Solid Mechanics | 14. Similarity between Stress and Strain tensors by Abraham | Learn Smarter
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.

Typing
Memory
Math
English Adventures
Knowledge
14. Similarity between Stress and Strain tensors

The lecture discusses the similarities between stress and strain tensors, emphasizing their properties and the mathematical relationships. Key topics include principal directions and components, the diagonalization of matrices in principal coordinate systems, the application of Mohr's circle for strain, and strain compatibility conditions. The content underscores that concepts derived for stress tensors can also be applied to strain tensors due to their analogous framework.

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Sections

  • 1

    Similarity Between Stress And Strain Tensors

    This section explores the parallels between stress and strain tensors in solid mechanics, highlighting their similar mathematical structures and significant properties.

    Learning Practice

  • 1.1

    Principal Directions And Principal Components

    This section discusses principal directions and components of stress and strain tensors, highlighting their similarities.

    Learning Practice

  • 1.2

    Diagonality Of Matrix For In Principal Coordinate System

    This section explains how stress and strain matrices become diagonal in their respective principal coordinate systems, indicating no shear components.

    Learning Practice

  • 1.3

    Maximum Shear

    This section discusses the principles of maximum shear strain and its relationship with shear stress, illustrating the similarities between stress and strain tensors.

    Learning Practice

  • 1.4

    Mohr’s Circle

    Mohr's Circle for strain provides a graphical method to analyze normal and shear strains in different directions, similar to stress analysis.

    Learning Practice

  • 1.5

    Invariants

    This section discusses the invariants of the strain tensor, which are analogous to those of the stress tensor.

    Learning Practice

  • 1.6

    Decomposition Of The Tensors

    The section discusses the decomposition of strain tensors into volumetric and deviatoric parts, highlighting their physical significance.

    Learning Practice

  • 2

    An Alternate Physical Meaning Of Shear Strain

    This section presents an alternative interpretation of shear strain, highlighting its representation as a shear displacement and its relationship with the rigid translation of planes.

    Learning Practice

  • 3

    Strain Compatibility Conditions

    This section discusses strain compatibility conditions, highlighting how arbitrary strain matrices may fail to correspond to a consistent displacement function.

    Learning Practice

  • 3.1

    Another Interpretation

    This section discusses the concept of strain compatibility conditions, emphasizing the importance of path independence in strain integration and its implications in mechanics.

    Learning Practice

  • 3.2

    Special Case

    This section discusses the special case of plane strain conditions where five compatibility conditions are automatically satisfied.

    Learning Practice

  • 3.3

    An Example

    This section examines an example addressing strain compatibility conditions to validate the strain matrix derived from strain components.

    Learning Practice

References

ch14.pdf

Class Notes

Memorization

What we have learnt

  • Stress and strain tensors e...
  • Principal strain directions...
  • Invariants exist for both s...

Final Test

Revision Tests