Spacetime Interpretation of Torsion in Prismatic Bodies
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A non-linear theory for the plastic deformation of prismatic bodies is constructed which interpolates between Prandtl’s linear soap-film approximation and Nádai’s sand-pile model. Geometrically Prandtl’s soap film and Nádai’s wavefront are unified into a single smooth surface of constant mean curvature in three-dimensional Minkowski spacetime.
KeywordsTorsion Prismatic body Sandpile analogy Minkowski spacetime
Mathematics Subject Classification74C05 83A05
The first author was a Visiting Fellow Commoner at Trinity College, Cambridge during part of this collaboration. This research was supported by the Hungarian National Foundation (OTKA) Grant K104601. The authors thank Tamás Ther for his help with Fig. 1.
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