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 Free Access

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] C. M. Bender and S. A. Orszag, Advanced mathematical methods for scientists and engineers, McGraw-Hill, New York, 1978 MR 538168
  • [2] B. Bernstein and L. J. Zapas, Stability and cold drawing of viscoelastic bars, J. Rheology 25 (1), 83-94 (1981)
  • [3] G. Birkhoff and G. C. Rota, Ordinary differential equations, 2nd ed., Blaisdell, Waltham, 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, 191-201 (1975) MR 0471528
  • [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