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Related Concept Videos

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...
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...
Euler's Formula for Pin-Ended Columns01:21

Euler's Formula for Pin-Ended Columns

In structural engineering, the stability of columns under compressive axial loads is a critical consideration, described as buckling. A typical example involves a column PQ, which is pin-connected at both ends and subjected to a centric axial load F applied at one end, with a reaction force of F' = -F at the other end. Here, it is crucial to understand that when an applied load exceeds the critical load, buckling occurs as the system becomes unstable.
To calculate the critical load, envision...
Plastic Behavior01:21

Plastic Behavior

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 reloaded.
General Case of Eccentric Axial Loading01:12

General Case of Eccentric Axial Loading

Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from symmetrical bending, which are essential for designing structures to withstand different loading conditions.
Consider a member subjected to equal and opposite forces that are applied along a line that does not coincide with the member's neutral axis. In unsymmetrical bending,...
Unsymmetric Bending01:18

Unsymmetric Bending

Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from those in symmetrical bending, and are essential for designing structures to withstand different loading conditions. In unsymmetrical bending, the neutral axis—where stress is zero—does not necessarily align with the geometric axes of the cross-section. The orientation of the...

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Elastocapillary instability under partial wetting conditions: bending versus buckling.

Bruno Andreotti1, Antonin Marchand, Siddhartha Das

  • 1Physique et Mécanique des Milieux Hétérogènes, UMR 7636 ESPCI -CNRS, Université Paris-Diderot, 10 rue Vauquelin, F-75005 Paris, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2012
PubMed
Summary
This summary is machine-generated.

Flexible plates in liquid baths exhibit elastocapillary instability due to two bending mechanisms. Capillary forces cause buckling for certain contact angles and a novel torque-induced bending for all positive contact angles.

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Area of Science:

  • Physics
  • Materials Science
  • Fluid Dynamics

Background:

  • Elastocapillary phenomena involve the interplay between elastic deformation and surface tension.
  • Understanding instabilities in flexible structures submerged in liquids is crucial for various applications.

Purpose of the Study:

  • To theoretically analyze the elastocapillary instability of a flexible plate in a liquid bath.
  • To identify and differentiate the mechanisms causing plate bending under partial wetting conditions.

Main Methods:

  • Theoretical analysis of a flexible plate submerged in a liquid.
  • Investigation of capillary forces acting tangentially and normally to the plate surface.
  • Analytical determination of instability onset and bifurcation scenarios.

Main Results:

  • Two distinct destabilizing mechanisms identified: classical buckling and a novel torque-induced bending.
  • Buckling instability occurs for contact angles greater than π/2.
  • Torque-induced bending occurs for any positive contact angle (θ(e) > 0).
  • Two dimensionless parameters governing elastocapillary stability were identified.

Conclusions:

  • The study elucidates the complex elastocapillary behavior of flexible plates in partially wetting liquids.
  • Identified mechanisms provide a framework for predicting and controlling plate deformation.
  • Results are relevant for experimental conditions and material design.