Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Elastic-plastic boundaries in the propagation of plane and cylindrical waves of combined stress

Author: T. C. T. Ting
Journal: Quart. Appl. Math. 27 (1970), 441-449
DOI: https://doi.org/10.1090/qam/99812
MathSciNet review: QAM99812
Full-text PDF

Abstract | References | Additional Information

Abstract: A general study is given of plane and cylindrical wave propagation of combined stress in an elastic-plastic medium. The coefficients of the governing differential equations, when written in matrix notation, are symmetric matrices and can be divided into submatrices each of which has a special form. The relations between the stresses on both sides of an elastic-plastic boundary are derived. Also presented are the restrictions on the speed of an elastic-plastic boundary.

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

  • [1] R. Hill, The Mathematical Theory of Plasticity, Oxford, at the Clarendon Press, 1950. MR 0037721
  • [2] H. H. Bleich and Ivan Nelson, Plane waves in an elastic-plastic half-space due to combined surface pressure and shear, Trans. ASME Ser. E. J. Appl. Mech. 33 (1966), 149–158. MR 0198773
  • [3] Ning Nan, Elastic-plastic waves for combined stresses, Tech. Rep. No. 184, Dept. of Appl. Mech., Stanford University, Stanford, Calif., July 1968
  • [4] T. C. T. Ting and Ning Nan, Plane waves due to combined compressive and shear stresses in a half-space, J. Appl. Mech. 36, 189-197 (1969)
  • [5] Jeffrey T. Fong, Elastic-plastic wave in a half-space of a linearly work-hardening material for coupled shear loadings, Tech. Rept. No. 161, Div. of Eng. Mech., Stanford University, Stanford, Calif., May 1966
  • [6] T. C. T. Ting, Interaction of shock waves due to combined two shear-loadings, Int. J. Solids Structures 5, 415-435 (1969)
  • [7] R. J. Clifton, An analysis of combined longitudinal and torsional plastic waves in a thin-walled tube, Fifth U. S. National Congress of Appl. Mech., June 1966, pp. 465-480
  • [8] N. Cristescu, Quelques observations sur le cas des déformations planes, axial symétriques, du problème dynamique de la plasticité (théorie de Prandtl-Reuss), Com. Acad. R. P. Romîne 6 (1956), 19–28 (Romanian, with Russian and French summaries). MR 0081095
  • [9] R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
  • [10] R. J. Clifton, Elastic-plastic boundaries in combined longitudinal and torsional plastic wave propagation, J. Appl. Mech. 35, 782-786 (1968)
  • [11] R. J. Clifton and T. C. T. Ting, The elastic-plastic boundary in one-dimensional wave propagation, J. Appl. Mech. 35, 812-814 (1968)
  • [12] T. C. T. Ting, On the initial slope of elastic-plastic boundaries in longitudinal wave propagation in a rod, Tech. Rept. No. 187, Dept. of Appl. Mech., Stanford University, Stanford, Calif., Sept. 1968
  • [13] E. H. Lee, A boundary value problem in the theory of plastic wave propagation, Quart. Appl. Math. 10 (1953), 335–346. MR 0052301, https://doi.org/10.1090/S0033-569X-1953-52301-X
  • [14] Jean Mandel, Ondes plastiques dans un milieu indéfini à trois dimensions, J. Mécanique 1 (1962), 3–30 (French). MR 0147049

Additional Information

DOI: https://doi.org/10.1090/qam/99812
Article copyright: © Copyright 1970 American Mathematical Society

American Mathematical Society