Mechanical modeling of the petiole-lamina transition zone of peltate leaves.

Plant leaves have to deal with various environmental influences. While the mechanical properties of petiole and lamina are generally well studied, only few studies focused on the properties of the transition zone joining petiole and lamina. Especially in peltate leaves, characterised by the attachment of the petiole to the abaxial side of the lamina, the 3D leaf architecture imposes specific mechanical stresses on the petiole and petiole-lamina transition zone. Several principles of internal anatomical organisation have been identified. Since the mechanical characterisation of the transition zone by direct measurements is difficult, we explored the mechanical properties and load-bearing mechanisms by finite-element simulations. We simulate the petiole-lamina transition zone with five different fibre models that were abstracted from CT data. For comparison, three different load cases were defined and tested in the simulation. In the proposed model, the fibres are represented in a smeared sense, where we considered transverse isotropic behavior in elements containing fibres. In a pre-processing step, we determined the fibre content, direction, and dispersion and fed them into our model. The simulations show that initially, matrix and fibres carry the load together. After relaxation of the stresses in the matrix, the fibres carry most of the load. Load dissipation and stiffness differ according to fibre arrangement and depend, among other things, on orientation and cross-linking of the fibres and fibre amount. Even though the presented method is a simplified approach, it is able to show the different load-bearing capacities of the presented fibre arrangements. STATEMENT OF SIGNIFICANCE: In plant leaves, the petiole-lamina transition zone is an important structural element facilitating water and nutrient transport, as well as load dissipation from the lamina into the petiole. Especially in peltate leaves, the 3D leaf architecture imposes specific mechanical stresses on the petiole-lamina transition zone. This study aims at investigating its mechanical behavior using finite-element simulations. The proposed continuum mechanical anisotropic viscoelastic material model is able to simulate the transition zone under different loads while also considering different fibre arrangements. The simulations highlight the load-bearing mechanisms of different fibre organisations, show the mechanical significance of the petiole-lamina transition zone and can be used in the design of a future biomimetic junction in construction.

Mechanical investigations of the peltate leaf of Stephania japonica (Menispermaceae): Experiments and a continuum mechanical material model.

Stephania japonica is a slender climbing plant with peltate, triangular-ovate leaves. Not many research efforts have been devoted to investigate the anatomy and the mechanical properties of this type of leaf shape. In this study, displacement driven tensile tests with three cycles on different displacement levels are performed on petioles, venation and intercostal areas of the Stephania japonica leaves. Furthermore, compression tests in longitudinal direction are performed on petioles. The mechanical experiments are combined with light microscopy and X-ray tomography. The experiments show, that these plant organs and tissues behave in the finite strain range in a viscoelastic manner. Based on the results of the light microscopy and X-ray tomography, the plant tissue can be considered as a matrix material reinforced by fibers. Therefore, a continuum mechanical anisotropic viscoelastic material model at finite deformations is proposed to model such behavior. The anisotropy is specified as the so-called transverse isotropy, where the behavior in the plane perpendicular to the fibers is assumed to be isotropic. The model is obtained by postulating a Helmholtz free energy, which is split additively into an elastic and an inelastic part. Both parts of the energy depend on structural tensors to account for the transversely isotropic material behavior. The evolution equations for the internal variables, e.g. inelastic deformations, are chosen in a physically meaningful way that always fulfills the second law of thermodynamics. The proposed model is calibrated against experimental data, and the material parameters are identified. The model can be used for finite element simulations of this type of leaf shape, which is left open for the future work.