Continuity conditions at wave fronts in coupled thermoplasticity
Author:
A. D. Fine
Journal:
Quart. Appl. Math. 25 (1967), 121-128
DOI:
https://doi.org/10.1090/qam/99906
MathSciNet review:
QAM99906
Full-text PDF Free Access
Abstract |
References |
Additional Information
Abstract: The mass, momentum, and energy conservation requirements at wave fronts (or surfaces of discontinuity) are reduced to a form suitable for use in the coupled thermoplastic analysis. Constitutive equations are introduced in these relations, and, for one-dimensional situations, it is shown that an isothermal (or adiabatic) wave front separating regions of elastic and plastic behavior will propagate with the same speed as an isothermal (or adiabatic) surface of discontinuity lying completely inside a domain of plastic deformation. A new thermoplastic coupling parameter is obtained from an example involving spherical symmetry.
- Bruno A. Boley and Jerome H. Weiner, Theory of thermal stresses, John Wiley & Sons, Inc., New York London, 1960. MR 0112414
- P. Chadwick, Thermoelasticity. The dynamical theory, Progress in solid mechanics, Vol. 1, North-Holland Publishing Co., Amsterdam, 1960, pp. 263–328. MR 0113406
- B. A. Boley and I. S. Tolins, Transient coupled thermoelastic boundary value problems in the half-space, Trans. ASME Ser. E. J. Appl. Mech. 29 (1962), 637–646. MR 147052
A. D. Fine and H. Kraus, On wave propagation in thermoplastic media, Trans. ASME Ser. E J. App. Mech. (to appear)
O. W. Dillon, Jr., Coupled thermoplasticity, J. Mech. Phys. Solids 11, 21 (1963)
- P. Chadwick and B. Powdrill, Application of the Laplace transform method to wave motions involving strong discontinuities, Proc. Cambridge Philos. Soc. 60 (1964), 313–324. MR 163507
- Joseph B. Keller, Geometrical acoustics. I. The theory of weak shock waves, J. Appl. Phys. 25 (1954), 938–947. MR 67654
- A. E. H. Love, A treatise on the Mathematical Theory of Elasticity, Dover Publications, New York, 1944. Fourth Ed. MR 0010851
R. Von-Mises, Mechanik der Festen Koerper im Plastich Deformablen Zustand, Goettinger Nachrichten, math.-phys. Klasse, (1913) 582
- P. Chadwick and B. Powdrill, Singular surfaces in linear thermoelasticity, Internat. J. Engrg. Sci. 3 (1965), 561–595 (English, with French, German, Italian and Russian summaries). MR 0189349, DOI https://doi.org/10.1016/0020-7225%2865%2990009-1
B. A. Boley and J. H. Weiner, Theory of thermal stresses, Wiley, New York, 1960, pp. 41, 27
P. Chadwick, Thermoelasticity. The dynamical theory, Progress in Solid Mechanics 1, 263 (1960)
B. A. Boley and I. S. Tolins, Transient coupled thermoelastic boundary value problems in the half-space, Trans. ASME Ser. E J. App. Mech. 29, 637 (1962)
A. D. Fine and H. Kraus, On wave propagation in thermoplastic media, Trans. ASME Ser. E J. App. Mech. (to appear)
O. W. Dillon, Jr., Coupled thermoplasticity, J. Mech. Phys. Solids 11, 21 (1963)
P. Chadwick and B. Powdrill, Application of the Laplace transform method to wave motions involving strong discontinuities, Proc. Cambridge Philos. Soc. 60, 313 (1960)
J. B. Keller, Geometrical acoustics. I, Theory of weak shock waves, J. App. Phys. 25, 938 (1954)
A. E. H. Love, A treatise on the mathematical theory of elasticity, 4th Ed., Dover, New York, 1944, p. 295, 104
R. Von-Mises, Mechanik der Festen Koerper im Plastich Deformablen Zustand, Goettinger Nachrichten, math.-phys. Klasse, (1913) 582
P. Chadwick and B. Powdrill, Singular surfaces in linear thermoelasticity, Int. J. Engrg. Sci. 3, 561 (1965)
Additional Information
Article copyright:
© Copyright 1967
American Mathematical Society
