Homogenization towards chiral Cosserat continua and applications to enhanced Timoshenko beam theories

A homogenization methodology for the construction of effective Cosserat substitution media heterogeneous materials is proposed, combining a variational principle in linear elasticity with extended Hill-Mandel lemma accounting introduced generalized kinematics. The proposed method general and can be applied to wide class architected composites prone such micropolar effects. microscopic displacement field initially continuum splits into homogeneous part polynomial kinematic measures fluctuation involving localization operators. tensors moduli are formulated as integrals over representative unit cell utilizing localizators, solution classical, higher-order problems. has chief advantage delivering size-independent remedy deficiencies most existing higher order schemes towards continua literature. Based on developed method, tetrachiral lattice made reinforcement computed elaborate an enhanced Timoshenko microstructured beam model exhibiting couplings between different deformation modes induced by response its underlying microstructure.