PLANT BIOPHYSICS - Y. I. Posudin - 2004

I. PHYSICAL PROPERTIES OF PLANT CELLS AND TISSUES

1. MECHANICAL PROPERTIES

1.5. ELASTIC PROPERTIES OF THE PLANT STEM

Bending deformation. Under the action of an external force F (such as wind), a plant stem bends. This force causes certain layers to stretch while others are compressed (Fig. 1.6). Elastic forces arise within the stem, creating a restoring moment that counteracts the moment of force F. It is evident that the outer layers of the stem play the primary role in generating this counteracting moment, whereas the central layers play no significant part. Consequently, removing the central part of the stem does not alter its bending resistance. Mathematical calculations indicate that maximum bending resistance is exhibited by hollow tubes in which The ratio of inner to outer diameter is 8:11. This exact ratio is found in the stems of most plants. A prime example of a plant lacking a central stem core is bamboo. This plant serves as an essential source of raw Materials, food, and building materials for 2.2 billion people worldwide, with certain bamboo species growing at rates of up to one meter per day. The Young's modulus of bamboo tissue is 2 · 10¹⁰ N·m^-2, meaning that bamboo is more elastic than a steel rod, which has a Young's modulus of 2.1 · 10¹¹ N·m^-2. At the same time, the mass-to-volume ratio of bamboo is 600 kg·m^-3, compared to 7800 kg·m^-3 for steel.

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Fig. 1.6. Diagram showing The Effect of an external force F on rod deformation, resulting in the generation of a counteracting moment M.

Measurement of elastic parameters of the plant stem. It is well known that plants can adapt to mechanical environmental factors such as wind. Many plants limit their height and increase stem diameter in response to constant mechanical stimulation [Nobel, 1981]. This adaptive process is accompanied by corresponding Changes in the Elastic properties of the stem. A diagram of the experimental setup used to investigate how the elastic properties of xylem (the vascular tissue responsible for the primary transport of Water and minerals in plants) depend on mechanical stimulation is shown in Fig. 1.7 [Hepworth, Vincent, 1999]. The plants were divided into four groups: one served as a control, while the others were subjected to airflow of varying intensity twenty times a day for 2 minutes over an 8-week period. The airflow caused the stems In the second group to deflect by 3.5 cm, the third group by 10.5 cm, and the fourth group by 17 cm (deflections were measured at a height of 15 cm from the soil surface). The bending resistance of the stem was evaluated using the flexural rigidity index:

where F is the applied force, h is the plant height, and σ is the mechanical stress.

Fig. 1.7. Diagram of the device for studying the dependence of xylem elastic properties on mechanical stimuli [Hepworth, Vincent, 1999].

Research results on the plant (Nicotiana tabacum "Samsun") indicate that the plant responds to continuous mechanical stimuli by increasing the thickness of the cylinder formed by the xylem tissue.

Review Questions

1. What is material density and what units is it measured in?

2. State Hooke's law.

3. What is mechanical stress and what units is it measured in?

4. What is deformation? What are the MAIN TYPES OF deformation?

5. What does Young's modulus characterize?

6. What is Poisson's ratio?

7. What types of stresses occur in a plant Cell?

8. What forces arise within a plant stem?