1976
DOI: 10.1007/bf00248882
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Cauchy's theorem in classical physics

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Cited by 70 publications
(23 citation statements)
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“…Moreover, in [9,8] it was shown that the linear dependence of the traction upon the normal for almost all points could be derived from the same balance law, thus avoiding the continuity condition. In [8] the notion of Cauchy flux was also introduced, which has changed the basic concept in this kind of analysis. The main idea was to replace the exerted traction by the resultant (called Cauchy flux) on the material surface, thus specifying properties on the resultant and possibly avoiding those on the traction field.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…Moreover, in [9,8] it was shown that the linear dependence of the traction upon the normal for almost all points could be derived from the same balance law, thus avoiding the continuity condition. In [8] the notion of Cauchy flux was also introduced, which has changed the basic concept in this kind of analysis. The main idea was to replace the exerted traction by the resultant (called Cauchy flux) on the material surface, thus specifying properties on the resultant and possibly avoiding those on the traction field.…”
Section: Introductionmentioning
confidence: 99%
“…Also, notions like "almost all n-intervals" are more transparent than "almost all subbodies". This alternative approach seems to be more in the spirit of [12,9,8] (see, e.g., [12,Theorem 4] and [8,Theorem 8]). On the other hand, situations of this kind are typical in classical measure theory, where each set function, defined on n−intervals and satisfying suitable conditions, can be uniquely extended to a measure defined on all Borel subsets.…”
Section: Introductionmentioning
confidence: 99%
“…Whatever is the preference, the procedure proposed here applies. 2 Throughout this paper it is assumed that all vector, or tensor, fields defined on the pair ( , x) are bouded almost everywhere, and that the associated fluxes a s d A are additive on regions with pairwise disjoint interiors [Gurtin and Martins 1976].…”
Section: Classical Continuamentioning
confidence: 99%
“…In this light the treatment of Gurtin & Martins [24] in 1976 can be considered as an extraction of the essential ingredients. They circumvented the difficulties with a system of subbodies by the restriction to planar polygonal surfaces and they introduced the notion of a Cauchy flux as an additive mapping f on surfaces such that, with a constant c > 0,…”
Section: Introductionmentioning
confidence: 99%
“…Furthermore Gurtin, Williams & Ziemer [28] showed that the subclass of normalized sets of finite perimeter (i.e., sets that coincide with their measure-theoretic interior) form a Boolean algebra and, therefore, satisfy all of Noll's axioms for subbodies. On the other hand, it turned out in [24] that it is sufficient for the derivation of the tensorial structure of a contact interaction as in (1.1) to consider the quite small class of subbodies having piecewise planar polygonal boundaries. Noll & Virga [42] proposed the class of fit regions for subbodies (bounded regularly open sets with finite perimeter and negligible boundary) which lies somewhere in between the previously mentioned classes.…”
Section: Introductionmentioning
confidence: 99%