A nonlinear finite viscoelastic formulation relative to the viscous intermediate configuration applied to plants

Abstract In the contribution at hand, a new formulation for finite strain viscosity relative to the viscous intermediate configuration is presented. The evolution of the viscous deformations is based upon a new numerical approach, which allows for a consistent consideration of anisotropic finite strain viscoelasticity, according to the authors knowledge. A standard Maxwell model is used to describe viscous behaviour at finite deformations. Furthermore, the orthotropic Yeoh material model is extended to include a distinction between behaviour under tensile and compression loading. The proposed formulation is validated, and parameters of the model are identified by material tests on Sorghum bicolor plants. Subsequently, numerical examples are shown to demonstrate the capabilities of the model. In general, the proposed Yeoh material formulation is shown to accurately represent the inability of fibres to carry compression loading. Furthermore, the viscoelastic approach, developed relative to the viscous intermediate configuration, is demonstrated to be capable of producing plausible results. Additionally, the mechanical behaviour of Sorghum bicolor plants is simulated using the introduced formulation. The results show that the contribution at hand describes a novel methodology to simulate the viscoelastic behaviour of plant materials reliably.