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This work presents a hyper-viscoelastic model based on the Hencky-logarithmicstrain tensor to model the response of a Tire Derived Material (TDM) undergoingmoderately large deformations. TDM is a composite made by cold forging a mix ofrubber fibers and grains, obtained by grinding scrap tires, and polyurethanebinder. The mechanical properties are highly influenced by the presence ofvoids associated with the granular composition and low tensile strength due tothe weak connection at the grain-matrix interface. For these reasons, TDM useis restricted to applications concerning a limited range of deformations.Experimental tests show that a central feature of the response is connected tohighly nonlinear behavior of the material under volumetric deformation whichconventional hyperelastic models fail in predicting. The strain energy functionpresented here is a variant of the exponentiated Hencky strain energy proposedby Neff et al., which for moderate strains is as good as the quadratic Henckymodel and in the large strain region improves several important features from amathematical point of view. The proposed form of the exponentiated Henckyenergy possesses a set of parameters uniquely determined in the infinitesimalstrain regime and an orthogonal set of parameters to determine the nonlinearresponse. The hyperelastic model is additionally incorporated in a finitedeformation viscoelasticity framework that accounts for the two maindissipation mechanisms in TDMs, one at the microscale level and one at themacroscale level. The model is capable of predicting different deformationmodes in a certain range of frequency and amplitude with a unique set ofparameters with most of them having a clear physical meaning. Moreover, bycomparing the predictions from the proposed constitutive model withexperimental data we conclude that the new constitutive model gives accurateprediction.

The exponentiated Hencky strain energy in modelling tire derived material for moderately large deformations