In recent years, Embedded Finite Element (EFE) techniques have garnered significant research interest for investigating the micro- and mesoscale behavior of composite materials. This interest is primarily driven by the reduced preprocessing time required for mesh generation and the avoidance of voxel-based models, which often misrepresent stress fields at fiber–matrix interfaces [1]. Nonetheless, EFE models currently found in the literature typically rely on 3D solid elements [2] to resolve stress distributions accurately. This approach introduces numerical challenges related to element aspect ratios and skewness; consequently, achieving acceptable accuracy often necessitates a prohibitively high number of elements. As a result of the interest in EFE, commercial software has incorporated them within their product solutions. It is possible to embed truss, beam, or plate elements into 3D models. However, they suffer from two main limitations: (i) they only couple translational degrees of freedom, leaving rotational ones unconstrained, and (ii) they do not account for volume redundancy [3]. To address these shortcomings, this work proposes an EFE framework that couples high-order kinematic fields and eliminates the volume redundancy inherent in conventional EFE solutions. The former is achieved by adopting the Carrera Unified Formulation (CUF) [4] as a versatile generator of low- to high-order models, which is then integrated into a perturbed Lagrangian formulation to enforce kinematic compatibility [5]. The latter is managed by introducing a corrective term into the variational principle. The results demonstrate strong agreement with benchmark solutions while achieving a significant reduction in computational cost. ACKNOWLEDGEMENTS Alberto Racionero acknowledges the supported by the Grants for research activity of young PhD holders, part of the UC3M Own Research Program (Ayudas para la Actividad Investigadora de los Jóvenes Doctores, del Programa Propio de Investigación de la UC3M). Alfonso Pagani also acknowledges the support of the Italian Ministry of University and Research through the program FARE-III Edition (project LOUD, No. R20EENHZEJ). REFERENCES [1] Kim, H. J., and Swan, C. C., “Voxel-based meshing and unit-cell analysis of textile composites,” International Journal for Numerical Methods in Engineering, Vol. 56, No. 7, 2003, pp. 977–1006 [2] Tabatabaei, S. A., Lomov, S. V., and Verpoest, I. “Assessment of embedded element technique in meso-FE mode