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Related Concept Videos

Deformations in a Transverse Cross Section01:21

Deformations in a Transverse Cross Section

When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...
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.
Simpson's Rule II01:28

Simpson's Rule II

In warehouse roofing applications, corrugated or curved metal sheets are commonly used to improve structural strength, water drainage, and ventilation efficiency. To accurately estimate material requirements and optimize design parameters, engineers must determine the curved surface area of these sheets. Because the sheet profiles often repeat smoothly along their length, they can be effectively approximated by parabolic curves, enabling the use of numerical integration techniques for area...
Shearing Strain01:20

Shearing Strain

The shearing strain represents a cubic element's angular change when subjected to shearing stress. This type of stress can transform a cube into an oblique parallelepiped without influencing normal strains. The cubic element experiences a significant transformation when exposed solely to shearing stress. Its shape alters from a perfect cube into a rhomboid, clearly demonstrating the effect of shearing strain. The degree of this strain is considered positive if it reduces the angle between the...
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...
Deformation in a Circular Shaft01:10

Deformation in a Circular Shaft

One of the distinctive characteristics of circular shafts is their ability to maintain their cross-sectional integrity under torsion. In other words, each cross-section continues to exist as a flat, unaltered entity, simply rotating like a solid, rigid slab. To understand the distribution of shearing stress within such a shaft, consider a cylindrical section inside this circular shaft. This section has a length of L and a radius of R, with one end fixed. The radius of the cylindrical section is...

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Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes
06:34

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Published on: January 6, 2023

Scaling relation for a compact crumpled thin sheet.

Wubin Bai1, Yen-Chih Lin, Tzon-Kun Hou

  • 1Department of Physics, National Tsing Hua University, Hsinchu, Taiwan, Republic of China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
PubMed
Summary
This summary is machine-generated.

Researchers designed a high-pressure chamber to study material crumpling. Findings reveal a new scaling relation and a bundled-layer model explaining material behavior under pressure.

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Area of Science:

  • Materials Science
  • Physics
  • Soft Matter Physics

Background:

  • Understanding material behavior under extreme conditions is crucial.
  • Previous studies on material crumpling often focused on the power-law regime.

Purpose of the Study:

  • To investigate material crumpling beyond the established power-law regime.
  • To develop a comprehensive model explaining material behavior at both low and high pressures.

Main Methods:

  • Designed and utilized a novel high-pressure chamber for material deformation studies.
  • Collected and analyzed data on material volume ratio and pressure across various sheet properties.

Main Results:

  • Observed a smooth transition to a high-pressure crumpled state with <50% air and ordered domains.
  • Identified a universal scaling relation by collapsing data onto a master line using volume ratio and pressure.
  • Deduced a bundled-layer model that explains six key properties at both low and high pressures.

Conclusions:

  • The bundled-layer model successfully unifies experimental and theoretical findings for material crumpling.
  • This work provides insights into structural reorganization driving mechanical changes in soft-matter systems.
  • The developed model has implications for diverse soft-matter systems exhibiting pressure-induced structural changes.