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 Free Access
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.
- R. Hill, The Mathematical Theory of Plasticity, Oxford, at the Clarendon Press, 1950. MR 0037721
- 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 198773
Ning Nan, Elastic-plastic waves for combined stresses, Tech. Rep. No. 184, Dept. of Appl. Mech., Stanford University, Stanford, Calif., July 1968
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)
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
T. C. T. Ting, Interaction of shock waves due to combined two shear-loadings, Int. J. Solids Structures 5, 415–435 (1969)
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
- 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 French and Russian summaries). MR 81095
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
R. J. Clifton, Elastic-plastic boundaries in combined longitudinal and torsional plastic wave propagation, J. Appl. Mech. 35, 782–786 (1968)
R. J. Clifton and T. C. T. Ting, The elastic-plastic boundary in one-dimensional wave propagation, J. Appl. Mech. 35, 812–814 (1968)
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
- E. H. Lee, A boundary value problem in the theory of plastic wave propagation, Quart. Appl. Math. 10 (1953), 335–346. MR 52301, DOI https://doi.org/10.1090/S0033-569X-1953-52301-X
- Jean Mandel, Ondes plastiques dans un milieu indéfini à trois dimensions, J. Mécanique 1 (1962), 3–30 (French). MR 147049
R. Hill, The mathematical theory of plasticity, Clarendon Press, Oxford, 1950
H. H. Bleich and I. Nelson, Plane waves in an elastic-plastic half-space due to combined surface pressure and shear, J. Appl. Mech. 33, 149–158 (1966)
Ning Nan, Elastic-plastic waves for combined stresses, Tech. Rep. No. 184, Dept. of Appl. Mech., Stanford University, Stanford, Calif., July 1968
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)
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
T. C. T. Ting, Interaction of shock waves due to combined two shear-loadings, Int. J. Solids Structures 5, 415–435 (1969)
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
N. Cristescu, Some observations about the case of plane axial-symmetric deformations in the dynamic problem of plasticity (Prandtl-Reuss theory), Com. Acad. R. P. Romane (1) 6, 19–28 (1956)
R. Courant and D. Hilbert, Methods of mathematical physics, Vol. II, Interscience, New York, 1962
R. J. Clifton, Elastic-plastic boundaries in combined longitudinal and torsional plastic wave propagation, J. Appl. Mech. 35, 782–786 (1968)
R. J. Clifton and T. C. T. Ting, The elastic-plastic boundary in one-dimensional wave propagation, J. Appl. Mech. 35, 812–814 (1968)
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
E. H. Lee, A boundary value problem in the theory of plastic wave propagation, Quart. Appl. Math. 10, 335–346 (1953)
Jean Mandel, Ondes plastiques dans un milieu indéfini á trois dimensions, J. Mécanique (1) 1, 3–30 (1962)
Additional Information
Article copyright:
© Copyright 1970
American Mathematical Society
