A modified secant formulation to predict the overall behavior of elasto-viscoplastic particulate composites
Résumé
To model the mechanical response of rate-dependent elasto-viscoplastic (or equivalently non-linear viscoelastic) particulate composites, the proposed approach consists in linearizing the (nonlinear) relation between the viscous strain rate and the stress. To obtain a tractable problem, the linearized properties (viscous modulus, stress-free strain rate) are chosen uniform per phase: in each phase, they are computed for reference stresses per phase. Thus, we obtain a fictitious linear viscoelastic solid whose microstructure is the same as the previous one and submitted to additional uniform stress-free strains per phase. For two-phases isotropic particulate composites, this general formulation associated to Hashin-Shtrikman estimates of the above-mentioned fictitious linear viscoelastic solid yields closed-form expressions of the time evolution of the effective behavior as well as phase-averaged mechanical fields expressed as a set of nonlinear first-order differential equations. Since the linearized properties in the matrix phase are based on the second-order moment of the stress field, these estimates coincides with the upper bound in the purely viscoplastic regime. These estimates are also consistent with the one given for non aging linear viscoelastic composites (correspondence principle). Finally, full-field computations are used to asses the quality of these estimates for various loading conditions varying from a pure shear to a pure differential swelling loading for moderate to highly contrasted behaviors and including non monotonic and non radial effects.
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