The homogenization approach is based on the idea that the properties of a heterogeneous medium can be determined by analyzing a small portion of it [1]. In other words, Representative Volume Element (RVE) is a sample for the entire area. It needs to be underlined that the RVE includes the micro-structural property of effective materials and expands to the global domain, where uniformly applied strain or stress exists with a boundary condition [1,2,3], which does not require extensive and full-scale simulations. Meanwhile, this strategy is only applicable when the homogeneities are dual orders of magnitude that are below the effective medium’s characteristic length [1,2,3].

The idea of lattice material homogenization is represented where the RVE is a square unit cell. A body Ω with a periodic lattice with a t at the traction boundary Γt, a displacement d at the displacement boundary Γd, and a body force f is inserted by a homogenized body Ω¯¯¯. The mechanical properties of RVE are to be determined by the macroscopic behavior of Ω and Ω¯¯¯ are equivalent [1].