, bridging the gap between idealized theories and complex biological or engineering applications.
Author(s): Li J, Wu H, Huang W
Publication type: Article
Publication status: Published
Journal: International Journal of Non-Linear Mechanics
Year: 2026
Volume: 187
Print publication date: 01/08/2026
Online publication date: 31/03/2026
Acceptance date: 23/03/2026
Date deposited: 15/04/2026
ISSN (print): 0020-7462
ISSN (electronic): 1878-5638
Publisher: Elsevier Ltd
URL: https://doi.org/10.1016/j.ijnonlinmec.2026.105363
DOI: 10.1016/j.ijnonlinmec.2026.105363
Data Access Statement: Data will be made available on request.
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