Continuous Bodies, Impenetrability, and Contact Interactions
The View from the Applied Mathematics of Continuum Mechanics
Bibliographic Data
| ID | 8399322 |
|---|---|
| Authors | Sheldon R Smith (University of California, Los Angeles, corresponding author) |
| Year | 2007 |
| Volume | 58 |
| Issue | 3 |
| Pages | 503-538 |
| Publication date | 2007-09-01 |
| Peer Reviewed | Yes |
| Open Access | No |
| Type | ARTICLE |
| Venue | The British Journal for the Philosophy of Science (JOURNAL) |
| Journal identifiers | ISSN: 0007-0882 • E-ISSN: 1464-3537 |
| Publisher | Oxford University Press (PUBLISHER • GB) |
| DOI | 10.1093/bjps/axm025 |
| OpenAlex | W2040211147 |
| Language | EN |
| Citations received | 3 |
| References cited | 17 |
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 Argument2. The ‘Axiom of Impenetrability’ in Continuum Mechanics2.1. The status of Kinematical principles in continuum mechanics2.1.1. Vortex sheets (slip surfaces)2.2. Violations of the axiom of impenetrability on sets of measure zero3. Axioms of Body4. Contact Forces and Equations of Motion5. Contact Action and the Structure of Continuous Bodies6. ‘Real Contact’ and Contact in Continuum Mechanics7. Bodies as Open or Closed Sets8. Contact Action and Fields of Force9. Conclusion
Action (physics) · Art · Classical mechanics · Epistemology · Formalism (music) · Mechanics · Physics · Quantum mechanics · Slip (aerodynamics) · Theoretical physics · Logic, programming, and type systems · Mathematics · Philosophy
| Unique citing works | 3 |
|---|---|
| Citations per year | 0,25 |
| Citation span | 2014 - 2026 (13) |
| Citation velocity | current |
| Highly cited | No |
| Citation types | Neutral: 3 |