Extension of the Nonuniform Transformation Field Analysis to linear viscoelastic composites in the presence of aging and swelling

Abstract This study presents a micromechanical modeling by the Nonuniform Transformation Field Analysis (NTFA) of the viscoelastic properties of heterogeneous materials with aging and swelling constituents. The NTFA proposed by Michel and Suquet (2003, 2004) is a compromise between analytical models and full-field simulations. Analytical models, which are available only for specific microstructures, provide effective constitutive relations which can be used in macroscopic structural computations, but often fail to deliver sufficiently detailed information at small scale. At the other extreme, full-field simulations provide detailed local fields, in addition to the composite effective response, but come at a high cost when used in nested Finite Element Methods. The NTFA method is a technique of model reduction which achieves a compromise between both approaches. It is based on the observation that the transformation strains (viscous strains, eigenstrains) often exhibit specific patterns called NTFA modes. It delivers both effective constitutive relations and localization rules which allow for the reconstruction of local fields upon post-processing of macroscopic quantities. A prototype of the materials of interest here is MOX (mixed oxides), a nuclear fuel which is a three-phase particulate composite material with two inclusion phases dispersed in a contiguous matrix. Under irradiation, its individual constituents, which can be considered as linear viscoelastic, are subject to creep, to aging (time dependent material properties) and to swelling (inhomogeneous eigenstrains). Its overall behavior is therefore the result of the combination of complex and coupled phenomena. The NTFA is applied here in a three-dimensional setting and extended to account for inhomogeneous eigenstrains in the individual phases. In the present context of linear viscoelasticity the modes can be identified following two procedures, either in each individual constituent, as initially proposed in Michel and Suquet (2003, 2004), or globally on the volume element, resulting into two slightly different models. For non aging materials, the predictions of both models are in excellent agreement with full-field simulations for various loading conditions, monotonic as well as non proportional loading, creep and relaxation. The model with global modes turns out to be as predictive as the original one with less internal variables. For aging materials, satisfactory results for the overall as well as for the local response of the composites are obtained by both models at the expense of enriching the set of modes. The prediction of the global model for the local fields is less accurate but remains acceptable. Use of the global NTFA model is therefore recommended for linear viscoelastic composites.