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
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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.
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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)
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)
N. Cristescu, Dynamic plasticity, John Wiley & Sons, New York, 1967
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L. D. Landau and E. M. Lifschitz, Fluid mechanics, Pergamon, Oxford, 1959
C. M. Bender and S. A. Orszag, Advanced mathematical methods for scientists and engineers, McGraw-Hill, New York, 1978
B. Bernstein and L. J. Zapas, Stability and cold drawing of viscoelastic bars, J. Rheology 25 (1), 83–94 (1981)
G. Birkhoff and G. C. Rota, Ordinary differential equations, 2nd ed., Blaisdell, Waltham, 1969
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)
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)
N. Cristescu, Dynamic plasticity, John Wiley & Sons, New York, 1967
J. L. Ericksen, Equilibrium of bars, J. Elasticity 5, 191–201 (1975)
L. D. Landau and E. M. Lifschitz, Fluid mechanics, Pergamon, Oxford, 1959
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Article copyright:
© Copyright 1982
American Mathematical Society
