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Generalized Hooke's Law

Generalized Hooke's Law

The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.

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Hyperelastic models for hydration of cellular tissue.

R G M van der Sman¹

¹Agrotechnology and Food Sciences Group, Wageningen University & Research, the Netherlands. ruud.vandersman@wur.nl.

|August 19, 2015

Summary

This study models plant cell walls as elastic shells to understand hydration. Hyperelastic models reveal how turgor pressure influences cell volume and water holding capacity in plant foods.

Area of Science:

Biophysics
Materials Science
Plant Biology

Background:

Cells with cell walls (bacteria, plants, fungi) are modeled as pressurized elastic shells.
The cell vacuole and membrane are represented by a pressurized internal cavity, and the cell wall by a hydrated elastic shell.

Purpose of the Study:

To develop hyperelastic models for swelling elastic shells under internal pressurization.
To elucidate the contribution of cell membrane integrity and turgor pressure to the water holding capacity of plant foods.

Main Methods:

Development of hyperelastic models for swelling elastic shells.
Application of Cloizeaux's scaling law for osmotic pressure to derive analytical expressions for cell volume vs. turgor pressure.
Simulation of shell swelling with microfibril-embedded cell walls to model strain hardening and anisotropic expansion.

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Main Results:

Approximate analytical expressions for cell volume versus turgor pressure were derived, showing good agreement with numerical solutions.
Simulations demonstrated strain hardening and anisotropic cell expansion in shells embedded with microfibrils.

Conclusions:

The study provides insights into the mechanical behavior of hydrated cell walls and their role in water retention.
Findings have implications for understanding food hydration, plant science, and the physics of responsive gels.