Journal Article

Continuous Bodies, Impenetrability, and Contact Interactions: The View from the Applied Mathematics of Continuum Mechanics

Sheldon R. Smith

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 58, issue 3, pages 503-538
Published in print September 2007 | ISSN: 0007-0882
Published online July 2007 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/axm025
Continuous Bodies, Impenetrability, and Contact Interactions: The View from the Applied Mathematics of Continuum Mechanics

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Many philosophers have claimed that there is a tension between the impenetrability of matter and the possibility of contact between continuous bodies. This tension has led some to claim that impenetrable continuous bodies could not ever be in contact, and it has led others to posit certain structural features to continuous bodies that they believe would resolve the tension. Unfortunately, such philosophical discussions rarely borrow much from the investigation of actual matter. This is probably largely because actual matter is not continuous, and so it might seem as if discussion of the structure of continuous bodies is merely within the realm of philosophical thought experiments rather than actual scientific investigation. However, classical continuum mechanics models actual matter as if it were continuous, and it has implications about the structure of continuous bodies and about what contact and impenetrability are. This paper describes the relevant notions from classical continuum mechanics so as to resolve the alleged tension between contact and impenetrability. 1

The ‘Problem’ of Contact Interaction in a Continuous Medium: the Root Argument

2

The ‘Axiom of Impenetrability’ in Continuum Mechanics

2.1

The status of Kinematical principles in continuum mechanics

2.1.1

Vortex sheets (slip surfaces)

2.2

Violations of the axiom of impenetrability on sets of measure zero

3

Axioms of Body

4

Contact Forces and Equations of Motion

5

Contact Action and the Structure of Continuous Bodies

6

‘Real Contact’ and Contact in Continuum Mechanics

7

Bodies as Open or Closed Sets

8

Contact Action and Fields of Force

9

Conclusion

Journal Article.  18076 words.  Illustrated.

Subjects: Philosophy of Science ; Science and Mathematics

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