Generalized FVDAM theory for the analysis of periodic heterogeneous materials with elastic–plastic phases undergoing infinitesimal deformation is constructed to overcome the limitations of the original or 0th-order version of the theory, and to concomitantly extend the theory's range of modeling capabilities. The 0th-order theory suffers from intrinsic constraints stemming from limited displacement field representation at the local level, which results in the deterioration of pointwise continuity of interfacial tractions and displacements with increasing plasticity, requiring greater unit cell discretization. The generalization is based on a higher-order displacement field representation within individual subvolumes of a discretized analysis domain, in contrast with the second-order expansion employed in the 0th-order theory. The higher-order displacement field is expressed in terms of elasticity-motivated surface-averaged kinematic variables which are subsequently related to corresponding static variables through a generalized local stiffness matrix. Comparison of local fields in metal matrix composites with large moduli contrasts obtained using the generalized FVDAM theory, its predecessor and finite-element method illustrates substantial improvement in the pointwise satisfaction of interfacial continuity conditions at adjacent subvolume faces in the presence of plasticity, producing smoother stress and plastic strain distributions and excellent interfacial conformability with smaller unit cell discretizations. The generalized theory offers several advantages relative to the Q9-based finite-element method, including direct relationship between static and kinematic variables across subvolume faces and superior satisfaction of pointwise traction continuity which facilitate modeling of various interfacial phenomena, such as fiber/matrix cracks illustrated herein.