The constitutive equations for rate sensitive plastic materials
Author:
P. Perzyna
Journal:
Quart. Appl. Math. 20 (1963), 321-332
MSC:
Primary 73.35
DOI:
https://doi.org/10.1090/qam/144536
MathSciNet review:
144536
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Abstract: The principal aim of the present paper is to generalize the one-dimensional constitutive equations for rate-sensitive plastic materials to general states of stress. The dynamical yield conditions for elastic, visco-plastic materials are discussed and new relaxation functions are introduced. Solutions of the relaxation equations for such materials are given.
- S. R. Bodner and P. S. Symonds, Plastic deformation in impact and impulsive loading of beams, Plasticity: Proceedings of the Second Symposium on Naval Structural Mechanics, Pergamon, Oxford, 1960, pp. 488–500. MR 0118091
J. D. Campbell, The yield of mild steel under impact loading, J. Mech. Phys. Solids 3, 54–62 (1954)
J. D. Campbell and J. Duby, The yield behavior of mild steel in dynamic compression, Proc. Roy. Soc. 236A, 24–40 (1956)
D. S. Clark and P. E. Duwez, The influence of strain rate on some tensile properties of steel, Proc. Amer. Soc. Testing Materials 50, 560–575 (1950)
- Alfred M. Freudenthal, Fatigue, Handbuch der Physik, herausgegeben von S. Flügge. Bd. 6. Elastizität und Plastizität, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958, pp. 591–613. MR 0094945
K. Hohenemser and W. Prager, Über die Ansätze der Mechanik isotroper Kontinua, Zeitschrift f. angew. Math. u. Mech. 12, 216–226 (1932); see also W. Prager, Mécanique des solides isotropes au delà, du domaine élastique, Mémorial Sci. Math. 87, Paris, 1937, Eq. (47) on p. 27
- L. E. Malvern, The propagation of longitudinal waves of plastic deformation in a bar of material exhibiting a strain-rate effect, J. Appl. Mech. 18 (1951), 203–208. MR 0041688
P. Perzyna, The study of the dynamical behavior of rate sensitive plastic materials, to be published
- William Prager, Linearization in visco-plasticity, Österreich. Ing.-Arch. 15 (1961), 152–157. MR 0137397
- William Prager, Introduction to mechanics of continua, Introductions to Higher Mathematics. Ginn and Co., Boston, Mass.-Toronto-London, 1961. MR 0126974
- V. V. Sokolovskiĭ, The propagation of elastic-viscous-plastic waves in bars, Akad. Nauk SSSR. Prikl. Mat. Meh. 12 (1948), 261–280 (Russian). MR 0026902
S. R. Bodner and P. S. Symonds, Plastic deformation in impact and impulsive loading of beams, “Plasticity” (Edited by E. H. Lee and P. S. Symonds), Pergamon Press, New York, 1960, 488–500
J. D. Campbell, The yield of mild steel under impact loading, J. Mech. Phys. Solids 3, 54–62 (1954)
J. D. Campbell and J. Duby, The yield behavior of mild steel in dynamic compression, Proc. Roy. Soc. 236A, 24–40 (1956)
D. S. Clark and P. E. Duwez, The influence of strain rate on some tensile properties of steel, Proc. Amer. Soc. Testing Materials 50, 560–575 (1950)
A. M. Freudenthal, The mathematical theories of the inelastic continuum, Handbuch der Physik VI, Springer-Verlag, Berlin, 1958
K. Hohenemser and W. Prager, Über die Ansätze der Mechanik isotroper Kontinua, Zeitschrift f. angew. Math. u. Mech. 12, 216–226 (1932); see also W. Prager, Mécanique des solides isotropes au delà, du domaine élastique, Mémorial Sci. Math. 87, Paris, 1937, Eq. (47) on p. 27
L. E. Malvern, The propagation of longitudinal waves of plastic deformation in a bar of material exhibiting a strain-rate effect, J. Appl. Mech. 18, 203–208 (1951)
P. Perzyna, The study of the dynamical behavior of rate sensitive plastic materials, to be published
W. Prager, Linearization in visco-plasticity, Oesterreichisches Ing.-Arch. I5, 152–157 (1961)
W. Prager, Introduction to mechanics of continua, Ginn and Company, Boston, 1961
V. V. Sokolovskii, Propagation of elastic-visco-plastic waves in bars, (in Russian), Prikl. Mat. Mekh. 12, 261–280 (1948)
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Article copyright:
© Copyright 1963
American Mathematical Society
