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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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.
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