Some topics on a new class of elastic bodies

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 465, Issue 2105, 2009, Pages 1377-1392

  Bustamante, Roger ^a  

^a UNIVERSITY OF CHILE   (Chile)

Author keywords

Constraints; Elasticity; Green elastic material; Weak formulation

Indexed keywords

DEFORMATION;

CAUCHY STRESS TENSORS; CONSTRAINTS; ELASTIC BODY; ENERGY FUNCTIONS; GREEN ELASTIC MATERIAL; NEW CLASS; WEAK FORMULATION;

ELASTICITY;

EID: 67149109827     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2008.0427     Document Type: Article

References (24)

1. Blume, J. A. 1989 Compatibility conditions for left Cauchy-Green strain field. J. Elast. 21, 271-308. (doi:10.1007/BF00045780)
2. Bustamante, R. and Rajagopal, K. R. In press. A note on plain strain and stress problems for a new class of elastic bodies. Math. Mech. Solids.
3. Ciarlet, P. G. 1988 Mathematical elasticity Volume I: three dimensional elasticity. Amsterdam, The Netherlands: Elsevier/North Holland.
4. Dill, E. H. 1977 The complementary energy principle in nonlinear elasticity. Lett. Appl. Eng. Sci. 5, 95-106.
5. Eringen, A. C. 1980 Mechanics of continua, 2nd edn. New York, NY: Krieger Publishing Company.
6. Finzi, B. 1934 Integrazione delle equazioni indefinite della mecanica dei sistemi continui. Rend. Lincei. 19, 578-584.
7. Fosdick, R. L. 1966 Remarks on compatibility. In Modern developments in the mechanics of continua (ed. S. Eskinazi), pp. 109-127. New York, NY: Academic Press.
8. Love, A. E. H. 1944 Treatise on the mathematical theory of elasticity, 4th edn. New York, NY: Dover.
9. Mollica, F., Ventre, M., Sarracino, F., Ambrosio, L. and Nicolais, L. 2007 Implicit constitutive equations in the modeling of bimodulars materials: an application to biomaterials. Comput. Math. Appl. 53, 209-218. (doi:10.1016/j.camwa.2006.02.020)
10. Muskhelishvili, N. I. 1953 Some basic problems of the mathematical theory of elasticity. Groningen- Holland, The Netherlands: Noordhoff.
11. Noll, W. 1978 A general framework for problems in the statics of finite elasticity. In Contemporary developments in continuum mechanics and partial differential equations (eds G. M. de La Penha and L. A. Medeiros), pp. 363-387. Amsterdam, The Netherlands: North Holland.
12. Ogden, R. W. 1975 A note on variational theorems in non-linear elastostatics. Math. Proc. Camb. Philos. Soc. 77, 609-615. (doi:10.1017/S0305004100051422)
13. Ogden, R. W. 1997 Non-linear elasticity. Mineola, NY: Dover.
14. Podio-Guidugli, P. 2000 A primer in elasticity. J. Elast. 58, 1-104. (doi:10.1023/A:1007672721487)
15. Rajagopal, K. R. 2003 On implicit constitutive theories. Appl. Math. 48, 279-319. (doi:10.1023 /A:1026062615145)
16. Rajagopal, K. R. 2007 The elasticity of elasticity. Z. Angew. Math. Phys. 58, 309-317. (doi:10. 1007/s00033-006-6084-5)
17. Rajagopal, K. R. and Saccomandi, G. 2005 On internal constraints in continuum mechanics. Diff. Equat. Nonlin. Mech. 2006, 18572. (doi:10.1155/DENM/2006/18572)
18. Rajagopal, K. R. and Srinivasa, A. R. 2007 On the response of non-dissipative solids. Proc. R. Soc. A 463, 357-367. (doi:10.1098/rspa.2006.1760)
19. Saada, A. S. 1993 Elasticity: theory and application. Malabar, FL: Krieger Publishing Company.
20. Spencer, A. J. M. 1971 Theory of invariants. In Continuum physics I (ed. A. C. Eringen), pp. 239-535. New York, NY: Academic Press.
21. Truesdell, C. and Noll, W. 2004 The non-linear field theories of mechanics (ed. S. S. Antman), 3rd edn. Berlin, Germany: Springer
22. Truesdell, C. and Toupin, R. 1960 The classical field theories. In Handbuch der Physik, vol. III/1. Berlin, Germany: Springer.
23. Zheng, Q. S. 1994 Theory of representations for tensor functions-a unified invariant approach to constitutive equations. Appl. Mech. Rev. 47, 545-587.
24. Zhong-Heng, G. 1980 The unified theory of varational principles in nonlinear elasticity. Arch. Mech. 32, 577-596.