Viscoelastic effective properties for composites with rectangular cross-section fibers using the asymptotic homogenization method

Oscar Cruz-Gonzalez (1) , Reinaldo Rodríguez-Ramos (2) , José A. Otero (3) , Julian Bravo-Castillero (4) , Raúl Guinovart-Díaz (4) , Raúl Martínez-Rosado (3) , Federico J Sabina (5) , Serge Dumont (6, 7) , Frédéric Lebon (1) , Igor Sevostianov (8)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
2 Universidad de La Habana [Cuba]
3 ITESM - Tecnológico de Monterrey = Monterrey Institute of Technology
4 Facultad de Matematica y Computacion
5 IIMAS - Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas [México]
6 UNIMES - Université de Nîmes
7 IMAG - Institut Montpelliérain Alexander Grothendieck
8 Department of Mechanical and Aerospace Engineering [Las Cruces]

The present work deals with the estimation of the linear viscoelastic effective properties for composites with periodic structure and rectangular cross-section fibers, using the two-scale asymptotic homogenization method (AHM). As a particular case, the effective properties for a layered medium with transversely isotropic properties are obtained. Two times the homogenization method, in different directions, according to the geometrical configuration of the composite material is applied for deriving the analytical expressions of the viscoelastic effective properties for a composite material with rectangular cross-section fibers, periodically distributed along one axis. In addition to that, models with different creep kernels, in particular, the Rabotnov’s kernel are analyzed. Finally, the numerical computation of the effective viscoelastic properties is developed for the analysis of the results. Moreover, a numerical algorithm using FEM is developed in the present work. Comparisons with other approaches are given as a validation of the present model.

Domaines: Mécanique des solides [physics.class-ph]

Oscar Cruz-Gonzalez, Reinaldo Rodríguez-Ramos, José A. Otero, Julian Bravo-Castillero, Raúl Guinovart-Díaz, et al.. Viscoelastic effective properties for composites with rectangular cross-section fibers using the asymptotic homogenization method. Generalized Models and Non-classical Approaches in Complex Materials 1, pp.203-222, 2018, ⟨10.1007/978-3-319-72440-9_10⟩. ⟨hal-02336710⟩