We present an automated framework to identify effective constitutive models for nonhomogeneous hyperelastic materials from full-field representative volume element (RVE) simulations. Full-scale finite element analyses provide reaction forces, stresses, and homogenized energies under uniaxial, biaxial, and shear loading, using both strain-controlled and stress-controlled protocols. The macroscopic strain-energy density is represented by a feature library built from functions of isotropic and anisotropic invariants. Model identification is posed as a constrained optimization problem that enforces equilibrium, matches reaction forces, and fits the homogenized strain energy, resulting in an analytic effective material model with data-driven coefficients. To compute homogenized deformation gradients and to treat the invariants as known quantities within the optimization, we use an isogeometric discretization with higher-order smoothness. Benchmark studies on microstructures composed of two base materials (Neo-Hookean and Mooney-Rivlin) and on varying inclusion intensities show that the identified effective models predict homogenized strain-energy and stress--strain responses across multiple loading paths, in agreement with the underlying full-scale simulations. Overall, the approach supports data-driven multiscale modeling of nonlinear, anisotropic microstructured materials.