Rate equations for locally adjusted homogenization of viscoelastic composites

Understanding of the long-term inelastic properties of materials including composites is an important problem in solid mechanics. A few elaborated models of homogenization exist for elastic particulate composites; however, for viscoelastic composites this task proves sufficiently more challenging, even for the case of isotropic linear media. The complexity of this task requires taking into account the accumulation of spatially non-uniform inelastic strains in the matrix of a composite. The promising way is the development of approaches that utilize the concept of internal variables; yet, correct identification of the variables is also a complicated problem. The paper describes a model for a viscoelastic particulate composite which consists of rate equations and involves internal variables. The derivation is based on the Eshelby solution and the elastic-viscoelastic correspondence principle. The model is capable of calculating the mechanical response, including average and local strains and stresses in the composite phases, for an arbitrary load history. Material of the composite matrix is assumed to be isotropic. Ageing viscoelasticity implying time-dependent mechanical properties can be taken into account. The model is verified against published results for similar approaches. The proposed method can help in assessing viscoelastic behavior, including creep, of various particulate composites and microscopically inhomogeneous media.