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.

**[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