A nonlinear theory of plasticity for plane strain
Author:
E. M. Shoemaker
Journal:
Quart. Appl. Math. 24 (1966), 19-27
MSC:
Primary 73.99
DOI:
https://doi.org/10.1090/qam/193840
MathSciNet review:
193840
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Abstract: A nonlinear theory of plasticity is proposed which facilitates the solution of a restricted class of plane strain problems. An anisotropic approximation to a real material is utilized with the characteristic directions chosen a priori. The formulation is in terms of displacements and sufficient displacement boundary conditions must be prescribed in order to solve the resulting classical wave equation. Subsequently, the stress field is determined, corresponding to any nonlinear monotonic relation between shear stress and strain, by direct integration of the equilibrium equations. Uniqueness restricts the class of problems suitable to the theory. Classical isotropic theory will be closely approximated in problems where the deviatoric stress field is predominantly uniform. The theory is illustrated by the solution of an indentation problem.
W. Prager and P. G. Hodge, Theory of perfectly plastic solids, Wiley, New York, 1951
- E. T. Onat and W. Prager, The necking of a tension specimen in plane plastic flow, J. Appl. Phys. 25 (1954), 491–493. MR 62627
S. B. Batdorf and B. Budiansky, Polyaxial stress-strain relations of strain-hardening metal, J. of Applied Mech. 21 (1954)
- R. Hill, On the problem of uniqueness in the theory of a rigid-plastic solid. I, J. Mech. Phys. Solids 4 (1956), 247–255. MR 79420, DOI https://doi.org/10.1016/0022-5096%2856%2990033-3
- R. Hill, Discontinuity relations in mechanics of solids, Progress in Solid Mechanics, Vol. II, North-Holland, Amsterdam, 1961, pp. 245–276. MR 0128115
A. S. Balchan and H. G. Drichamer, High pressure electrical resistance cell and calibration points above 100 kilobars, Rev. Sci. Instruments 32 (1961)
- E. M. Shoemaker, A theory of linear plasticity for plane strain, Arch. Rational Mech. Anal. 14 (1963), 283–300. MR 157550, DOI https://doi.org/10.1007/BF00250707
W. Prager and P. G. Hodge, Theory of perfectly plastic solids, Wiley, New York, 1951
E. T. Onat and W. Prager, The necking of a tension specimen in plane plastic flow, J. of Applied Physics 25 (1954)
S. B. Batdorf and B. Budiansky, Polyaxial stress-strain relations of strain-hardening metal, J. of Applied Mech. 21 (1954)
R. Hill, On the problem of uniqueness in the theory of a rigid-plastic solid. I, J. of the Mech. and Physics of Solids 4 (1956)
R. Hill, Discontinuity relations in mechanics of solids, Progress in Solid Mechanics, Vol. II, North-Holland, Amsterdam, 1961
A. S. Balchan and H. G. Drichamer, High pressure electrical resistance cell and calibration points above 100 kilobars, Rev. Sci. Instruments 32 (1961)
E. M. Shoemaker, A Theory of linear plasticity for plane strain, Arch, for Rational Mech. and Anal. 14 (1963)
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Article copyright:
© Copyright 1966
American Mathematical Society