Shear localization with an Arrhenius flow law

SIAM Journal on Applied Mathematics

Volumn 60, Issue 6, 2000, Pages 1867-1886

  Flemming, R P ^a   Olmstead, W E ^b   Davis, S H ^b  

^a HARVEY MUDD COLLEGE   (United States)

^b Northwestern University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; DIFFUSION; HEAT TRANSFER; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; SHEARING; STRESSES; THERMAL EFFECTS; THERMOPLASTICS;

ARRHENIUS FLOW; RESPONSE CURVES; SHEAR BANDS;

SHEAR DEFORMATION;

EID: 0034478368     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139999350548     Document Type: Article

References (16)

1. Y. BAI (1990), Adiabatic shear banding, Res. Mechanica, 31, pp. 133-203.
2. Y. BAI (1982), Thermo-plastic instability in simple shear, J. Mech. Phys. Solids, 30, pp. 195-207.
3. T. J. BURNS (1990), A mechanism for shear band formation in the high strain rate torsion test, J. Appl. Mech., 112, pp. 836-844.
4. H. T.-Z. CHEN, A. S. DOUGLAS, AND R. MALEK-MADANI (1989), An asymptotic stability condition for inhomogeneous simple shear, Quart. Appl. Math, 47, pp. 247-262.
5. H. T. DAVIS (1962), Introduction to Nonlinear Differential and Integral Equations, Dover, New York.
6. D. W. DROTT AND R. ARIS (1969), Communications on the theory of diffusion and reaction - I: A complete parametric study of the first-order, irreversible exothermic reaction in a flat slab of catalyst, Chem. Engrg. Sci., 24, pp. 541-551.
7. A. K. KAPILA (1983), Asymptotic Treatment of Chemically Reacting Systems, Pitman, Boston.
8. H. B. KELLER AND D. S. COHEN (1967), Some positone problems suggested by nonlinear heat generation, J. Math Mech., 16, pp. 1361-1376.
9. U. F. KOCHS, A. S. ARGON, AND M. F. ASHBY (1975), Thermodynamics and Kinetics of Slip, Pergamon Press, Oxford, UK.
10. J. H. MADDOCKS AND R. MALEK-MADANI (1992), Stability of localized steady state solutions in thermoplasticity, Internat. J. Solids Structures, 29, pp. 2039-2061.
11. W. E. OLMSTEAD, S. NEMAT-NASSER, AND L. NI (1994), Shear bands as surfaces of discontinuity, J. Mech. Phys. Solids, 42, pp. 697-709.
12. T. G. SHAWKI AND R. J. CLIFTON (1989), Shear band formation in thermal viscoplastic materials, Mech. Mat., 8, pp. 13-42.
13. J. W. WALTER (1992), Numerical experiments on adiabatic shear band formation in one dimension, Int. J. Plasticity, 8, pp. 657-693.
14. T. W. WRIGHT (1987), Steady shearing in a viscoplastic solid, J. Mech. Phys. Solids, 35, pp. 269-282.
15. T. W. WRIGHT AND R. C. BATRA (1985), The initiation and growth of adiabatic shear bands, Int. J. Plasticity, 1, pp. 205-212.
16. F. J. ZERILLI AND R. W. ARMSTRONG (1987), Dislocation mechanics based constitutive relations for material dynamics calculations, J. Appl. Phys., 61, p. 1816.