A hierarchical asymptotic homogenization approach for viscoelastic composites. Issue 21 (20th October 2021) - Cruz-González, Oscar Luis; Ramírez-Torres, Ariel; Rodríguez-Ramos, Reinaldo; Penta, Raimondo; Bravo-Castillero, Julián; Guinovart-Díaz, Raúl; Merodio, José; Sabina, Federico J.; Lebon, Frederic
Abstract: Effective properties of non-aging linear viscoelastic and hierarchical composites are investigated via a three-scale asymptotic homogenization method. In this approach, we consider the assumption of a generalized periodicity in the different structural levels and their characterization through the so-called stratified functions . The expressions for the associated local and homogenized problems, and the effective coefficients are derived at each level of organization by using the correspondence principle and the Laplace-Carson transform. Considering isotropic components and a perfect contact at the interfaces between the constituents, analytical solutions, in the Laplace-Carson space, are found for the local problems and the effective coefficients are computed. An interconversion procedure between the effective relaxation modulus and the effective creep compliance is carried out for obtaining information about both viscoelastic properties. The numerical inversion to the original temporal space is also performed. Finally, we exploit the potential of the approach and study the overall properties of a hierarchical viscoelastic composite structure representing the dermis.