Strain-Rate-Dependent Deformation Behavior of Carbon-Black-Filled Rubber under Monotonic and Cyclic Straining


Article Preview

The constitutive equation of rubber is derived by employing a nonaffine molecular chain network model for an elastic deformation behavior and the reptation theory for a viscoelastic deformation behavior. The results reveal the roles of the individual springs and dashpot, and the strain rate dependence of materials and disentanglement of molecular chains in the monotonic and cyclic deformation behaviors, particularly softening and hysteresis loss, that is, the Mullins effect, occurring in stress-stretch curves under cyclic deformation processes.



Key Engineering Materials (Volumes 340-341)

Edited by:

N. Ohno and T. Uehara




Y. Tomita et al., "Strain-Rate-Dependent Deformation Behavior of Carbon-Black-Filled Rubber under Monotonic and Cyclic Straining", Key Engineering Materials, Vols. 340-341, pp. 1017-1024, 2007

Online since:

June 2007




[1] L. Mullins, Softening of rubber by deformation. Rubber Chem. Technol. 42(1969) 339.

[2] J.S. Bergstrom and M.C. Boyce, Mechanical behavior of particle filled elastomers. Rubber Chem. Technol. 72 (1999) 633.

[3] Y. Tomita, T. Adachi and S. Tanaka, Modelling and application of constitutive equation for glassy polymer based on nonaffine network theory. Eur. J. Mech. A/Solids 16 (1997) 475.

[4] M. Doi and S.F. Edwards. The Theory of Polymer Dynamics. (1986), 16-28. Oxford University Press.

[5] K. Yashiro, T. Itho and Y. Tomita, Molecular dynamics simulation of deformation behavior in amorphous polymer: nucleation of chain entanglements and network structure under uniaxial tension. Int. J. Mech. Sci., 45(2003)1863-1876.


[6] E. M. Arruda and M. C. Boyce, A three-dimensional constitutive model for large stretch behavior of rubber materials. J. Mech. Phys. Solids 41 (1993) 389.

[7] J. S. Bergstrom and M. C. Boyce, Large strain time-dependent behavior of filled elastomers. Mech. Mater. 32 (2000) 627.


[8] Y, Higa and Y. Tomita, Computational prediction of mechanical properties of nickel-based superalloy with gamma prime phase precipitates. Advance Materials and Modeling of Mechanical Behavior, III, pp.1061-1066, eds. F. Ellyin and J.W. Provan, Fleming Printing Ltd., Victoria, B.C., Canada (1999).

[9] Yoshihiro Tomita, Wei Lu, Masato Naito and Yasuhiro Furutani Numerical Evaluation of Micro- to Macroscopic Mechanical Behavior of Carbon-Black-Filled Rubber Int. J. Mech. Sci. 48-2 (2005) 108-116.