Solid Mechanics | 15. Need for stress-strain relation by Abraham | Learn Smarter
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15. Need for stress-strain relation

The relationship between stress and strain is crucial for understanding material behavior under external loads. This chapter introduces the stress-strain relation and focuses on formulating the linear stress-strain relationship and its implications in solid mechanics. The importance of additional equations, known as constitutive relations, is emphasized to solve equilibrium equations for deformed bodies.

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Sections

  • 1

    Need For Stress-Strain Relation

    The section discusses the necessity of establishing a stress-strain relationship to analyze the behavior of a deformed body under external loads.

    Learning Practice

  • 2

    Linear Stress-Strain Relation

    This section discusses the linear relationship between stress and strain in solid mechanics, emphasizing its necessity for solving equilibrium equations.

    Learning Practice

  • 2.1

    Taylor’s Expansion

    This section explores Taylor's expansion as a method to relate stress to strain in solid mechanics.

    Learning Practice

  • 2.2

    Independent Components In Tensor C

    This section discusses the independent components of the stiffness tensor C and the symmetries associated with stress and strain tensors.

    Learning Practice

  • 2.2.1

    Minor Symmetry

    This section discusses minor symmetry within the stiffness tensor in the context of solid mechanics, highlighting its implications for the independence of stress and strain components.

    Learning Practice

  • 2.2.2

    Major Symmetry

    This section discusses Major Symmetry in the stiffness tensor, explaining its implications for material constants and energy considerations.

    Learning Practice

  • 3

    Voigt Notation

    Voigt Notation simplifies the representation of stress and strain tensors in solid mechanics by reducing them to six independent components.

    Learning Practice

References

ch15.pdf

Class Notes

Memorization

What we have learnt

  • The stress-strain relation ...
  • Lagrangian description is u...
  • The stiffness tensor has ma...

Final Test

Revision Tests