Effective continuum model of grid material based on couple-stress theory

The effective properties of grid material based onclassical continuum model have been widely investigated. Moreover, gridmaterial is often used as thin-walled structures and the corresponding sizeof macro-structure (L) has the same magnitude with the characteristic length(l_m) of the grid material. The purpose of this paper is to introduce aneffective couple-stress continuum model to describe the performance of gridmaterial when L \approx l_m and to recommend a method to calculatethe effective moduli of the model. The representative volume element(RVE) method Dirichlet boundary conditions is proposed. The effective beamstiffness of couple-stress continuum is deduced with a new parameter\delta as for the couple-stress influence factor. The theoreticalanalysis is validated with finite elements (FE) solutions with the casesof some typical grid materials. The results show that couple-stresscontinuum model can be used to evaluate grid material and obtain theeffective material parameters. The couple-stress effect is obvious onlywhen L \approx l_m. Furthermore, thecharacteristic length of the grid material is influenced by the relativitydensity, the size of the base cell and the geometry.