Modelling biomechanics of bark patterning in grasstrees

Holly Dale, Adam Runions, David Hobill, and Przemyslaw Prusinkiewicz

Abstract

Background and Aims Bark patterns are a visually important characteristic of trees, typically attributed to fractures occurring during secondary growth of the trunk and branches. An understanding of bark pattern formation has been hampered by insufficient information regarding the biomechanical properties of bark and the corresponding difficulties in faithfully modelling bark fractures using continuum mechanics. This study focuses on the genus Xanthorrhoea (grasstrees), which have an unusual bark-like structure composed of distinct leaf bases connected by sticky resin. Due to its discrete character, this structure is well suited for computational studies.

Methods A dynamic computational model of grasstree development was created. The model captures both the phyllotactic pattern of leaf bases during primary growth and the changes in the trunk's width during secondary growth. A biomechanical representation based on a system of masses connected by springs is used for the surface of the trunk, permitting the emergence of fractures during secondary growth to be simulated. The resulting fracture patterns were analysed statistically and compared with images of real trees.

Key Results The model reproduces key features of grasstree bark patterns, including their variability, spanning elongated and reticulate forms. The patterns produced by the model have the same statistical character as those seen in real trees.

Conclusions The model was able to support the general hypothesis that the patterns observed in the grasstree bark-like layer may be explained in terms of mechanical fractures driven by secondary growth. Although the generality of the results is limited by the unusual structure of grasstree bark, it supports the hypothesis that bark pattern formation is primarily a biomechanical phenomenon.

Reference

Holly Dale, Adam Runions, David Hobill, and Przemyslaw Prusinkiewicz. Modelling biomechanics of bark patterning in grasstrees. Annals of Botany 114(4), pp. 629-641, 2014.

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