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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.

Hooke's Law

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Hooke's law, a pivotal principle in material science, establishes that the strain a material undergoes is directly proportional to the applied stress, defined by a factor called the modulus of elasticity or Young's modulus.

Residual Stresses in Bending

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In the study of elastoplastic members subjected to bending moments, understanding the loading and unloading phases is crucial for assessing material behavior and structural integrity. During the loading phase, as the bending moment increases, the material initially responds elastically, adhering to Hooke's Law, where stress is directly proportional to strain. When the load exceeds the yield strength, plastic deformation occurs, resulting in permanent strain and deformation that remains even...

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When analyzing bending in symmetric members, it's crucial to understand how stresses distribute when subjected to bending moments. This stress distribution is effectively described by applying fundamental mechanics and material science principles, particularly Hooke's Law for elastic materials.
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To grasp the intricacy of real-world conditions where multiple loads are applied simultaneously to a structure, one might visualize a section passing through a specific point within a body, aligned parallel to the xy plane. This section is subjected to various forces, including original loads, normal forces, and shearing forces.
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Plastic Behavior

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A material's elastic behavior is characterized by the disappearance of stress once the load is removed, allowing the material to return to its original state. However, when stress surpasses the yield point, yielding commences, marking the onset of plastic deformation or permanent set. This change from elastic to plastic behavior is influenced by the peak stress value and the duration before the load is removed. An intriguing observation occurs when a specimen is loaded, unloaded, and...

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Related Experiment Video

Updated: Apr 25, 2026

Direct Force Measurements of Subcellular Mechanics in Confinement using Optical Tweezers

Direct Force Measurements of Subcellular Mechanics in Confinement using Optical Tweezers

Published on: August 31, 2021

Stiffness versus prestress relationship at subcellular length scale.

Elizabeth P Canović¹, D Thomas Seidl², Paul E Barbone²

¹Department of Biomedical Engineering, Boston University, Boston MA, USA.

Journal of Biomechanics

|August 21, 2014

Summary

Intracellular mechanical properties are poorly understood. This study reveals that cell prestress is linearly correlated with shear modulus, suggesting it unifies material properties across biological scales.

Keywords:

Cell mechanics Imaging Prestress Stiffness Traction forces

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Last Updated: Apr 25, 2026

Direct Force Measurements of Subcellular Mechanics in Confinement using Optical Tweezers

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Published on: August 31, 2021

Micropipette Aspiration of Substrate-attached Cells to Estimate Cell Stiffness

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Published on: September 27, 2012

A Novel Stretching Platform for Applications in Cell and Tissue Mechanobiology

A Novel Stretching Platform for Applications in Cell and Tissue Mechanobiology

Published on: June 3, 2014

Area of Science:

Biophysics
Cell Biology
Mechanobiology

Background:

Cellular mechanical properties are vital for cell function but vary locally and are poorly understood.
Existing research lacks detailed characterization of intracellular mechanical variations.

Purpose of the Study:

To investigate the relationship between intracellular shear modulus and prestress.
To determine if prestress acts as a unifying factor in cell mechanics across different length scales.

Main Methods:

Utilized data from a previous biomechanical imaging study.
Analyzed relationships between subcellular shear modulus and prestress.

Main Results:

Found positive linear correlations between subcellular shear modulus and prestress.
Observed consistency with previously reported behaviors at whole cell and tissue levels.

Conclusions:

Cellular prestress is a significant factor influencing mechanical properties.
Prestress may act as a unifying determinant of material properties in living matter across multiple length scales.