Topology optimization is a field of continuous growth in the last decades. And with the more extended use of the additive manufacturing of the last years, its study has gained even more industrial interest. The state of the art methods, such as SIMP, works with a density variable to define a threshold over a volume, considering a homogeneous material and Neumann boundary conditions. It ends with a binary structure where the final structure is differentiated from the volume to be removed after the optimization. The methodology proposed operates directly with the mechanical variables of the material instead of using an artificial density function. It gains versatility with a reduction of fitting parameters, from 2 in SIMP, to 1 in the methodology proposed. As well, instead of obtaining the results in terms of an artificial density, those are obtained directly with values of the local mechanical properties of the material, which makes it suitable for the optimization of orthotropic materials. Also, a dual formulation of the problem is presented and validated, so the optimization can be carried out with both Neumann and Dirichlet boundary conditions. The results then can be used to create a metamaterial structure with mimetic properties compared with the continuous design obtained. Examples with different loading conditions are presented, as well as with different boundary conditions and material types.