Buckling by disordered growth

TL;DR

This study investigates how disordered tissue growth affects buckling instabilities, revealing that variability can either promote or inhibit buckling depending on spatial growth patterns, with implications for developmental biology.

Contribution

The paper provides a combined analytical and numerical analysis of how spatially variable growth influences buckling thresholds in elastic rods, a simplified model relevant to biological tissue folding.

Findings

Variability can both increase and decrease buckling thresholds.

The shift in buckling threshold correlates with spatial moments of growth.

Biological systems may exploit growth variability to control buckling.

Abstract

Buckling instabilities driven by tissue growth underpin key developmental events such as the folding of the brain. Tissue growth is disordered due to cell-to-cell variability, but the effects of this variability on buckling are unknown. Here, we analyse what is perhaps the simplest setup of this problem: the buckling of an elastic rod with fixed ends driven by spatially varying growth. Combining analytical calculations for simple growth fields and numerical sampling of random growth fields, we show that variability can increase as well as decrease the growth threshold for buckling, even when growth variability does not cause any residual stresses. For random growth, we find that the shift of the buckling threshold correlates with spatial moments of the growth field. Our results imply that biological systems can either trigger or avoid buckling by exploiting the spatial arrangement of growth variability.