A rigorous homogenization method for the determination of the overall ultimate strength of periodic discrete media and an application to general hexagonal lattices of beams

A rigorous method for the homogenization of general elastoplastic periodic lattices is presented. A discrete unit cell problem with finite number of degrees of freedom is solved for the determination of the overall elastic stiffness and ultimate strength of the lattice. Both static and kinematic methods are developed. It is shown that the overall yield strength domain of a large specimen, subjected to the so-called kinematically uniform boundary conditions, is asymptotically equal to the homogenized yield strength domain, as the size of the specimen goes to infinity. The method is applied to metallic honeycomb materials with arbitrary non-uniform cell wall thickness. New results concerning non-symmetric material distribution in the cell edges of the honeycomb are obtained. The model shows that the effects of this type of defect on the overall properties are less important than the already known effects of symmetric non-uniform cell wall thickness. Good agreement is observed between the proposed analytical beam model predictions and the finite element computations.