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Related Concept Videos

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

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.
Generalized Hooke's Law01:22

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...
Members Made of Elastoplastic Material01:19

Members Made of Elastoplastic Material

The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
As the bending moment...
Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
Circular Shafts - Elastoplastic Materials01:24

Circular Shafts - Elastoplastic Materials

The study of solid circular shafts under stress shows that within the elastic limit, stress increases directly to the distance from the shaft's center. This relationship holds until the shaft reaches a critical point of stress, beyond which it begins to yield, marking the transition from elastic to plastic deformation. At this crucial juncture, the maximum torque the shaft can endure without permanent deformation is determined, signifying the limit of its elastic behavior.
As torque on the...
Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...

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High-pressure, High-temperature Deformation Experiment Using the New Generation Griggs-type Apparatus
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High-pressure, High-temperature Deformation Experiment Using the New Generation Griggs-type Apparatus

Published on: April 3, 2018

Geometry-induced rigidity in nonspherical pressurized elastic shells.

A Lazarus1, H C B Florijn, P M Reis

  • 1Elasticity, Geometry and Statistics Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

Physical Review Letters
|October 23, 2012
PubMed
Summary
This summary is machine-generated.

The local rigidity of indented elastic shells depends on curvature and pressure. This framework explains why eggshells are stiffer along their major axis, demonstrating geometry

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Related Experiment Videos

Last Updated: May 17, 2026

High-pressure, High-temperature Deformation Experiment Using the New Generation Griggs-type Apparatus
12:30

High-pressure, High-temperature Deformation Experiment Using the New Generation Griggs-type Apparatus

Published on: April 3, 2018

Ultrasonic Fatigue Testing in the Tension-Compression Mode
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Stress Distribution During Cold Compression of Rocks and Mineral Aggregates Using Synchrotron-based X-Ray Diffraction
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Stress Distribution During Cold Compression of Rocks and Mineral Aggregates Using Synchrotron-based X-Ray Diffraction

Published on: May 20, 2018

Area of Science:

  • Solid Mechanics
  • Materials Science
  • Applied Mathematics

Background:

  • Nonspherical elastic shells exhibit complex mechanical behaviors under indentation.
  • Understanding shell rigidity is crucial for applications ranging from biological structures to engineered materials.

Purpose of the Study:

  • To develop a predictive framework for the indentation of nonspherical pressurized elastic shells.
  • To rationalize the relationship between local shell rigidity, curvature, pressure differential, and material properties.

Main Methods:

  • Experimental investigation of shell indentation.
  • Combining classic spherical shell theory with recent analytical developments for pressurized shells.
  • Utilizing experimental data to guide and validate the predictive framework.

Main Results:

  • A predictive framework was established for shell indentation.
  • Demonstrated the dependence of local rigidity on geometric curvature, pressure differential, and material properties.
  • Explained the anisotropic stiffness of eggshells (stiffer along the major axis).

Conclusions:

  • Geometric factors significantly influence the mechanical response of indented shells.
  • The proposed framework is applicable across various length scales.
  • Findings provide insights into the structural mechanics of curved elastic bodies.