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Cracks in Tension-Field Elastic Sheets.

O Mahmood1, B Audoly1,2, S Roux3

  • 1Sorbonne Universités, UPMC Univ Paris 06, CNRS, Institut Jean Le Rond d'Alembert, 4 place Jussieu, 75005 Paris, France.

Physical Review Letters
|October 20, 2018
PubMed
Summary
This summary is machine-generated.

Wrinkling in thin elastic sheets causes them to soften significantly under compression. Numerical simulations reveal that multiple cracks can lead to a complete loss of tensile stiffness, even in a single material component.

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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Computational Engineering

Background:

  • Thin elastic sheets exhibit complex mechanical behavior, particularly under tension and compression.
  • Wrinkling significantly alters material properties, leading to reduced stiffness in compression.
  • Cracks introduce stress concentrations and can affect the overall structural integrity.

Purpose of the Study:

  • To numerically investigate the deformation of thin elastic sheets with multiple cracks under applied tension.
  • To analyze the stress distribution and singularity near crack tips.
  • To understand the interaction effects between multiple cracks on sheet stiffness.

Main Methods:

  • Utilized the tension-field material model for numerical simulations.
  • Modeled thin elastic sheets with multiple cracks of varying geometries.
  • Applied tensile loads to observe the sheet's response and stress patterns.

Main Results:

  • A single crack results in a St. Andrew's cross-shaped stress concentration pattern.
  • The stress singularity near a crack tip follows the usual r^{-1/2} but with nonuniversal angular dependence.
  • Significant interaction between multiple cracks was observed, leading to zero tensile stiffness in specific configurations.

Conclusions:

  • The tension-field model accurately captures the complex behavior of cracked elastic sheets.
  • Crack configuration critically influences the overall stiffness of the sheet.
  • A cracked sheet can exhibit zero tensile stiffness, highlighting the importance of crack interaction analysis.