This work presents a decoupled tensor-based multiscale computational framework for embedding unresolved mesoscale structural effects into continuum constitutive models. The approach addresses a fundamental limitation of classical multiscale modeling, where homogenization techniques fail to capture emergent structural mechanisms arising at intermediate length scales. The proposed formulation integrates nanoscale homogenization, microscale structural transformations, and a novel tensor-level embedding strategy that introduces mesoscale contributions directly into the effective stiffness tensor. In particular, the framework adopts an additive decomposition of the constitutive response, enabling the representation of stiffness amplification mechanisms without explicit geometric resolution. A key feature of the method is a decoupled stiffness formulation, in which dominant mesoscale effects are selectively incorporated into specific tensor components. This provides a computationally efficient alternative to fully resolved multiscale simulations, significantly reducing the computational cost while preserving predictive capability. The framework is implemented within a finite element environment using FEniCSx and validated through large-scale simulations involving meshes with millions of elements. Numerical verification is performed via mesh convergence analysis, including Richardson extrapolation and Grid Convergence Index (GCI). Model predictions are compared against experimental force–displacement data, demonstrating that classical microscale models underestimate stiffness, whereas the proposed mesoscale-enhanced formulation accurately captures the structural response in the pre-critical regime. The results confirm that a substantial portion of the effective stiffness arises from mesoscale structural mechanisms such as load-path activation, geometric confinement, and structural connectivity. These effects cannot be captured through conventional homogenization approaches and must be incorporated at the constitutive level. The proposed framework provides a general and scalable methodology for the analysis of hierarchical materials and complex structural systems, offering a paradigm shift from geometry-resolved multiscale modeling to tensor-embedded mesoscale physics.
SUAREZ et al. (Tue,) studied this question.