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Voigt and Reuss models for predicting changes in Young's modulus of dehydrating plant organs

Niklas, K.J.
Annals of botany 1992 v.70 no.4 pp. 347-355
plant physiology, mathematical models, modulus of elasticity, plant organs
A general modelling approach was used to predict the changes resulting from dehydration in the Young's modulus (E) of a terete organ with a simple anatomy (e.g. hypodermis of thick-walled tissue surrounding a parenchymatous core of ground tissue). Two general anatomical models were investigated: (1) an 'apoplast model' in which each cross section through the organ was considered as a composite elastic material consisting of a solid (cell wall) and liquid (protoplasm) phase; and (2) a 'core-rind model' in which the organ consisted of a thick-walled and a thin-walled tissue. For each of these two anatomical models, two composite material models were considered, i.e. a Voigt or Reuss equation was used to predict the changes in E attending dehydration. The predictions from the variants of the general model were evaluated on the basis of observed changes in E as cylindrical segments of the pseudopetioles of Spathiphyllum were allowed to desiccate at room temperature. Statistical comparisons between predicted and observed values of E revealed that one of the simple variants of the model, the 'Voigt apoplast model', was the most successful in predicting the observed trend seen in the changes in E. However, when the Voigt and Reuss apoplast models were combined, the 'hybrid' model provided estimates of changes in E that were statistically indistinguishable from those observed. Based on the hybrid model, it was estimated that roughly 76.7% of the tissues with a representative Spathiphyllum pseudopetiole operated according to a Voigt apoplast model.