Multi-scale simulation of plant stem reinforcement by brachysclereids: A case study in apple fruit peduncles.

Sclereid formation in addition to or in gaps of fragmented fibre rings is common in dicotyledonous plant stems. Whether this sclereid formation is force-triggered remains open so far. In fruit peduncles of several Malus species as modified plant stems, for example, the persistent fibre ring is displaced to the centre by formation of cortex parenchyma during growth. Parenchyma cells subsequently differentiate into an additional layer of brachysclereids, previously interpreted as an adaptation to continuously rising fruit loads. The present study pursues a multi-scale numerical modelling approach, to verify the important effect for different cellular architectures in both sclerenchyma categories on the stiffness of these tissues and the entire peduncle. First, different material properties are simulated analogue to plant tissues on the basis of three cell types. A regular three-dimensional and a random Voronoi microstructure combined with various mechanical cell wall parameters are applied. Using homogenisation simulations based on HILL's principle, numerical calculations predict a lower effective homogenised tissue stiffness of isodiametric brachysclereids compared to those of fibres, confirming experimentally obtained data from Malus fruit peduncles. Furthermore, a curved peduncle model with a complex arrangement of different material layers is generated. Diverse material sets are tested under three representative loadings, using an adaptive diffuse domain approach (AMDiS). The model explains the function of sclereids as considerable contributors to the stiffness against bending and tensile deformations, as well as torsion, especially in consequence of superimposed load conditions in the case of a curved plant stem.