Calculation of Structural Youngs Modulus

The bending test results are plotted as the deflection (in millimeters) on the y-axis against the force applied (in Newtons) on the x-axis. The bending test was successful if the value of r2 for the force-deflection curve is greater than 0.98 (i.e., if the entire measurement is in the linear elastic range), the specimen has not moved or slipped during the test accidentally, and the experiment has remained within the elastic range. Immediately after the experiment, the diameter of the stem segment is measured in three to six positions along its length in the direction of the force applied and perpendicular to it. The mean axial second moment of area (I) (in mm4) of the stem is then calculated from these measurements where the stem cross section is approximated as an ellipse:

where rj is the radial thickness of the stem in the direction of the applied force and r2 is the radial thickness in the perpendicular direction.

In three-point bending, the flexural stiffness (EI) (Nmm2) of the tested stem is calculated via:

where I is the distance (mm) between the two supports (Figure 2b) and b is the slope of the force-deflection curve (deflection/force) (mm/N).

In four-point bending, the flexural stiffness (EI) (Nmm2) of the tested stem is calculated via:

where I is the distance between the two internal supports, a is the distance between the outside pannier and the internal support (Figure 2c), and b is again the slope of the force-deflection curve (mm/N).

The structural Young's modulus of the stem (Estr) (MNm-2) is calculated via:

Estr = EIII

We use the term "structural Young's modulus" (Estr) as the parameter to describe a structure consisting of different tissues, i.e., a plant stem [7,15].

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