COMPLAS 2023

A Material Model for Nonlinear Anisotropic Viscoelastic Behavior of Plant Tissues of Stephania japonica

  • Macek, Domen (RWTH Aachen University)
  • Holthusen, Hagen (RWTH Aachen University)
  • Rjosk, Annabell (Technische Universität Dresden)
  • Ritzert, Stephan (RWTH Aachen University)
  • Reese, Stefanie (RWTH Aachen University)

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Plant leaves are exposed to a variety of environmental stresses. As a result, plants have evolved a wide variety of leaf shapes. The mechanical properties of leaves are determined by the internal composition and organization of different tissues. Not much research efforts have been devoted to investigate mechanical properties of the peltate leaf shape, which is characterized by the attachment of the leaf stalk to the underside of the leaf blade. The leaf components of Stephania japonica (Menispermaceae) show a complex fiber organization, which makes this plant particularly interesting for further analysis. It has been shown that tissues of such leaves have an anisotropic mechanical properties and behave in a viscoelastic manner in the finite strain range [1]. To model such behavior a continuum mechanical transversely isotropic viscoelastic material model at finite deformations is presented. The model is obtained by postulating a particular Helmholtz free energy, which is additively split into an elastic and an inelastic part. Both parts of the energy depend on the structural tensors to account for the transversely isotropic material behavior. The evolution equations are chosen in a physically meaningful way that always satisfies the second law of thermodynamics. To take advantage of the algorithmic differentiation in the numerical implementation, the model is formulated in the co-rotated framework [2]. The proposed model is calibrated against experimental data and material parameters are identified. Furthermore, several examples of finite element simulations are presented to illustrate the ability of the model to adequately reproduce the anisotropic viscoelastic behavior of plant tissues. REFERENCES [1] Macek D, Holthusen H, Rjosk A, Ritzert S, Lautenschläger T, Neinhuis C, Simon J.W., Reese S. Mechanical investigations of the peltate leaf of Stephania japonica (Menisper- maceae): Experiments and a continuum mechanical material model. Frontiers in Plant Science, Vol. 13, 994320, 2023. [2] Holthusen H., Rothkranz C., Lamm L.A., Brepols T., Reese S. Inelastic material formula- tions based on a co-rotated intermediate configuration–Application to bioengineered tissues. Journal of the mechanics and physics of solids, Vol. 172, 105174, 2023.