This research focuses on the mechanical characterization of structured metamaterials by assessing their ultimate strength through limit analysis applied to the Representative Volume Element (RVE). A new VFEM (Volterra-based Finite Element Method) formulation has been developed, which is grounded in self-equilibrated solutions obtained via finite elements for calculating the lower bound theorem, in combination with Melàn’s limit analysis. The approach incorporates a discrete mapping of Volterra dislocations within the structure, modeled using isoparametric representation. By applying conventional FEM techniques, the linear operator V, which connects self-equilibrated internal stresses to displacement-like nodal parameters, was derived through finite element discretization of displacements and strains. The study includes elastic homogenization of the mechanical properties of an elementary cell with a known geometry, specifically an isotropic truss and an octet truss. The study revealed the dependence of isotropic properties, validated through Zener’s theory, on the RVE’s density. The density satisfying Zener’s condition defines the isotropic geometry of the truss structure. For the isotropic case, the VFEM procedure was applied to verify the isotropy of the limit domain, comparing it with the Mises-Schleicher limit domain. The novelty of this work lies in establishing both linear and nonlinear limit loci for the material, offering a basis for future limit analyses of structures using the elementary volume approach proposed in this study.