Metamaterials are a class of artificial materials with unique mechanical properties that are not found in natural materials. They have attracted significant attention due to their potential for creating materials with tailored and superior properties. In particular, functionally graded metamaterials have emerged as promising materials for various applications due to their ability to exhibit smooth changes in their properties in a preferred direction allowing to have localized properties. However, accurately modeling the mechanical response of these materials poses significant challenges due to their complex microstructure and multiscale nature. In this work, a novel finite element method for modeling the mechanical response of functionally graded metamaterials is presented. This approach involves creating two meshes, one at the microscale and the other at the macroscale, and homogenizing the contribution of the microscale in the macroscale stiffness boxes. To take advantage of the smooth change of the microstructure, we update the micro stiffness matrix using the Sherman-Morrison formula, which speeds up the code without losing accuracy. This method allows us to capture the behavior of functionally graded metamaterials with minimum approximations. Furthermore, our approach can be extended beyond elasticity to model plasticity, hyperelasticity, and fracture. This can be achieved by introducing suitable constitutive models for these material behaviors and incorporating them into our finite element framework.