Elasto-plastic material model of green beech wood

Abstract

Physically modelling the mechanical response of a tree by numerical simulation depends on having accurate data on the mechanical properties of green hardwood. Lacking such data, we developed and validated an orthotropic elasto-plastic (E-P) material model, based on the results of experiments performed on European beech (Fagus sylvatica L.) green wood, capable of including both the non-linearity and orthotropic properties of the material. We selected 655 clear samples with the special orthotropic structure of annual rings. All samples were prepared immediately after felling; their moisture content (MC) was 80% on average. The mechanical responses in normal directions and shear are represented by bi-linear stress-strain curves. The E-P model was validated by comparing the force-deflection response of three-point bending of green wood samples in a finite-element method (FEM) simulation (the average relative error was 4.6% for point-wise and 1.7% for integral-wise comparison). The output of this work was a consistent set of material constants for the E-P material model that is now available for the structural analysis of beech wood with MC above to fibre saturation point (FSP), especially green wood, subjected to relatively high loads (such that a plastic deformation appears) and that can very well predict a non-linear response above the proportional limits.