<p>This study introduces a computational approach using the two-scale asymptotic homogenization method to analyze the effective behavior of composites with layered periodic structures, avoiding the use of integral transforms, which are associated with the theoretical basis in the elastic-viscoelastic correspondence principle. By combining quadrature techniques with an efficient arrangement of Lambda functions, this method automates the calculation of effective coefficients, speeding up intricate simulations in periodic media. The Dischinger and Scott Blair-Rabotnov kernels are considered in elastic and viscoelastic bi-phasic layered composites. The numerical results of the present model are compared with semi-analytical calculations reported in the literature for different cases of layered composite problems. The developed algorithm demonstrates strong potential for improving the accuracy, robustness, and adaptability of computational homogenization techniques in the analysis and design of advanced composite materials.</p>