RESUMEN
The asymptotic homogenization method is applied to characterize the effective behaviour of periodic multi-laminated micropolar elastic heterogeneous composites under perfect contact conditions. The local problem formulations and the analytical expressions for the effective stiffness and torque coefficients are derived for the centrosymmetric case. One of the main findings in this work is the analysis of the rotations effect of the layers' constitutive properties on the mechanical response of bi-laminated composites. The effects of microstructure and interfacial interactions on the composite's mechanical behaviour are captured through the independent effective moduli. Comparisons with the classical elastic case show the approach validation. Some numerical examples are shown. Furthermore, considering the micropolar media's prevalence in bio-inspired systems, the model's applicability is evaluated for reconstructing bone fractures using multi-laminated biocomposites. An important finding in this bio-inspired simulation is related to the analysis of a periodic bi-laminated micropolar composite whose isotropic constituents are a bioceramic material and a compact bone. This artificial bio-inspired material should integrate with host tissue to support cell growth and be stable and compatible. These characteristics are crucial in the enhancement of the fractured bone.
RESUMEN
In this work, several mathematical models for the spread of viruses and diseases are presented. In particular, the work focuses on the coronavirus disease 2019 (COVID-19) pandemic. A multi-population model is presented for the study of the interaction of various populations and the contagion of the virus between them. A second model on vaccination is presented, which allows analyzing the behavior of the disease taking into account the effectiveness of the vaccine and the speed of COVID-19 after the vaccination process. Finally, both models are applied to analyze the epidemic in Cuba. For this study, the official data reported by the Cuban Ministry of Health from March 2020 to August 2021 is used.