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Knowledge
The chapter explores longitudinal strain and shear strain in solid mechanics, emphasizing their mathematical formulations and physical implications. It describes how longitudinal strain affects the size of a body while shear strain alters the angles between elements, leading to distortion. The significance of the deformation gradient tensor and its application in various contexts is also discussed throughout the chapter.
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Sections
References
ch12.pdfClass Notes
Memorization
What we have learnt
- Longitudinal strain is deri...
- Shear strain measures chang...
- The importance of distingui...
Final Test
Revision Tests
What we have learnt
- Longitudinal strain is derived from stretch and depends on gradients of displacement.
- Shear strain measures changes in angles between line elements, providing insights into the shape distortion of materials.
- The importance of distinguishing between significant and insignificant terms in deformation formulations is highlighted.
Key Concepts
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Term: Longitudinal Strain
Definition: A measure of the deformation representing the elongation of a body in the direction of applied stress.
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Term: Shear Strain
Definition: The measure of deformation representing the change in shape of an object by measuring the relative displacement of its layers.
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Term: Deformation Gradient Tensor
Definition: A mathematical representation that describes the transformation of a material point due to deformation, relating the reference configuration to the current state.