Modeling of the effective and macroscopic ageing behavior of viscoelastic composite materials

¹ MMC, Faculty of Sciences and Techniques of Tangier, Abdelmalek Essaadi University, Tetouan, Morocco
² Department of Physics, Faculty of Sciences of Tetouan, Abdelmalek Essaadi University, Tetouan, Morocco
³ Research Center STIS, team M2CS, Department of Appl. Math. and Info., ENSET, Mohammed V University, Rabat, Morocco
⁴ Department of Mechanical Engineering, Faculty of Engineering, KAU, Jeddah, Saudi Arabia

^* Corresponding author: mohamed.lstm@gmail.com

Abstract

In this work, a mathematical modeling is developed to estimate the ageing macroscopic response and effective behavior of viscoelastic composites. The modeling is developed directly in time domain by considering the Volterra tensorial integral product describing the local behavior and governing equations. The ageing dynamic Green’s tensor is introduced in order to solve the partial differential equations for the time dependent displacement and make the transition between local and macroscopic fields. The localization tensor making the scale transition is obtained through using the heterogeneity problem and the Mori-Tanaka mean field approach. Once this step is completed, averaging techniques are used to derive the effective ageing behavior of viscoelastic composites. To compute the macroscopic response and the effective behavior a numerical scheme is used. Numerical results are presented with respect to the shape and volume fraction of inclusions and for different ageing viscoelastic composites.