A generalization of Hencky's strain-energy density to model the large deformations of slightly compressible solid rubbers

Mechanics of Materials

Volumn 41, Issue 8, 2009, Pages 943-950

  Horgan, C O ^a   Murphy, J G ^b  

^a University of Virginia   (United States)

^b DUBLIN CITY UNIVERSITY   (Ireland)

Author keywords

Constitutive modeling; Experimental data; Hencky strain energy function; Slightly compressible rubber

Indexed keywords

AXIAL STRETCH; COMPRESSION TESTS; CONSTITUTIVE MODELING; CONSTITUTIVE RELATIONS; EXPERIMENTAL DATA; HENCKY STRAIN-ENERGY FUNCTION; ISOTROPIC SOLIDS; LARGE DEFORMATIONS; LINEARIZATION PROCESS; POWER LAW RELATION; POWER-LAW RELATIONSHIP; SLIGHTLY COMPRESSIBLE RUBBER; SOLID RUBBER; SPECIAL FORMS; STRAIN ENERGY DENSITY; STRAIN ENERGY FUNCTIONS; STRESS RESPONSE; VOLUME CHANGE;

COMPRESSION TESTING; DEFORMATION; KINEMATICS; STRAIN ENERGY;

RUBBER;

EID: 65649116760     PISSN: 01676636     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mechmat.2009.03.001     Document Type: Article

References (22)

1. Anand L. On H. Hencky's approximate strain-energy function for moderate deformations. J. Appl. Mech. 46 (1979) 78-82
2. Aron M. On certain deformation classes of compressible Hencky materials. Math. Mech. Solids 11 (2006) 467-478
3. Beatty M.F., and Stalnaker D.O. The Poisson function of finite elasticity. J. Appl. Mech. 108 (1986) 807-813
4. Bechir H., Chevalier L., Chaouche M., and Boufala K. Hyperelastic constitutive model for rubber-like materials based on the first Seth strain measures invariant. Eur. J. Mech. A/Solids 25 (2006) 110-124
5. Blatz P.J., and Ko W. Application of finite elasticity theory to the deformation of rubbery materials. Trans. Soc. Rheol. 6 (1962) 223-251
6. Bruhns O.T., Xiao H., and Meyers A. Hencky's elasticity model with the logarithmic strain measure: a study on Poynting effect and stress response in torsion of tubes and rods. Arch. Mech. 52 (2000) 489-509
7. Bruhns O.T., Xiao H., and Meyers A. Constitutive inequalities for an isotropic elastic strain-energy function based on Hencky's logarithmic strain tensor. Proc. R. Soc. Lond. A 457 (2001) 2207-2226
8. Bruhns O.T., Xiao H., and Meyers A. Finite bending of a rectangular block of an elastic Hencky material. J. Elasticity 66 (2002) 237-256
9. Christensen R.G., and Hoeve C.A.J. Comparison between theoretical and experimental values of the volume changes accompanying rubber extension. J. Polym. Sci. A1 8 (1970) 1503-1512
10. Copeland L.E. The thermodynamics of a strained elastomer, II. Compressibility. J. Appl. Phys. 19 (1948) 445-449
11. Fong J.T., and Penn R.W. Construction of a strain-energy function for an isotropic elastic material. Trans. Soc. Rheol. 19 (1975) 99-113
12. Hencky H. Uber die Form des Elastizitatsgesetzes bei ideal elastischen Stoffen. Z. Techn. Phys. 9 (1928) 215-220
13. Horgan C.O., and Murphy J.G. Constitutive models for almost incompressible isotropic elastic rubber-like materials. J. Elasticity 87 (2007) 133-146
14. Horgan C.O., and Murphy J.G. The effects of compressibility on inhomogeneous deformations for a class of almost incompressible isotropic nonlinearly elastic materials. J. Elasticity 88 (2007) 207-221
15. Horgan, C.O., Murphy, J.G., 2009a. Compression tests and constitutive models for the slight compressibility of elastic rubber-like materials. Int. J. Eng. Sci. (A.J.M. Spencer Memorial Volume), in press, doi:10.1016/j.ijengsci.2008.10.009.
16. Horgan C.O., and Murphy J.G. Constitutive modeling for moderate deformations of slightly compressible rubber. J. Rheol. 53 (2009) 153-168
17. Murphy J.G. Strain energy functions for a Poisson power law function in simple tension of compressible hyperelastic materials. J. Elasticity 60 (2000) 151-164
18. Penn R.W. Volume changes accompanying the extension of rubber. Trans. Soc. Rheol. 14 (1970) 509-517
19. Rivlin, R.S., 1997. Collected Papers of R.S. Rivlin. In: Barenblatt, G.I., Joseph, D.D. (Eds.), vol. 1. Springer-Verlag, New York.
20. Rivlin R.S., and Saunders D.W. Large elastic deformations of isotropic materials. VII. Experiments on the deformation of rubber. Phil. Trans. R. Soc. Lond. A 243 (1951) 251-288
21. Storåkers B. On material representation and constitutive branching in finite compressible elasticity. J. Mech. Phys. Solids 34 (1986) 125-145
22. 2. Rubber Chem. Technol. 37 (1964) 850-865