Stress fields in plane irrotational flows of viscous and perfectly plastic continua
Author:
Wan Lee Yin
Journal:
Quart. Appl. Math. 40 (1982), 129-135
MSC:
Primary 73E99; Secondary 73F99
DOI:
https://doi.org/10.1090/qam/666669
MathSciNet review:
666669
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Abstract: The viscous and viscoplastic stress fields in three families of plane irrotational flows are determined by using the properties of complex analytic functions. In these flows the slip line fields are defined by the continuation of an orthogonal pair of characteristics that are straight lines, logarithmic spirals or Cornu’s spirals, respectively. The three families of solutions comprise all plane flows which, when subjected to changes in the time scale, continue to satisfy the dynamical equations of a viscoplastic continuum in the sense of Bingham.
D. R. Owens and W.-L. Yin, A class of exact solutions of the dynamical equations for rigid-viscoplastic bodies, Rheol. Acta 16, 223–226 (1977)
D. R. Owen and W.-L. Yin, On the possibility of detecting invariance of material response to changes in time scale, ZAMP 26, 605–610 (1975)
- Alfred M. Freudenthal and Hilda Geiringer, The mathematical theories of the inelastic continuum, Handbuch der Physik, herausgegeben von S. Flügge. Bd. 6. Elastizität und Plastizität, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958, pp. 229–433. MR 0093963
- Eugene Jahnke and Fritz Emde, Tables of Functions with Formulae and Curves, Dover Publications, New York, N. Y., 1945. 4th ed. MR 0015900
- R. Hill, The Mathematical Theory of Plasticity, Oxford, at the Clarendon Press, 1950. MR 0037721
- Herbert E. Salzer, Complex zeros of the error function, J. Franklin Inst. 260 (1955), 209–211. MR 71880, DOI https://doi.org/10.1016/0016-0032%2855%2990732-8
D. R. Owens and W.-L. Yin, A class of exact solutions of the dynamical equations for rigid-viscoplastic bodies, Rheol. Acta 16, 223–226 (1977)
D. R. Owen and W.-L. Yin, On the possibility of detecting invariance of material response to changes in time scale, ZAMP 26, 605–610 (1975)
A. M. Freudenthal and G. Geiringer, The mathematical theories of the inelastic continuum, in Encyclopedia of physics, vol. VI, Elasticity and plasticity, edited by S. Flügge, Springer-Verlag, Berlin (1958)
E. Jahnke and F. Emde, Tables of functions with formulae and curves, 4th Ed., Dover Publications, New York (1945), pp. 36–38
R. Hill, Mathematical theory of plasticity, Clarendon Press, Oxford (1950)
H. E. Salzer, Complex zeros of the error function, J. Franklin Inst. 260, 209–211 (1955)
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Article copyright:
© Copyright 1982
American Mathematical Society