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Related Concept Videos

Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

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...
Elastic Strain Energy for Normal Stresses01:22

Elastic Strain Energy for Normal Stresses

Strain energy quantifies the energy stored within a material due to deformation under loading conditions, a fundamental concept in materials science and engineering. The strain energy can be modeled when a material is subjected to axial loading with uniformly distributed stress. In this scenario, the stress experienced by the material is the internal force divided by the cross-sectional area, and the strain induced is directly proportional to this stress through the modulus of elasticity.
If...
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...
Members Made of Elastoplastic Material01:19

Members Made of Elastoplastic Material

The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
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Dynamic Modulus of Elasticity of Concrete01:16

Dynamic Modulus of Elasticity of Concrete

The dynamic modulus of elasticity assesses how a concrete structure deforms under impact or dynamic loads. It is typically higher than the static modulus of elasticity, measured under slow, steady loading conditions.
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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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Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
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Published on: January 18, 2022

A generalized solid-state nudged elastic band method.

Daniel Sheppard1, Penghao Xiao, William Chemelewski

  • 1Department of Chemistry and Biochemistry, University of Texas at Austin, Austin, Texas 78712-0165, USA.

The Journal of Chemical Physics
|February 25, 2012
PubMed
Summary
This summary is machine-generated.

A new generalized solid-state nudged elastic band (G-SSNEB) method efficiently models solid-solid phase transitions. It reveals how transition mechanisms change with system size, impacting materials science research.

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Area of Science:

  • Materials Science
  • Computational Chemistry
  • Solid-State Physics

Background:

  • Solid-solid phase transitions are crucial in materials science.
  • Accurately predicting transformation pathways is computationally challenging.
  • Existing methods often struggle to incorporate both atomic and unit-cell dynamics.

Purpose of the Study:

  • To introduce a generalized solid-state nudged elastic band (G-SSNEB) method.
  • To enable robust calculation of reaction pathways for solid-solid transformations.
  • To develop a method insensitive to the choice of periodic cell.

Main Methods:

  • Unified description of crystal structure combining atomic and cell degrees of freedom.
  • Application of the G-SSNEB method to the rock-salt to wurtzite transition in CdSe.
  • Utilizing density functional theory for force and stress tensor calculations.

Main Results:

  • The G-SSNEB method is robust for mechanisms driven by atomic motion or unit-cell deformation.
  • Demonstrated a size-dependent transition mechanism in CdSe.
  • Observed a shift from concerted transformation in small cells to nucleation in large cells.

Conclusions:

  • The G-SSNEB method provides an efficient and versatile approach for studying solid-state transformations.
  • The findings highlight the importance of considering cell size effects on phase transition mechanisms.
  • This method can be applied to various systems using first-principles calculations.