9 components of strain for a cubic

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SUMMARY

The discussion focuses on the derivation of strain components for a cubic structure, specifically addressing why the shear strain components εxy, εxz, εyx, εzx, εyz, and εzy are expressed as γ_xy / 2, γ_xz / 2, γ_yx / 2, γ_zx / 2, γ_yz / 2, and γ_zy / 2. The key takeaway is that these relationships arise from the definition of engineering shear strain, which is half the corresponding tensor component. The participants seek clarity on the mathematical reasoning behind this formulation.

PREREQUISITES
  • Understanding of strain tensor components in continuum mechanics
  • Familiarity with the concept of shear strain in material science
  • Basic knowledge of cubic structures in solid mechanics
  • Proficiency in mathematical notation used in engineering mechanics
NEXT STEPS
  • Study the derivation of the strain tensor in three-dimensional elasticity
  • Learn about the physical significance of shear strain in material deformation
  • Explore the relationship between engineering strain and true strain
  • Investigate applications of strain analysis in finite element modeling
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Students and professionals in mechanical engineering, civil engineering, and materials science who are studying the mechanics of materials and strain analysis in cubic structures.

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Homework Statement


why the strain of εxy , εxz , εyx , εzx , εyz , εzy is γ_xy / 2 , γ_xz / 2, γ_yx / 2, γ_zx / 2 , γ_yz / 2 ,
and γ_zy / 2 ?

how to get that ?.

Homework Equations

The Attempt at a Solution


Taking an example of εxy , what does γ_xy / 2 mean ? [/B]
 

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why γ_xy / 2 will become half ?
 
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