Micromechanical modelling of porous viscoelastic composite materials

¹ Modeling and Control, Department of Mathematics, Faculty of Sciences and Techniques of Tangier, AEU, Tangier, Morocco
² Department of Physics, Faculty of Sciences of Tetouan, Abdelmalek Essaadi University, Tetouan, Morocco
³ Research Centre STIS, team M2CS, Department of Applied Mathematics and Informatics, ENSET, MV University, Rabat, Morocco.
⁴ Department of Mechanical Engineering, Faculty of Engineering, KAU, Jeddah, Saudi Arabia

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

Abstract

Modelling and predicting the effective behavior of non-ageing viscoelastic composites have attracted the attention of many researchers. Actually, predicting the effective behavior and the macroscopic overall response while taking into account the constituents properties and shape of inclusions as well as their volume fractions is a challenging topic. In this work, porous viscoelastic composites are considered. The porous effect is introduced as a solid voided inclusions embedded in a viscoelastic matrix. The effective behavior is modelled by delayed integropartial differential equations. The resolution of the resulting equations is done through a methodological approach based on the Volterra tensorial products and the dynamic Green‘s tensor. Thus, the localization equations relating the local and the global fields are derived. After that, the Mori-Tanaka mean field micromechanical model assumptions are applied to derive the Mori-Tanaka‘s localization tensor. Once this step is completed, the effective properties are obtained through mean field techniques. The effective properties are given through tensorial convolution products. A numerical algorithm is elaborated for the computation of direct and inverse tensorial convolution products. For the validation of the developed modelling a comparison with Laplace-Carson approach is done.