Thoughts on the Concept of Stress

In Section 5 below we use the notation for volume integrals as explained in Chapter 4 of Vol.II of [FDS]. In particular, let a mapping h : D −→ W be given whose domain D is a region in a Euclidean space, a vector space, or the real line, and whose codomain W is a linear space. Then, the volume integral of h over a suitable subregion P of D, if meaningful, is denoted by ∫ P h or ∫ P h(x)dx. In the latter case, the dx should be read as ”the dummy is x” and it should be used only if the mapping h is not described by a single symbol but only by symbols for its values. In this case, the letter x can be replaced by any other letter without change of meaning, provided only that this letter is not used for other purposes in the same context. For surface integrals, we use darz instead of just dz to say that we deal with surface-area integration and that the dummy is z.