Sequential linearization method for viscous/elastic heterogeneous materials

The paper addresses the problem of suitable approximation of the interaction between phases in heterogeneous materials that exhibit both viscous and elastic properties. A novel approach is proposed in which linearized subproblems for an inhomogeneity–matrix system with viscous or elastic interaction rules are solved sequentially within one incremental step. It is demonstrated that in the case of a self-consistent averaging scheme, an additional accommodation subproblem, besides purely viscous and elastic subproblems, is to be solved in order to estimate the material response satisfactorily. By examples of an isotropic two-phase material it is shown that the proposed approach provides acceptable predictions in comparison with the existing models.