PLANT BIOPHYSICS - Y. I. Posudin - 2004

I. PHYSICAL PROPERTIES OF PLANT CELLS AND TISSUES

1. MECHANICAL PROPERTIES

1.2. ELASTIC PARAMETERS

The mechanical properties of plants and plant products are governed by the interactions between their constituent atoms and molecules, manifesting as resistance to external forces. The mechanical properties of plant objects are characterized by the relationship between stress—a specific state arising under the Influence of External forces—and mechanical strain, which is A change in the relative positions of particles within a material medium. This leads to an alteration in the shape and dimensions of the body or its parts, thereby changing the interparticle interaction forces. A strain is termed elastic if it appears and disappears simultaneously with the load and is not accompanied by energy dissipation. Plastic strain refers to the deformation that remains after the load is removed and is accompanied by energy dissipation. If the strain does not disappear completely upon load removal, it is called elasto-plastic; if the magnitude of the strain is clearly time-dependent yet reversible, it is designated as viscoelastic. Strain induces an elastic force within the deformed body.

Hooke's law for uniaxial tension (compression): the elastic force F_пр arising from the deformation of a body is proportional to its elongation x:

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where k is the elastic constant, which depends on the dimensions and material of the body.

Hooke's law can also be formulated and expressed as follows: for small, purely elastic deformations, the normal stress σ is proportional to the relative elongation ε:

where σ is the normal mechanical stress (Н·м²), defined as The ratio of the elastic force modulus Е_пр to the cross-sectional area S of the body:

where is the relative elongation of the body, and E is Young's modulus. Young's modulus characterizes the Elastic properties of a substance; it is defined as the stress required to produce a unit relative deformation.

The dependence of mechanical stress σ on relative elongation is called the stress-strain curve (Fig. 1.1). Several characteristic regions and points can be identified here: point A is termed the proportional limit, corresponding to the maximum stress σ up to which Hooke's law still holds; point B is the elastic limit—the stress at which the deformation remains purely elastic; BC is the yield plateau, where deformation occurs without an increase in stress; point C is the yield point; point D, corresponding to the maximum stress σ_макс that the body can withstand before failure, is called the ultimate tensile strength; and point E corresponds to the rupture of the body, which occurs at a stress lower than σ_mаx.

Fig. 1.1. Stress-strain curve—a graphical representation of the dependence of mechanical stress σ on relative elongation ε (details in the text).

The application of a compression (or tension) force uniformly distributed across the entire surface of a body induces volumetric (hydrostatic) compression (or tension) deformation. The relative decrease (increase) in volume ΔV/V in this case is determined by Hooke's law: for small elastic deformations, the normal stress σ is proportional to the relative volume change ΔV/V caused by this stress σ:

where σ is the normal mechanical stress; is the relative decrease (increase) in the volume of the body, and K is the bulk modulus (incompressibility modulus). The bulk modulus characterizes the elastic properties of a substance; it is defined by the stress that causes a unit relative decrease (increase) in the volume of the body.

The relative longitudinal compression (tension) of a body is accompanied by its relative transverse expansion (contraction) ΔD/D, where D is the transverse dimension of the body, and ΔD is The change in the transverse dimension. The ratio of the relative transverse expansion (contraction) ΔD/D to the relative longitudinal expansion (contraction) ΔL/L is called Poisson's ratio μ:

For instance, Poisson's ratio ranges from 0.21 to 0.34 for apple flesh, and from 0.45 to 0.49 for potato.