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Related Concept Videos

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...
Plastic Deformations01:19

Plastic Deformations

Plastic deformation represents a fundamental concept in materials science, which explains the irreversible change in the shape of a material when it experiences stress beyond its elastic capability. This phenomenon is important in structural engineering, especially in designing and analyzing cantilever beams—structures that are securely fixed at one end and bear loads at the opposite end. When these beams are subjected to loads within their elastic range, they will return to their original...
Plastic Deformations01:14

Plastic Deformations

It is essential to understand how structural members behave under plastic deformation when the bending stress exceeds the material's yield strength. This state of deformation permanently alters the shape of the member, in contrast to the linear elastic behavior observed before yielding. The strain at any point in the member is expressed in terms of maximum strain. Notably, the neutral axis, which coincides with the centroid during elastic bending, shifts away from the centroid under plastic...
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.
Residual Stresses in Bending01:18

Residual Stresses in Bending

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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Related Experiment Video

Updated: Jun 25, 2026

Measurement of Chladni Mode Shapes with an Optical Lever Method
04:39

Measurement of Chladni Mode Shapes with an Optical Lever Method

Published on: June 5, 2020

Extensional edge modes in elastic plates and shells.

J Kaplunov1, A V Pichugin, V Zernov

  • 1Department of Mathematical Sciences, Brunel University, Uxbridge, United Kingdom. julius.kaplunov@brunel.ac.uk

The Journal of the Acoustical Society of America
|February 12, 2009
PubMed
Summary
This summary is machine-generated.

A newly found undamped localized mode is crucial for plane stress in elastic strips with a Poisson ratio of 0.29. The study distinguishes between low-frequency and high-frequency edge modes based on thickness variations.

Related Experiment Videos

Last Updated: Jun 25, 2026

Measurement of Chladni Mode Shapes with an Optical Lever Method
04:39

Measurement of Chladni Mode Shapes with an Optical Lever Method

Published on: June 5, 2020

Area of Science:

  • Solid Mechanics
  • Materials Science
  • Applied Mathematics

Background:

  • Localized modes at the edge of elastic structures are a recent area of research.
  • Understanding edge mode behavior is critical for predicting material failure and performance.
  • Plane stress conditions are common in thin structures and influence wave propagation.

Purpose of the Study:

  • To demonstrate the relevance of the undamped localized mode in the plane stress setting.
  • To investigate the existence criteria for this mode, specifically concerning the Poisson ratio.
  • To differentiate between low-frequency and high-frequency edge modes.

Main Methods:

  • Analytical investigation of elastic strip behavior under plane stress conditions.
  • Mathematical formulation to determine the conditions for the existence of localized modes.
  • Frequency analysis to characterize edge modes based on their variation across the thickness.

Main Results:

  • The undamped localized mode exists in the plane stress setting for a Poisson ratio of 0.29.
  • A clear distinction is made between low-frequency edge modes (low thickness variation) and high-frequency edge modes (near thickness resonance).

Conclusions:

  • The undamped localized mode is a significant phenomenon in plane stress elasticity.
  • The Poisson ratio plays a critical role in the existence of these localized edge modes.
  • Frequency characteristics effectively differentiate between types of edge modes in elastic strips.