A finite element implementation of knowles stored-energy function: Theory, coding and applications

Archive of Mechanical Engineering

Volumn 58, Issue 3, 2011, Pages 319-346

  Suchocki, Cyprian ^a  

^a WARSAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Constitutive equation; Elasticity tensor; Finite element method; Hyperelasticity; Material Jacobian; Stored energy potential; Tangent modulus tensor

Indexed keywords

EID: 84860495943     PISSN: 00040738     EISSN: None     Source Type: Journal    
DOI: 10.2478/v10180-011-0021-7     Document Type: Article

References (25)

1. "ABAQUS Verification Manual", ABAQUS, Inc. Providence, 2008.
2. Bonet J., Wood R. D.: "Nonlinear continuum mechanics for finite element analysis", 1997, Cambridge University Press, Cambridge.
3. Bouchart V.: "Experimental study and micromechanical modeling of the behavior and damage of reinforced elastomers", Ph.D. thesis, University of Sciences and Technologies, 2008, Lille.
4. Bouvard J. L., Ward D. K., Hossain D., Marin E. B., Bammann D. J., Horstemeyer M. F.: "A general inelastic internal state variable model for amorphous glassy polymers", Acta Mechanica, 213, 2010, pp. 71-96.
5. Ciambella J., Destrade M., Ogden R. W.: "On the ABAQUS FEA model of finite viscoelasticity", Rubber Chemistry and Technology, 82, 2, 2009, pp. 184-193.
6. Dettmar J.: "A finite element implementation of Mooney-Rivlin's strain energy function in Abaqus", Technical Report, University of Calgary, Department of Civil Engineering, 2000, Calgary.
7. Elleuch R., Taktak W.: "Viscoelastic Behavior of HDPE Polymer using Tensile and Compressive Loading", Journal of Materials Engineering and Performance, 15, 1, 2006, pp. 111-116. (Pubitemid 43294050)
8. Fung Y. C.: "Foundations of solid mechanics", 1969, PWN, Warsaw (in Polish).
9. Holzapfel G. A.: "Nonlinear solid mechanics", 2010 John Wiley & Sons Ltd., New York.
10. Jemioło S.: "A study on the hyperelastic properties of isotropic materials", Scientific Surveys Warsaw University of Technology, Building Engineering, 140, OW PW, 2002 Warsaw (in Polish).
11. Knowles J. K.: "The finite anti-plane shear field near the tip of a crack for a class of incompressible elastic solids", International Journal of Fracture, 13, 1977, pp. 611-639.
12. Knowles J. K.: "On the dissipation associated with equilibrium whocks in finite elasticity", Journal of Elasticity, 9, 1979, pp. 131-158.
13. Knowles J. K., Sternberg E.: "Discontinous deformation gradients near the tip of a crack in finite anti-plane shear: an example", Journal of Elasticity, 10, 1980, pp. 81-110. (Pubitemid 10472497)
14. Miehe Ch.: "Numerical computation of algorithmic (consistent) tangent moduli in larde-strain computational inelasticity", Computer methods in applied mechanics and engineering, 134, 1996, pp. 223-240.
15. Ogden R. W.: "Non-linear elastic deformations", 1997, Dover Publications, Inc., Mineola, New York.
16. Ogden R. W.: "Nonlinear Elasticity with Application to Material Modelling", 2003, Lecture Notes, 6, IPPT PAN, Warsaw.
17. Ostrowska-Maciejewska J.: "Mechanics of deformable bodies", 1994, PWN, Warsaw (in Polish).
18. Ostrowska-Maciejewska J.: "Foundations and applications of tensor calculus", 2007, IPPT PAN, Warsaw (in Polish).
19. Perzyna P.: "Theory of viscoplasticity", 1966, PWN, Warsaw (in Polish).
20. Sobieski W.: "GNU Fortran with elements of data visualization", 2008, W UWM, Olsztyn (in Polish).
21. Soares J. P.: "Constitutive modeling for biodegradable polymers for application in endovascular stents", 2008, Ph.D. thesis, Texas A&M University.
22. Soares J. P., Rajagopal K. R., Moore J. E. Jr.: "Deformation-induced hydrolysis of a degradable polymeric cylindrical annulus", 2010, Biomechanics and Modeling in Mechanobiology, 9, pp. 177-186.
23. Stein E., Sagar G.: "Convergence behavior of 3D finite elements for Neo-Hookean material", 2008, Engineering Computations: International Journal for Computer-Aided-Engineering and Software, 25(3), pp. 220-232.
24. Skalski K., Pawlikowski M., Suchocki C.: "Constitutive equations and functional adaptation of bone tissue", in R. Bedzinski ed., "Technical Mechanics part XII: Biomechanics", 2011, IPPT PAN, Warsaw (in Polish).
25. Weiss J. A.: "A constitutive model and finite element representation for transversely isotropic soft tissues", 1994, Ph.D. thesis, University of Utah, Salt Lake City.