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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.
Chapter 138 sections
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.
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.
A measure of the change in volume per unit volume of a small region within a deformed body.
A mathematical representation that includes both the symmetric (strain) and anti-symmetric (rotation) parts of the displacement gradient tensor.
Describes the infinitesimal local rotations occurring within the material as it deforms.
Total Questions
2
Estimated Time
4 min
Passing Score
70%
1 more question available