Linear relationship between the first invariants of the stress and strain tensors in theories of plasticity with strain hardening

International Applied Mechanics

Volumn 43, Issue 3, 2007, Pages 291-302

  Shevchenko, Yu N ^a   Terekhov, R G ^a   Tormakhov, N N ^a  

^a S P TIMOSHENKO INSTITUTE OF MECHANICS   (Ukraine)

Author keywords

Eulerian and Lagrangian coordinates; First invariants; Linear relationship; Solid body; Stress and strain tensors

Indexed keywords

EULERIAN AND LAGRANGIAN COORDINATES; FIRST INVARIANTS; LINEAR RELATIONSHIP; SOLID BODY; STRESS AND STRAIN TENSORS;

LINEAR SYSTEMS; PLASTICITY; PROBLEM SOLVING; STRAIN MEASUREMENT; TENSORS;

STRESS-STRAIN CURVES;

EID: 34548188285     PISSN: 10637095     EISSN: 15738582     Source Type: Journal    
DOI: 10.1007/s10778-007-0024-8     Document Type: Article

References (15)

1. N. N. Tormakhov, S. P. Gemma, S. M. Zakharov, and A. V. Marishchuk, A Strain Gauge [in Russian], USSR Inventor's Certificate No. 1288492 MKI G-01B 5/30, Byul. Izobr., No. 5 (1987).
2. P. W. Bridgman, Studies in Large Plastic Flow and Fracture, McGraw Hill, New York (1952).
3. A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, Cambridge Univ. Press (1959).
4. N. N. Malinin, Applied Theory of Plasticity and Creep [in Russian], Mashinostroenie, Moscow (1975).
5. V. V. Novozhilov, Theory of Elasticity [in Russian], Sudpromgiz, Leningrad (1958).
6. N. I. Chernyak, Mechanical Properties of Steel under Small Plastic Strains [in Russian], Izd. AN USSR, Kyiv (1962).
7. Yu. N. Shevchenko, M. E. Babeshko, and R. G. Terekhov, Thermoviscoelastoplastic Deformation of Structural Members [in Russian], Naukova Dumka, Kyiv (1992).
8. Yu. N. Shevchenko and R. G. Terekhov, Physical Equations of Thermoviscoplasticity [in Russian], Naukova Dumka, Kyiv (1982).
9. Yu. N. Shevchenko, R. G. Terekhov, and N. N. Tormakhov, "Constitutive equations for describing the elastoplastic deformation of elements of a body along small-curvature paths in view of the stress mode," Int. Appl. Mech., 42, No. 4, 421-430 (2006).
10. Yu. N. Shevchenko, N. N. Tormakhov, and R. G. Terekhov, "Specification of scalar functions of the tensor-nonlinear constitutive equations in the theory of plasticity," Int. Appl. Mech., 36, No. 10, 1329-1338 (2000).
11. M. E. Babeshko and Yu. N. Shevchenko, "Elastoplastic axisymmetric stress-strain state of laminated shells made of isotropic and transversely isotropic materials with different moduli," Int. Appl. Mech., 41, No. 8, 910-916 (2005).
12. V. V. Piskun, "Elastoplastic deformation of compound disk under impulsive loading," Int. Appl. Mech., 41, No. 4, 421-425 (2005).
13. V. G. Savchenko, "Nonaxisymmetric deformation of solids of revolution made of elastic orthotropic materials with different tensile and compressive moduli," Int. Appl. Mech., 41, No. 7, 748-756 (2005).
14. Yu. N. Shevchenko and I. V. Prokhorenko, "Thermoelastoplastic stress-strain state of rectangular plates," Int. Appl. Mech., 41, No. 10, 1130-1137 (2005).
15. M. Zyczkowski, Combined Loadings in the Theory of Plasticity, PWN, Warsaw (1981).