The desire for a more realistic simulation of heterogeneous materials, such as fiber-reinforced composites, is driving the recent research trend from conventional first-order homogenization methods to higher-order homogenization methods, such as the distribution-enhanced homogenization framework (DEHF) [1]. The former uses only the average microscopic behavior to obtain the macroscopic behavior. The latter allows macroscopic behavior to be determined by considering higher-order descriptors of the microscopic structure. Then, macroscopic constitutive equations are formulated in a series expansion on the microscopic constitutive equations and moments of arbitrary order of the microscopic field variables. Increasing the order of the moment expansion results in increased fidelity of the macroscopic approximation of the microscopic constitutive behavior. However, this increase in the approximation order requires more computational effort to solve. This contribution presents an efficient model hierarchy based on the DEHF. To this end, a model adaptivity is developed allowing to switch from DEHF with lower-order to high-order moments through a loopwise error model control to enhance the accuracy and the quality of computational results for two-scale heterogeneous materials. The proposed adaptive procedure is driven by a goal-oriented a posteriori error estimation based on duality techniques [2]. Finally, several numerical examples illustrate the effectiveness of the proposed adaptive approach in comparison with the full-field homogenization method. REFERENCES [1] Allerman C., Luscher D.J., Bronkhorst C. and Ghosh S., Distribution-enhanced homogenization framework and model for heterogeneous elasto-plastic problems. Journal of the Mechanics and Physics of Solids, Vol. 85, 176–202 (2015). [2] Tchomgue S. A., Mahnken R., Caylak I. and Ostwald R., Error representations for goal-oriented a posteriori error estimation in elasto-plasticity with applications to mesh adaptivity. Engineering Computations, EC-12-2023-0975.R2.