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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...
Flexural Stress01:16

Flexural Stress

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.
Hooke's Law states that within the material's elastic limits, stress is directly proportional to strain. In a member experiencing a bending moment, the strain at any point is relative to its distance...
Bending of Curved Members - Strain Analysis01:14

Bending of Curved Members - Strain Analysis

The mechanics of deformation in curved members, such as beams or arches, under bending moments, involve complex responses. When such a member, symmetric about the y-axis and shaped like a segment of a circle centered at point C, is subjected to equal and opposite forces, its curvature and surface lengths change significantly. This alteration results in the shift of the curvature's center from C to C', indicating a tighter curve.
The important part of bending analysis for such a member is the...
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...
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...
Residual Stresses01:26

Residual Stresses

Residual stresses reside in a structure even after removing the original stress inducer. This phenomenon often arises from varied plastic deformations across different parts of a structure. Consider a rod stretched beyond its yield point. It will not regain its original length due to permanent deformation. Even after load removal, the rod does not entirely lose stress because of uneven plastic deformations, resulting in residual stresses. The computation of these stresses in structures is...

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Related Experiment Video

Updated: May 18, 2026

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics
14:14

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Published on: April 16, 2017

Spontaneous wrinkle branching by gradient stiffness.

Yong Ni1, Dong Yang, Linghui He

  • 1Department of Modern Mechanics, CAS Key Laboratory of Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China. yni@ustc.edu.cn

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2012
PubMed
Summary
This summary is machine-generated.

Coherency loss explains hierarchical wrinkling patterns in compressed films. Controlling stiffness gradients allows for predictable, branched wrinkle formation, guiding future hierarchical wrinkling designs.

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Controlled Strain of 3D Hydrogels under Live Microscopy Imaging
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Controlled Strain of 3D Hydrogels under Live Microscopy Imaging

Published on: December 4, 2020

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Last Updated: May 18, 2026

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics
14:14

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Published on: April 16, 2017

Controlled Strain of 3D Hydrogels under Live Microscopy Imaging
07:41

Controlled Strain of 3D Hydrogels under Live Microscopy Imaging

Published on: December 4, 2020

Area of Science:

  • Materials Science
  • Mechanics of Materials
  • Surface Engineering

Background:

  • Hierarchical wrinkling patterns are observed in compressed thin films on substrates.
  • Understanding the formation mechanisms of these complex patterns is crucial for material design.

Purpose of the Study:

  • To introduce the concept of coherency loss to explain wrinkle branching.
  • To provide a model and simulation for predicting hierarchical wrinkling patterns.
  • To offer guidelines for controlling wrinkle formation through stiffness gradient patterning.

Main Methods:

  • Development of a theoretical model based on coherency loss.
  • Numerical simulations using the Föppl-von Kármán plate theory on compliant substrates.
  • Analysis of the relationship between stiffness inhomogeneity and wrinkle branching.

Main Results:

  • Wrinkle branching occurs when the stiffness inhomogeneity zone exceeds the coherency persistent length.
  • The size and amplitude of stiffness inhomogeneities directly influence the formation of branched wrinkles.
  • Simulations show excellent agreement with experimental observations of branched wrinkles.

Conclusions:

  • Coherency loss is a key mechanism driving hierarchical wrinkling.
  • Patterning stiffness gradients offers a method for controlling complex wrinkle formations.
  • This research provides a framework for designing and fabricating hierarchical wrinkled surfaces.