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Related Concept Videos

Hooke's Law01:26

Hooke's Law

Hooke's law, a pivotal principle in material science, establishes that the strain a material undergoes is directly proportional to the applied stress, defined by a factor called the modulus of elasticity or Young's modulus.
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Plasticity is the property where an object loses its elasticity and undergoes irreversible deformation, even after the deformation forces are eliminated. If a material deforms irreversibly without increasing stress or load, then this is called ideal plasticity. For example, when a force is applied to an aluminum rod, it changes its shape, but it does not return to its original shape once the force is removed. Plastic deformation or ductility is thus a permanent deformation or change in the...
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Brittle materials, including glass, cast iron, and stone, exhibit unique characteristics. They fracture without considerable change in their elongation rate, indicating that their breaking and ultimate strength are equivalent. Such materials also show lower strain levels at the point of rupture. The failure in brittle materials predominantly results from normal stresses, as evidenced by the rupture created along a surface perpendicular to the applied load. These materials do not display...
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Strain and Elastic Modulus

The quantity that describes the deformation of a body under stress is known as strain. Strain is given as a fractional change in either length, volume, or geometry under tensile, volume (also known as bulk), or shear stress, respectively, and is a dimensionless quantity. The strain experienced by a body under tensile or compressive stress is called tensile or compressive strain, respectively. In contrast, the strain experienced under bulk stress and shear stress is known as volume and shear...
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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.
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Performing Microscope-Mounted Y-Shaped Cutting Tests
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Published on: January 20, 2023

Length scales at which classical elasticity breaks down for various materials.

R Maranganti1, P Sharma

  • 1Department of Mechanical Engineering, University of Houston, Houston, TX 77204, USA.

Physical Review Letters
|August 7, 2007
PubMed
Summary

Classical continuum elasticity fails at the nanoscale due to nonlocal effects. This study estimates these critical length scales for various materials, revealing when discrete matter structure impacts elastic behavior.

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Area of Science:

  • Materials Science
  • Solid Mechanics
  • Nanotechnology

Background:

  • Classical continuum elasticity theory assumes material homogeneity, failing at small length scales.
  • Size-dependent elastic behavior in nanomaterials is influenced by surface energy and nonlocal interactions.
  • Nonlocal effects stem from the discrete nature of matter and interatomic force fluctuations.

Purpose of the Study:

  • To determine the characteristic length scales at which nonlocal elasticity becomes significant.
  • To investigate the manifestation of nonlocal effects across diverse material classes.
  • To bridge the gap in understanding nonlocal elasticity compared to well-characterized surface energy effects.

Main Methods:

  • Utilized empirical molecular dynamics simulations.
  • Employed lattice dynamics, including both empirical and ab initio approaches.
  • Estimated nonlocal elasticity length scales for various materials.

Main Results:

  • Provided quantitative estimates for nonlocal elasticity length scales.
  • Identified material-specific length scales where continuum elasticity breaks down.
  • Covered semiconductors, metals, amorphous solids, and polymers.

Conclusions:

  • Nonlocal elasticity is a critical factor in nanoscale mechanical behavior.
  • The study establishes material-dependent length scales for nonlocal effects.
  • Findings are crucial for accurate modeling of nanomaterials.