Solid Mechanics | 13. Local Volumetric Strain by Abraham | Learn Smarter
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13. Local Volumetric Strain

The discussion centers on local volumetric strain and the local rotation tensor as essential concepts in continuum mechanics. It explains how volumetric strain is defined through the change in volume of small elements under deformation, and how displacement gradients relate to the strain tensor and local rotation. The chapter highlights the independence of volumetric strain from the choice of line elements and describes the physical significance of infinitesimal rotations in deformable bodies.

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Sections

  • 1

    Local Volumetric Strain

    This section introduces the concept of local volumetric strain as a measure of volume change in deformable bodies.

    Learning Practice

  • 1.1

    Formula For Volumetric Strain

    This section discusses the concept of local volumetric strain and introduces the formula for calculating it during deformation.

    Learning Practice

  • 2

    Strain Tensor

    This section focuses on local volumetric strain and the strain tensor, essential concepts in understanding deformation in solid mechanics.

    Learning Practice

  • 3

    Local Rotation Tensor

    This section discusses the local rotation tensor and its relation to deformation in solid mechanics, particularly focusing on the mapping of reference configurations to deformed states.

    Learning Practice

  • 3.1

    Rodrigues’ Rotation Formula

    Rodrigues' Rotation Formula provides a mathematical representation for rotations in three-dimensional space, applicable for small and large angles.

    Learning Practice

  • 3.1.1

    An Example For Rotation

    This section discusses local rotation in a body undergoing deformation, specifically focusing on the rotation matrix and its application in analyzing small rotations.

    Learning Practice

  • 3.2

    Extracting The Axis And Angle Of Local Rotation

    This section discusses the concepts of local rotation through the axial vector and the angle of rotation derived from the skew-symmetric part of the displacement gradient tensor.

    Learning Practice

  • 3.2.1

    An Example

    This section illustrates the concept of local rotation and strain in a coordinate system through a practical example.

    Learning Practice

References

ch13.pdf

Class Notes

Memorization

What we have learnt

  • Local volumetric strain qua...
  • The volumetric strain is de...
  • The strain tensor encompass...

Final Test

Revision Tests