Universal motions for constrained simple materials

International Journal of Non-Linear Mechanics

Volumn 34, Issue 3, 1999, Pages 469-484

  Pucci, Edvige ^a   Saccomandi, Giuseppe ^a  

^a UNIVERSITY OF PERUGIA   (Italy)

Author keywords

Constrained elasticity; Simple materials; Universal motions

Indexed keywords

EID: 0011700930     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7462(98)00033-X     Document Type: Article

References (23)

1. R.S. Rivlin, in: G.I. Barenblatt, D.D. Joseph (Eds), Collected Papers, Springer, New York, 1997.
2. J.L. Ericksen, Deformations possible in every isotropic, incompressible, perfectly elastic body, ZAMP 5 (1954) 466-488.
3. J.L. Ericksen, Deformations possible in every isotropic compressible, perfectly elastic material, J. Math. Phys. 34 (1965) 126-128.
4. M.F. Beatty, Topics in finite elasticity: hyperelasticity of rubber, elastomers, and biological tissues - with examples, Appl. Mech. Rev. 40 (1987) 1699-1733.
5. J.F. Bell, The decrease of volume during loading to and coaxiality to finite plastic strain, Meccanica 31 (1996) 461-472.
6. M.F. Beatty, M.A. Hayes, Deformations of an elastic, internally constrained material, part 1: homogeneous deformations, J. Elasticity 29 (1992) 1-84.
7. E. Pucci, G. Saccomandi, Universal generalized plane deformations in constrained elasticity, Math. Mech. Solids 3 (1998) 201-216.
8. E. Pucci and G. Saccomandi, Some universal solutions for totally inextensible isotropic constrained materials, Quart. J. Mech. Appl. Math. 49 (1996) 147-162.
9. C. Truesdell, W. Noll, The Nonlinear Field Theories of Mechanics, Handbuch der Physik III/3, Springer, New York, 1965.
10. M.M. Carroll, Controllable deformations in incompressible simple materials, Int. J. Engng. Sci. 5 (1967) 515-525.
11. B.D. Coleman, C. Truesdell, Homogeneous motions of incompressible materials, ZAMM 45 (1965) 547-551.
12. R.L. Fosdick, Dynamically possible motions of incompressible isotropic simple materials, Arch. Rat Mech. Anal. 29 (1968) 272-288.
13. C. Truesdell, Solutio generalis et accurata problematum quamplurimorum de motu corporum elasticorum imcomprimibilium in deformatibus valde magnis. Arch. Rat Mech. Anal. 11, 106-113; Addendum, 1963 ibid. 12 (1962) 427-428.
14. C. Truesdell, Solutio generalis et accurata problematum quamplurimorum de motu corporum elasticorum imcomprimibilium in deformatibus valde magnis. Arch. Rat Mech. Anal. 11, 106-113; Addendum, 1963 ibid. 12 (1962) 427-428.
15. C.C. Wang, Proof that all dynamic universal solutions are quasi-equilibrated, ZAMM 50 (1970) 311-314.
16. F. Andreussi, P. Podio Guidugli, Thermomechanical constraints in simple materials, Bull. Acad. Polonaise de Sci. XXI (1973) 199-205.
17. P. Podio-Guidugli, M. Vianello, Constraint manifolds for isotropic solids, Arch. Rat. Mech. Anal. 105 (1989) 105-121.
18. M.A. Hayes, K.R. Rajagopal, Inhomogeneous finite amplitude motions in a neo-Hookean solid, Proc. R. Ir. Acad. 92A (1992) 137-147.
19. A.W. Marris, J.F. Shiau, Universal deformations in isotropic incompressible hyperelastic materials when the deformation tensor has equal proper values, Arch. Rat. Mech. Anal. 36 (1970) 135-160.
20. L.C. Martins, F.P. Duda, Plane deformations with constant strain invariants. Programa da engenharia mecanica relatorio interno 7/97 Universidade Federal do Rio de Janeiro (1997).
21. R.L. Fosdick, Remarks on compatibility. In: S. Eskinazi (Ed), Modern Developments in the Mechanics of Continua, Academic Press, New York, (1966) pp. 109-127.
22. M.F. Beatty, M.A. Hayes, Deformations of an elastic, internally constrained material, part 2: nonhomogeneous deformations, Quart. J. Mech. Appl. Math. 45 (1992) 663-709.
23. M.M. Carroll, Some results on finite amplitude elastic waves. Acta Mech. III (1967) 167-181.