Modeling and Numerical Simulations with Compressible Damaged Hyperelastic Law: Application to the Laminated Rubber Bearing

Maha Zaghdoudi, Zohra Gaiech, Lamia Bejaoui, Zoubeir Tourki, Adnane Boukamel

Laboratoire de Mécanique de Sousse, Université de Sousse (ENISo) Technop?le de Sousse, Sousse, Tunisia.
Laboratoire de Mécanique et d’Acoustique de Marseille, Technop?le de Chateau-Gombert, Marseille Cedex, France.

DOI: 10.4236/msa.2012.311119                

Abstract

Hyperelastic model with damage induced compressibility is implemented in the ABAQUS software using the subrou- tine Umat. A thermodynamic model is proposed taking into account the nonlinearity of the material behavior. Within the present work, the behavior of laminated rubber bearing structure is studied for two geometrical sets of materials (A-type and equivalent material) under complex monotonic loading conditions. A new geometric edge of laminated rubber bearing is proposed in order to reduce the development costs of the structure. The proposed model allowed finding a good homogenized damage distribution for the same overall stiffness.

Keywords

Elastomer and Rubber; Failure Analysis; Mechanical Behavior

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	R. S. Rivlin and D. W. Saunders, “Large Elastic Deformations of Isotropic Materials. VII. Experiments on the Deformation of Rubber,” Philosophical Transactions of the Royal Society of London Serie A, Vol. 243, 1951, pp. 251-288. doi:10.1098/rsta.1951.0004
[2]	L. R. G. Treloar, “Stress-Strain Data for Vulcanized Rubber under Various Types of Deformation,” Transactions Faraday Society, Vol. 40, 1944, pp. 59-70. doi:10.1039/tf9444000059
[3]	R. W. Ogden, “Non Linear Elastic Deformations,” Editora Horwood, Halsted Press, New York, 1984, p. 532.
[4]	R. J. Farris, “The Influence of Vacuole Formation on the Response and Failure of Filled Elastomers,” Transactions of the Society of Rheology, Vol. 12, 1968, pp. 315-334. doi:10.1122/1.549111
[5]	N. A. Hocine, A. Hamdi, M. N. Abdelaziz, P. Heuillet and F. Za?ri, “Experimental and Finite Element Investigation of Void Nucleation in Rubber-Like Materials,” Inter national Journal of Solids and Structures, Vol. 48, 2011, pp. 1248-1254. doi:10.1016/j.ijsolstr.2011.01.009
[6]	F. Jazzar, “Numerical Simulation of the Quasi-Incompressible Hyperelastic Behaviour of Rubber with Steel Plates Structures and Experimental Validation,” PhD. Thesis, Aix-Marseille II University, 1993.
[7]	F. Andrieux, “On Damaged Visco-Hyperelastic Media,” PhD. Thesis, UTC Compiegne, 1996.
[8]	F. Andrieux, K. Saanouni and F. Sidoroff, “On Hyperelastic Solids with Damage Induced Compressibility,” Mechanics of Solids and Structures, Vol. 324, 1997, pp. 281-288.
[9]	F. Andrieux, K. Saanouni and F. Sidoroff, “Damaged Hyperelastic Solid with an Induced Volume Variation. Effect of Loading Paths,” Damage Mechanics in Engineering Materials, Vol. 46, 1998, pp. 503-520.
[10]	J. A. Weiss, “A Constitutive Model and Finite Element Representation for Transversely Isotropic Soft Tissues,” PhD. Thesis, University of Utah, 1994.
[11]	J. A. Weiss, B. N. Maker and S. Govindjee, “Finite Element Implementation of Incompressible, Transversely Isotropic Hyperelasticity,” Computer Methods in Applied Me chanics and Engineering, Vol. 135, 1996, pp. 107-128. doi:10.1016/0045-7825(96)01035-3
[12]	M. Itskov and N. Aksel, “A Class of Orthotropic and Transversely Isotropic Hyperelastic Constitutive Models Based on a Polyconvex Strain Energy Function,” International Journal of Solids and Structures, Vol. 41, 2004, pp. 3833-3848. doi:10.1016/j.ijsolstr.2004.02.027
[13]	J. Lema?tre and J. L. Chaboche, “Mechanics of Solid Materials,” 2nd Edition, Greco-Dunod, Paris, 2001.
[14]	C. W. Macosco, “Rheology Principles, Measurements and Applications,” VCH Publishers, New York, 1994