Viscoelasticity with aging caused by solidification of nonaging constituent

The classical viscoelastic models for aging materials such as concrete, which consist of Volterra history-integral equations, found only limited applications since they required storing the entire stress or strain history. Although the subsequent introduction of the Dirichlet series expansion of the creep or relaxation function reduces these requirements by leading to a set of linear differential equations equivalent to aging Kelvin or Maxwell chain models, problems arose in the identification of the aging moduli of these models. This paper refines and extends a recent formulation that remedies these problems by considering the aging to result from the progressive solidification of a basic constituent that behaves as a nonaging viscoelastic material. The new possibilities explored involve the alternative use of the relaxation function for characterizing the nonaging constituent, and the expansion of both the compliance and relaxation functions of the constituent into Dirichlet series. In this way, one recovers the rate-type equations of an aging Kelvin or Maxwell chain in which all the moduli vary proportionally to a single aging function v(t). Some convenient advantages are the well-posedness of the problem of moduli identification, with always positive values, and the nonexistence of creep or relaxation reversal upon load removal.