Abstract
As already discussed with broad strokes in Sect. 1.1, deformation is the change in the distances between material points, which, in turn, leads to changes in shape and/or size of the body. All real materials undergo some deformation under the influence of forces. To quantify the deformation of a solid body relative to some reference configuration, it is important to introduce the notions of stretch and strain.
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Notes
- 1.
Some authors write this in the form of a millionth of a unit of length divided by the same unit of length, for example μm/m (“micrometer per meter”) or μin/in (“microinch per inch”). Apart from unwarranted redundancy, there is nothing wrong with this way of expressing strain, but there is a tendency to neglect the “per meter” or “per inch” that can lead to misinterpretation. If we were to cancel the “m” or “in” in the fractional representation, we would be left with μ, and that would be all right if this symbol were not still being used (especially in astronomy and the semiconductor industry) to denote the micron, an old name for micrometer (μm), perhaps in order to avoid confusion between this last term (stressed on the third syllable) and micrometer, stressed on the second syllable and denoting a measuring instrument. (No such confusion occurs when British or Canadian spelling is used, because the metric unit is then written micrometre.)
- 2.
This is derived by taking the square-root of the algebraic identity \({(1+\zeta)}^{2} = 1 + 2\zeta {+\zeta}^{2}\) and ignoring the second-order term ζ 2.
- 3.
Note that the same symbol, ω, is used for it as for the angular velocity defined in Sect. 2.1 (page 56).
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Lubliner, J., Papadopoulos, P. (2014). Deformation and Strain. In: Introduction to Solid Mechanics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6768-7_5
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DOI: https://doi.org/10.1007/978-1-4614-6768-7_5
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