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Spacetime Interpretation of Torsion in Prismatic Bodies

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Abstract

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.

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References

  1. Prandtl, L.: Zur torsion von prismatischen stäben. Z. Phys. 4, 758–770 (1903)

    MATH  Google Scholar 

  2. Nádai, A.: Z. Angew. Math. Mech. 3, 442 (1923)

    Article  MATH  Google Scholar 

  3. Alouges, F., Desimone, A.: Plastic torsion and related problems. J. Elast. 55, 231–237 (1999)

    Article  MATH  Google Scholar 

  4. Chakrabarty, J.: Theory of Plasticity. McGraw-Hill, New York (1987), p. 18 & ff

    Google Scholar 

  5. de Saint-Venant, B.: De la torsion de prismes, avec des considérations sur leur flexion. Mém. Savants étrang. 24, 233 (1855)

    Google Scholar 

  6. Nádai, A.: Plasticity: A Mechanics of the Plastic State of Matter. McGraw-Hill, New York (1931)

    Book  MATH  Google Scholar 

  7. Nádai, A.: Theory of Flow and Fracture of Solids. McGraw-Hill, New York (1950)

    Google Scholar 

  8. Gibbons, G.W.: Born-Infeld particles and Dirichlet p-branes. Nucl. Phys. B 514, 603 (1998). arXiv:hep-th/9709027

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Born, M., Infeld, L.: Foundations of the new field theory. Proc. R. Soc. A 144, 425 (1935)

    Article  ADS  Google Scholar 

  10. Born, M.: Théorie non-linéare du champ électromagnétique. Ann. Inst. Poincaré 7, 155 (1939)

    MathSciNet  Google Scholar 

  11. Pryce, M.H.: The two-dimensional electrostatic solutions of Born’s new field equations. Proc. Camb. Philos. Soc. 31, 50 (1935)

    Article  ADS  Google Scholar 

  12. Pryce, M.H.: On a uniqueness theorem. Proc. Camb. Philos. Soc. 31, 625 (1935)

    Article  ADS  Google Scholar 

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Acknowledgements

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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Authors and Affiliations

  1. Dept. Mechanics, Materials, and Structures, Budapest University of Technology and Economics, Müegyetem rkp 3, 1111, Budapest, Hungary

    G. Domokos

  2. D.A.M.T.P., Cambridge University, Wilberforce Road, Cambridge, CB3 0WA, UK

    G. W. Gibbons

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  1. G. Domokos
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  2. G. W. Gibbons
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Correspondence to G. Domokos.

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Domokos, G., Gibbons, G.W. Spacetime Interpretation of Torsion in Prismatic Bodies. J Elast 110, 111–116 (2013). https://doi.org/10.1007/s10659-012-9384-3

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