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Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

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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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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...
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Topological Defects in Solids with Odd Elasticity.

Lara Braverman1,2, Colin Scheibner1,2, Bryan VanSaders1

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|January 14, 2022
PubMed
Summary
This summary is machine-generated.

Odd elasticity, a new form of elasticity, alters how topological defects affect materials. This can change the stability of dislocation pairs and enable self-propulsion of dislocations through active core processes.

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Area of Science:

  • Solid-state physics
  • Materials science
  • Continuum mechanics

Background:

  • Crystallography traditionally models point particles with potential-gradient forces.
  • Deviations from this assumption lead to odd elasticity in the continuum limit.
  • Odd elasticity introduces new moduli beyond conventional elastic constants.

Purpose of the Study:

  • To investigate the impact of odd elastic moduli on topological defects.
  • To explore the self-propulsion mechanisms of dislocations beyond classical forces.
  • To bridge continuum theory with microscopic active processes in materials.

Main Methods:

  • Theoretical analysis within continuum mechanics.
  • Molecular dynamics simulations to model dislocation behavior.
  • Isolation and analysis of active plastic processes at dislocation cores.

Main Results:

  • Odd elastic moduli significantly modify strain fields around topological defects.
  • The stability of bound dislocation pairs can be reversed by odd elasticity.
  • Dislocations can exhibit self-propulsion driven by active core work cycles, competing with Peach-Koehler forces.

Conclusions:

  • Odd elasticity represents a significant extension to classical elasticity theory.
  • Active core processes offer a novel mechanism for dislocation motion.
  • Findings have implications for materials with spinning particles, vortex-like structures, and advanced robotic metamaterials.