A Mathematical Model for Predicting the Relaxation of Creep Strains in Materials
Issue: 2012 - Volume 2 [Issue 3]
Marc Delphin Monsia *
Département de Physique, Université d’Abomey-Calavi, Abomey-Calavi, Bénin, 09 B.P. 305, Cotonou, Bénin.
*Author to whom correspondence should be addressed.
To describe the time dependent response of a variety of viscoelastic materials, a one-dimensional nonlinear rheological mathematical model with constant material parameters is developed by using the stress decomposition theory. The model represents, under relaxation of stress, the time versus deformation variation as a decay Gompertz-type function, which is able to reproduce the qualitative decay sigmoid shape of the experimental creep relaxation data of a variety of materials. Numerical applications performed shown that the model is very sensitive to material parameters variation and particularly to the total deformation experienced by the material of interest under creep process. It is also found that the damping viscosity relative increase reduces significantly the magnitude of the maximum value of the rate of recovery.
Keywords: Gompertz-type model, logarithmic elastic force, Kelvin-Voigt model, mathematical modeling, viscoelasticity