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Related Concept Videos

Thin-Walled Hollow Shafts01:15

Thin-Walled Hollow Shafts

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In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution...
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Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

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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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Transformation of Plane Stress01:18

Transformation of Plane Stress

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Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's...
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Deformations in a Transverse Cross Section01:21

Deformations in a Transverse Cross Section

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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...
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Unsymmetric Loading of Thin-Walled Members01:23

Unsymmetric Loading of Thin-Walled Members

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Thin-walled members with non-symmetrical cross-sections are vital to engineering structures, offering material efficiency and structural integrity. However, unsymmetrical loading on these members leads to complex stress distributions, resulting in simultaneous bending and twisting can cause deformation or structural failure. The interaction between bending and twisting requires detailed analysis to ensure structural resilience.
The concept of the shear center is crucial in countering the...
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Plastic Behavior01:21

Plastic Behavior

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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...
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Effect of initial geometry on crumpled thin shells.

Chang-Yi Lyu1, Hong-Yue Huang1, Hung-Chieh Fan Chiang1

  • 1National Tsing Hua University, Department of Physics, Hsinchu 30013, Taiwan, Republic of China.

Physical Review. E
|February 7, 2025
PubMed
Summary
This summary is machine-generated.

Crumpling of 3D objects differs from flat sheets due to corners. These geometric features, not just material properties, alter mechanical behavior, replacing power-law relationships with buckling transitions in hollow structures.

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Area of Science:

  • * Mechanics of Materials
  • * Statistical Physics
  • * Geometric Structures

Background:

  • * Crumpled sheets exhibit distinct mechanical and energetic properties, including power-law relationships.
  • * Previous studies primarily focused on flat sheets, limiting applicability to 3D objects.
  • * Daily objects like milk cartons and cans demonstrate varied crumpling behaviors.

Purpose of the Study:

  • * To investigate the crumpling properties of 3D hollow objects, specifically cubical boxes.
  • * To compare the crumpling behavior of 3D objects with that of flat sheets.
  • * To identify key geometric features influencing crumpling deviations.

Main Methods:

  • * Employed molecular dynamics simulations.
  • * Conducted experimental investigations.
  • * Systematically analyzed the contributions of sides, corners, and boundaries.

Main Results:

  • * Identified corners as the primary cause of deviations from flat sheet crumpling properties.
  • * Observed the absence of the typical power-law relationship, replaced by a buckling transition.
  • * Demonstrated that various corner types (sharp, curved, rounded) significantly impact crumpling.

Conclusions:

  • * Geometric features, particularly corners, are crucial for understanding the crumpling of 3D objects.
  • * The mechanical properties of 3D hollow objects deviate from those of flat sheets due to corner effects.
  • * Understanding these deviations is essential for analyzing everyday objects and phenomena.