Analysing and modelling of secondary growth stresses in plant stems have been conducted for many years by using data of indirect measurement methods, as e.g. strain sensors, or of direct methods, as e.g. pressure probe measurements, for determining the stress. These methods and models have several drawbacks and in particular cannot be used for assessing growth stresses in fossil plants. Therefore we present a new approach and show that our mathematical/physical model can make accurate assumptions on the magnitude of stresses in rather small bodied centri-symmetric woody plant stems, both recent and fossil. The model is based on Lam'e's theories on the deformation of thick walled cylinders as well as on physical experiments with technical cellular solids. Tissues with different radial widths, Young's moduli and Poisson ratios can be defined in the model.
It allows describing with very good approximation the growth stresses measured at the inner surface of the sclerenchymatous cortex cylinder of Aristolochia macrophylla, a recent lianescent plant. Encouraged by these results, we applied the theoretical model to two fossil model woody plants, the 'seed fern' species Lyginopteris oldhamia (300 Myr old) and Calamopitys sp. (340Myr old). In these fossil 'seed ferns', the model is used for recalculating the values of stresses in the inner primary cortex tissues and to verify whether the deformation observed in thin-ground sections of the very good preserved petrified stem material is only in the elastic or also within the plastic range. Thus it also allows proving or disproving the assumption that the (sometimes large) deformations observed in the cortex tissues of the two fossil plant species occurred in vivo or are an artefact due to the fossilization process and later deformation.

Keywords: growth stress, secondary growth, stress-strain relationships, elastic deformation, plastic deformation, fossil plants