Abstract
In this chapter, we abandon the purely kinematic aspects of the motion of bodies and will focus on the actual forces causing the motion. Two distinct types of forces are recognised in continuum mechanics: body forces are conceived as acting on the particles of a body, and the surface (or contact) forces as arising from the action of one part of a body on an adjacent part across a separating surface. Just as there are many different strain measures, there are several different measures of the surface forces. We will see that the surface forces can be described as a second-order tensor. Thus, the surface forces can always be quantified by a set of nine numbers, and the various different definitions are all equivalent.
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- 1.
Discrete mass distributions, such as concentrated masses, are not considered in this book.
- 2.
The assumption that the stress vector \(\vec t_{(\vec n)}\) depends only on the outward unit normal vector \(\vec n\) and not on the differential geometric property of the surface, such as the curvature, was introduced by Cauchy and is referred to as the Cauchy assumption.
- 3.
Since the outward normal vector to a coordinate surface x k = const. is in the direction of − x k, without loss of generality, we denote the stress vector acting on this coordinate surface by \(-\vec t_k\) rather than \(\vec t_k\).
- 4.
The argument t is omitted to shorten the notation.
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Martinec, Z. (2019). Measures of Stress. In: Principles of Continuum Mechanics. Nečas Center Series. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-05390-1_3
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DOI: https://doi.org/10.1007/978-3-030-05390-1_3
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-05389-5
Online ISBN: 978-3-030-05390-1
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