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A 2D Boundary Element Method (BEM) Formulation to obtain the constitutive response of heterogeneous materials based on the Representative Volume Element (RVE) concept is developed to deal with dissipative phenomena over the domain and the phase debonding on the interface zone. Despite the formulation is written within a multiscale framework, in this work the analyses are performed only at microstructure level, but if a full coupled multiscale analysis is performed the computational cost becomes very expensive. Usually this kind of modelling is performed considering the Finite Element Method (FEM), but it is important to find other numerical solutions which are less expensive, but still accurate. To analyse metal matrix composites the RVEs are assumed to contain a ductile matrix, rigid inclusions and an interface zone where the phase debonding is modelled by a cohesive fracture model using embedded cohesive contact finite elements into the boundary element mesh. The RVE domain is discretized into cells to compute the domain integral written in terms of the inelastic forces, which have a part related to the plasticity phenomenon and another one referred to the cohesive-contact problem. The homogenized results are compared to a FEM model in order to validate the proposed formulation.