The manuscript offers a methodology to solve an analytical model of a heterogeneous elastic problem for curvilinear layered structures, using the two scales asymptotic homogenization method (AHM). The local problems and the mechanical properties of the local functions were derived. The analytical modeling for the linear elastic problem considering quasi-periodic multi-layered curvilinear composites and the corresponding homogenized problem were obtained. The analytic expression of the effective stress for curvilinear composites is presented. In order to validate the presented model, comparisons with a computational modeling and experimental results for Fibonacci laminated composite and wavy laminated structure are given. The methodology is applied to composites with thickness variation where the effective coefficients were computed and a comparison between the results reported by AHM and numerical analysis given by finite element method (FEM) is presented. Finally, the aorta is studied as a curvilinear laminated shell composite and the above results were used to determinate the effective elastic tensor for healthy and unhealthy aorta using AHM and FEM.

The manuscript offers a methodology to solve the local problem derived from the homogenization technique, considering composite materials with generalized periodicity and imperfect spring contact at the interface. The general expressions of the local problem for an anisotropic composite with perfect and imperfect contact at the interface are derived. The analytical solutions of the local problems are obtained by solving a system of partial differential equations. In order to validate the model, the effective properties of the structure presented in the literature are obtained as particular cases. The solution of the local problem is used to extend the study to more complex structures, such as, wavy laminates shell composites with imperfect spring type contact at the interface. Also, the results are compared with the results for perfect and imperfect contact models available in the literature.

The paper focuses on the calculation of the effective elastic properties of a laminated composite shell with imperfect contact between the layers. To achieve this goal, first the two-scale asymptotic homogenization method (AHM) is applied to derive the solutions for the local problems and to obtain the effective elastic properties of a two-layer spherical shell with imperfect contact between the layers. The results are compared with the numerical solution obtained by finite elements method (FEM). The limit case of a laminate shell composite with perfect contact at the interface is recovered. Second, the elastic properties of a spherical heterogeneous structure with isotropic periodic microstructure and imperfect contact is analyzed with the spherical assemblage model (SAM). The homogenized equilibrium equation for a spherical composite is solved using AHM and the results are compared with the exact analytical solution obtained with SAM.

The elastic properties of a spherical heterogeneous structure with isotropic periodic components is analyzed and a\ud methodology is developed using the two-scale asymptotic homogenization method (AHM) and spherical assemblage\ud model (SAM). The effective coefficients are obtained via AHM for two different composites: (a) composite with perfect\ud contact between two layers distributed periodically along the radial axis; and (b) considering a thin elastic interphase\ud between the layers (intermediate layer) distributed periodically along the radial axis under perfect contact. As a result,\ud the derived overall properties via AHM for homogeneous spherical structure have transversely isotropic behavior.\ud Consequently, the homogenized problem is solved. Using SAM, the analytical exact solutions for appropriate boundary\ud value problems are provided for different number of layers for the cases (a) and (b) in the spherical composite. The\ud numerical results for the displacements, radial and circumferential stresses for both methods are compared considering\ud a spherical composite material loaded by an inside pressure with the two cases of contact conditions between the layers\ud (a) and (b)