Numerical investigation of growth-induced buckling of soft filaments in confined spaces

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.