A complete analytical formulation for the elastoplastic behaviour of a composite material comprising one single array of reinforcing inclusions perfectly bonded to the matrix is developed in this paper. Fundamental relationships establish the link between the total stress and strain variables, and those pertaining to the individual constituents (matrix and reinforcement) regarded as superposed continuous phases. Assuming that each constituent behaves as an elastic perfectly plastic material, the constitutive equations governing the evolution of the reinforced material as a whole are derived. They reveal a hardening phenomenon arising from the non-compatibility between matrix and reinforcement plastic strains. It is shown in particular that the obtained constitutive law falls within the formalism of generalized standard plasticity: the reinforcement residual stress plays the role of a hardening parameter which controls the evolution of the yield surface, while the associated kinematic variable is the plastic strain discrepancy between matrix and reinforcement phases.
Owing to its inherent simplicity, the model is easily amenable to a numerical treatment for structural analysis. It is shown in particular how the classical iterative algorithm can be modified accordingly, and an illustrative application is finally presented in the field of civil engineering.