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

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

13. Local Volumetric Strain

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.

8 sections

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

Navigate through the learning materials and practice exercises.

  1. 1
    Local Volumetric Strain

    This section introduces the concept of local volumetric strain as a measure...

  2. 1.1
    Formula For Volumetric Strain

    This section discusses the concept of local volumetric strain and introduces...

  3. 2
    Strain Tensor

    This section focuses on local volumetric strain and the strain tensor,...

  4. 3
    Local Rotation Tensor

    This section discusses the local rotation tensor and its relation to...

  5. 3.1
    Rodrigues’ Rotation Formula

    Rodrigues' Rotation Formula provides a mathematical representation for...

  6. 3.1.1
    An Example For Rotation

    This section discusses local rotation in a body undergoing deformation,...

  7. 3.2
    Extracting The Axis And Angle Of Local Rotation

    This section discusses the concepts of local rotation through the axial...

  8. 3.2.1

    This section illustrates the concept of local rotation and strain in a...

What we have learnt

  • Local volumetric strain quantifies the change in volume per unit volume in a deforming body.
  • The volumetric strain is defined in terms of the original and deformed volumes of small elements.
  • The strain tensor encompasses both longitudinal and shear strains, and its components can be derived from displacement gradients.

Key Concepts

-- Local Volumetric Strain
A measure of the change in volume per unit volume of a small region within a deformed body.
-- Strain Tensor
A mathematical representation that includes both the symmetric (strain) and anti-symmetric (rotation) parts of the displacement gradient tensor.
-- Local Rotation Tensor
Describes the infinitesimal local rotations occurring within the material as it deforms.

Additional Learning Materials

Supplementary resources to enhance your learning experience.