Investigating Biomechanical Properties of A. tortilis as Related to their Habitat: A novel approach to characterize bending

The biomechanical properties of Acacia tortilis were investigated considering its habitat (wild vs. nursery). The plant materials were collected from partially urbanized area in Doha city and from Qatar Foundation Nursery. The results show that Acacia grown in field are more flexible than those grown in nursery. Young’s Modulus of Elasticity was found to be 191 MPa and 617 MPa and the Flexural Modulus was found to be 49 MPa and 575 MPa and the breaking force was found to be 210 and 550 N for nursery and field Acacia, respectively. The deflection angle was measured using sensitive flex sensors connected to Arduino boards and was found to be higher for field Acacia (50∘). Image processing techniques were used to mathematically describe the branch motion versus time diagrams. The plant part being investigated was covered with red tape and videotaped while subjected to a force causing it to bend. The stem was divided into 745 successive points and the change in their position with time taken frame by frame was converted into a change in position expressed through mathematical parameters. The bending movement of the branch was found to follow a power function H = (4001 − e0.06m). Highlight Field grown Acacia have higher values of Young’s and Flexural Moduli than nursery grown ones thus conferring them more elasticity and flexibility.

inertia are three important parameters that are used to describe the mechanical 1 behavior of a plant. Young's modulus of elasticity is used to characterize the overall 2 bending behavior of a stem regardless of its size and shape while flexural stiffness 3 characterizes the flexibility of the stem section. The area moment of inertia rather 4 than the diameter or the length is used to describe the geometry and the size of the

2-3 Three Point Bending Test
1 Three-point bending tests were performed using a bench-top testing machine 2 provided with two electronic sensors for measuring and recording the load force and To apply the force on the sample through the plunger, the crank was turned slowly at 5 a rate between 10 and 20 mm/minute. The materials testing machine was then 6 connected to the PASCO interface for data collection and recording. The force vs. 7 position graph was constructed. (ΔX, mm) was constructed and the slope was measured directly. The slope (F/ Δ X 1 3 ratio) reflects the effective stiffness of the measured plant part. According to the 1 4 elastic theory, the material's stiffness depends on its length, shape and the cross- (E b ) for the tested plant part was calculated as follows: where "I" is the area moment of inertia for the sample.

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Solving for E b , yields The area moment of inertia depends on the shape of the cross section of the  The value (EI) is an indicator for the plant stiffness and important for stem length and 2 3 corresponding plant height (Gere and Timoshenko, 1999). The plant sample ( fig. 6) was firmly fixed in the materials testing machine from its 2 7 two ends using two adapters that are connected to the load cell from one side and to machine was turned slowly to raise the cross-head to which the sample is attached 3 0 at a rate between 10 and 20 mm/minute and pulling the stem section apart while 3 1 both the load and the extension are being recorded until the stem breaks or slips.

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The PASCO Sparkvue software was used to record the force vs displacement graph 1 from which the breaking force was determined and the stress vs. strain graph 2 constructed. Several different materials mechanical properties including Young's 3 modulus, tensile strength, resilience modulus, ductility and yield strength could be 4 calculated from the data collected. However, in this study only Young's modulus 5 was calculated due to the slippage of the specimen.  first exhibit some temporary elongation within the elastic region then it will exhibit 1 6 plastic deformation after which if the sample is pulled far enough it will break into two 1 7 pieces. The maximum load that the sample can sustain is referred to as tensile suddenly buckles. At that point, the applied force is called the critical force (F crit ). When a tree stem is subjected to a wind force, it bends with an angle called the 5 deflection angle (α). The deflection angle represents the flexibility of the whole stem.

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It shows the bending capability of the stem section. Traditionally, the deflection angle the branch tip to reach or to touch the ground was not always a possible task as the 1 branch length in many cases were not enough to reach the ground and in other 2 cases it was broken before it could touch the ground. Moreover, generating the 3 equation and the graph representing this kind of movements require enormous 4 amount of data to ensure the accuracy and guarantee that the equation would give 5 real solutions. However, considering the nature of the problem, we assumed that the 6 equation would follow a polynomial function of n degree: Where X represents the weights hanged from the tip and F(x) represents the height 8 of the branch's tip from the ground.

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The equation might also be represented by a power function following the general (between 0 and 1).

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In this study, image processing technique (IPT) was used to mathematically describe 1 7 the actual bending movement of the tree. The continuous bending movement of 1 8 Acacia resulting from wind forces was simulated by tying a rope to the tip of Acacia branch under study and then stretching the rope using known forces.

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The movement of Acacia was tracked and videotaped. Python + Opencv were used 2 1 to plot the branch motion versus time diagrams and therefore to describe the 2 2 maximum forces the branch can tolerate. To do so, the plant part being investigated 2 3 (branch) was covered with red tape and videotaped while subjected to a force 2 4 causing it to bend ( fig. 11).

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The video was then filtered and processed using special image processing software 2 6 to highlight the bending branch. The color was converted to HSV color, and a red 2 7 color filter was applied using the site 1 1 opencv/). After that binary image was produced, the red pix was changed to white 1 pix and the rest of pixs changed to black. Then binary erosion and dilation functions 2 were used to remove the small noise. The bending movement of the branch was 3 then linearized and described mathematically using the site (https://scikit-4 learn.org/stable/auto_examples/linear_modal/plot_ols.html). force (F crit ) after which the sample breaks.
1 8 Table 2 shows the calculations for the flexural modulus for some of the samples in 1 9 the two Acacia groups.  T  h  e  s  t  u  d  y  a  r  e  a  s  h  o  w  i  n  g  t  h  e  l  o  c  a  t  i  o  n  o  f  s  a  m  p  l  e  s  c  o  l  l  e  c  t  i  o  n  p  o  i  n  t  e  d  a  t  i  n  r  e  d  .  3 .   The right upper panel shows the branch highlighted. The left panels show the branch after the color was converted to HSV and a red filter was applied to produce a binary image. The red pix was changed to white and the rest of pixs were changed to black. To watch the video, follow the link (https://youtu.be/TSjYAzsahTk). (colour in print)