Asymptotic calculation of buckling thresholds for rods with disordered growth

Perform asymptotic calculations to derive rigorous expressions for the buckling threshold of a clamped slender elastic rod with circular cross-section subjected to axisymmetric, spatially varying axial growth g(x, ζ), in order to confirm the leading-order analytical estimates and numerical results for threshold shifts induced by growth disorder.

Background

The paper analyzes how spatial variability in axial growth affects the buckling transition of a clamped elastic rod. Using analytical estimates for localized “growth islands” and extensive finite-element simulations of random growth fields, the authors show that growth disorder can both increase and decrease the buckling threshold and that the threshold shift correlates with spatial moments of the growth field.

While the work provides non-asymptotic analytical estimates that qualitatively match simulations, the authors note that obtaining asymptotically correct expressions for buckling thresholds is technically challenging. They indicate that a more rigorous asymptotic treatment would be required to firmly establish the threshold behavior and validate the leading-order rod-theory estimates against a derivation consistent with three-dimensional elasticity.