On evolution equations for elastic deformation and the notion of hyperelasticity

International Journal of Engineering Science

Volumn 47, Issue 1, 2009, Pages 76-82

  Rubin, M B ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Elastic deformation; Evolution equations; Hyperelasticity; Plasticity

Indexed keywords

CONSTITUTIVE EQUATIONS; CONTROL NONLINEARITIES; CONTROL THEORY; DIFFERENTIAL EQUATIONS; ELASTIC DEFORMATION; ELASTICITY; PROBABILITY DENSITY FUNCTION; STRAIN ENERGY;

ELASTIC PLASTICS; ELASTIC RANGES; EVOLUTION EQUATIONS; HYPER ELASTICITIES; HYPERELASTICITY; MATERIAL RESPONSES; NON LINEARITIES; STRAIN ENERGY FUNCTIONS; STRAIN MEASURES; VISCOPLASTIC MATERIALS; WORK CONDITIONS;

DEFORMATION;

EID: 57649097345     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijengsci.2008.07.003     Document Type: Article

References (19)

1. Truesdell C.A. Hypo-elasticity. J. Math. Mech. 4 (1955) 323-425
2. Truesdell C., and Noll W. The Nonlinear Field Theories of Mechanics (1965/1992), Springer-Verlag, Berlin
3. Ogden R.W. Non-linear Elastic Deformations (1984), Dover, New York
4. Bernstein B. Hypo-elasticity and elasticity. Arch. Ration. Mech. Anal. 6 (1960) 89-104
5. Olsen E.T., and Bernstein B. A class of hypo-elastic non-elastic materials and their thermodynamics. Arch. Ration. Mech. Anal. 86 (1984) 291-303
6. Bernstein B., and Rajagopal K.R. Thermodynamics of hypoelasticity. Z. Angew. Math. Phys. 59 (2008) 537-553
7. Rajagopal K.R. On implicit constitutive equations. Appl. Math. 48 (2003) 279-319
8. Rajagopal K.R. The elasticity of elasticity. J. Appl. Math. Phys. 58 (2007) 309-317
9. Rajagopal K.R., and Srinivasa A.R. On the response of non-dissipative solids. Proc. R. Soc. A 463 (2007) 357-367
10. Eckart C. The thermodynamics of irreversible processes. IV. The theory of elasticity and anelasticity. Phys. Rev. 73 (1948) 373-382
11. Besseling J.F. A thermodynamic approach to rheology. In: Parkus H., and Sedov L.I. (Eds). Proceedings of the IUTAM Symposium on Irreversible Aspects of Continuum Mechanics and Transfer of Physical Characteristics in Moving Fluids, Vienna (1966) (1968), Springer-Verlag, Wein 16-53
12. Leonov A.I. Nonequilibrium thermodynamics and rheology of viscoelastic polymer media. Rheol. Acta 15 (1976) 85-98
13. Rubin M.B. Plasticity theory formulated in terms of physically based microstructural variables - Part I: Theory. Int. J. Solids Struct. 31 (1994) 2615-2634
14. Rubin M.B. On the treatment of elastic deformation in finite elastic-viscoplastic theory. Int. J. Plasticity 12 (1996) 951-965
15. Rubin M.B. Physical reasons for abandoning plastic deformation measures in finite plasticity and viscoplasticity theory. Arch. Mech. 53 (2001) 519-539
16. Leonov A.I. On the conditions of potentiality in finite elasticity and hypo-elasticity. Int. J. Solids Struct. 37 (2000) 2565-2576
17. Xiao H., Bruhns O.T., and Meyers A. The integrability criterion in finite elastoplasticity and its constitutive implications. Acta Mech. 188 (2007) 227-244
18. Noll W. On the continuity of the solid and fluid states. Indiana Univ. Math. J. 4 (1955) 3-81
19. Onat E.T. The notion of state and its implications in thermodynamics of inelastic solids. In: Parkus H., and Sedov L.I. (Eds). Proceedings of the IUTAM Symposium on Irreversible Aspects of Continuum Mechanics and Transfer of Physical Characteristics in Moving Fluids Vienna (1966) (1968), Springer-Verlag, Wein 292-314