A geometric incompatibility by any other name

In growing elastic materials, residual stresses in their structure often accumulate when the preferred geometry of the growth process is constrained. As the stresses build, a mechanical instability can occur that reduces the stress while changing the growth morphology. This is known as a geometric incompatibility — a phenomenon observed in many plants. In this situation, the growth will proceed to minimize the elastic energy associated with the deformations.

In the context of rose petals, Zhang and the team investigated the growth process of around a hundred individual petals of different ages and species. Cutting strips from the petals to analyse their mechanical properties, they found that strips cut perpendicular to the petal edge would curve downwards, indicating a finite radial curvature that becomes more pronounced as the petal ages.