Homogenization approach in heterogeneous micropolar media
Reinaldo Rodríguez Ramos (Universidad de La Habana, Havana, Cuba)
Friday 13th May, 2022 16:15-17:00 Maths 311B AND ZOOM
In this work, the two-scale asymptotic homogenization method (AHM) is applied to three-dimensional heterogeneous micropolar (Cosserat) media with periodic structure. Micropolar elas-ticity generalizes the classic elasticity theory incorporating three degrees of freedom to describethe local reorientation of the microstructure (microrotations), in addition to the three ones associ-ated with the displacement at the macroscale. The two-scale AHM, based on the consideration oftwo length scales associated to the microscopic and macroscopic phenomena, is implemented for 3D heterogeneous micropolar materials. It starts from the statement of the problem based on themicroscopic-macroscopic description. Thus, the corresponding local problems, the homogenized problem and the effective Cosserat coefficients are obtained through asymptotic expansions for displacements and microrotations.In particular, micropolar bi-laminated composites with centro-symmetric cubic or isotropic con-stituents and perfect/imperfect contact conditions are studied. The corresponding local problems aresolved and the analytical expressions of the effective properties are reported. Numerical values ofthe stiffness, torque, Poisson’s ratio, Young’s modulus, twist Poison’s ratio and torsional modulusare computed and presented for different volume fractions of the constituents.
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