Extreme Poisson’s ratios recorded in the secondary phloem of Malvaceae: a highlight on the biomechanical function of bark

Abstract

In some angiosperm species, especially in the Malvaceae family, postural control and directional growth of the stem are enabled by the mechanical interaction between the growing cambium and the secondary phloem. A key feature of this motor mechanism is the ability to redirect the tangential stress induced in secondary phloem into a longitudinal stress enabling the control of stem orientation. Here we studied how the microstructure of the secondary phloem is optimized for this function. We measured the longitudinal-tangential Poisson’s ratio and the longitudinal modulus of elasticity of secondary phloem in 22 tree species including Malvaceae and other families. We modeled the microstructure of Malvaceae secondary phloem using finite elements. The Poisson’s ratio of secondary phloem from Malvaceae trees was found one to two orders of magnitude higher than for other species, reaching the highest values ever reported for a natural material. Mechanical modeling confirmed these results and showed that parameters of the microstructure of secondary phloem are set at value optimizing this Poisson’s ratio. This highlights that the specific microstructure of Malvaceae secondary phloem is designed to maximize the conversion of cambial growth pressure into a longitudinal mechanical stress enabling the directional growth.