Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Dynamic instability of a homogenous deformation of a thin elastic bar

Author: Timothy J. Burns
Journal: Quart. Appl. Math. 40 (1982), 357-361
MSC: Primary 73H10
DOI: https://doi.org/10.1090/qam/678208
MathSciNet review: 678208
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A linear stability analysis of a homogeneous deformation at constant strain-rate of a thin elastic bar is used to show that the deformation is unstable with respect to small perturbations in the case when the stress-strain relation is concave with a single maximum.

References [Enhancements On Off] (What's this?)

  • [1] Carl M. Bender and Steven A. Orszag, Advanced mathematical methods for scientists and engineers, McGraw-Hill Book Co., New York, 1978. International Series in Pure and Applied Mathematics. MR 538168
  • [2] B. Bernstein and L. J. Zapas, Stability and cold drawing of viscoelastic bars, J. Rheology 25 (1), 83-94 (1981)
  • [3] Garrett Birkhoff and Gian-Carlo Rota, Ordinary differential equations, Second edition, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1969. MR 0236441
  • [4] T. J. Burns, D. E. Grady, and L. S. Costin, On a criterion for thermoplastic shear instability, Amer. Inst. Phys. Conf. Ser. No. 78, Chapt. 7, 372-375 (1981)
  • [5] L. S. Costin et al., On the localization of plastic flow in mild steel tubes under dynamic torsional loading, Amer. Inst. Phys. Conf. Ser. No. 47, Chapt. 1, 90-100 (1979)
  • [6] N. Cristescu, Dynamic plasticity, John Wiley & Sons, New York, 1967
  • [7] J. L. Ericksen, Equilibrium of bars, J. Elasticity 5 (1975), no. 3–4, 191–201 (English, with French summary). Special issue dedicated to A. E. Green. MR 0471528, https://doi.org/10.1007/BF00126984
  • [8] L. D. Landau and E. M. Lifschitz, Fluid mechanics, Pergamon, Oxford, 1959

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73H10

Retrieve articles in all journals with MSC: 73H10

Additional Information

DOI: https://doi.org/10.1090/qam/678208
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society