Secondary growth stresses in recent and fossil plants: Physical/mathematical modelling and experimental validation

•Our model is able to describe elastic deformations in natural cellular materials.•The deformations in the cortex of an extant liana are mainly in the elastic range.•The deformations in the cortex of two fossil plants are mainly in the plastic range.•These deformations occurred in vivo and are not a fossilization artefact.•The model helps to understand stresses and strains caused by secondary growth.

Secondary growth, i.e. the increase in size of the secondary vascular cambial tissues causes stresses and strains in the surrounding cortical tissues. In extant plants, these stresses can be measured by biomechanical methods. In contrast, the stresses in the once living tissues of fossil plants cannot be measured experimentally. To overcome this problem, we present a mathematical/physical model that allows for calculating the magnitude of tissues stresses in rather small bodied centri-symmetric woody fossil plant stems. The model allows for determining whether the cortical tissue deformations caused by secondary cambial growth are mainly within the elastic or within the plastic range. The modelling is based on stress-strain equations for thick-walled cylinders as well as on physical testing of technical cellular solids. This allows for taking into account tissues with different radial widths, Young's moduli and Poisson's ratios.The model shows that (1) growth stresses at the inner surface of the outer sclerenchymatous cortex of Aristolochia macrophylla, an extant lianescent plant, are mainly within an elastic range, and also indicate that (2) cortical tissue stresses and strains of two fossil woody plants, the 'seed ferns' Lyginopteris oldhamia (300 Myr b.c.) and Calamopitys sp. (340 Myr b.c.), were mainly within a plastic range. Based on the proposed model, morphometric measurements of different tissues in fossil plants such as the analysed 'seed ferns' and other fossil plants with vascular secondary growth like arborescent lycopsids and horsetails can be used for recalculating the values of stresses in the primary cortical tissues.