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research-article

Large amplitude oscillatory shear from viscoelastic model with stress relaxation

[+] Author and Article Information
Alberto Garinei

Department of Sustainability Engineering Guglielmo Marconi University Roma, Via Plinio 44, 00193
a.garinei@unimarconi.it

Francesco Castellani

Department of Engineering University of Perugia Perugia, Via G. Duranti 93, 06125
francesco.castellani@unipg.it

Davide Astolfi

Department of Engineering University of Perugia Perugia, Via G. Duranti 93, 06125
davide.astolfi@unipg.it

Edvige Pucci

Department of Engineering University of Perugia Perugia, Via G. Duranti 93, 06125
edvige.pucci@unipg.it

Lorenzo Scappaticci

Department of Sustainability Engineering Guglielmo Marconi University Roma, Via Plinio 44, 00193
l.scappaticci@unimarconi.it

1Corresponding author.

ASME doi:10.1115/1.4038186 History: Received July 17, 2017; Revised October 10, 2017

Abstract

The analytic response for the Cauchy extra-stress in LAOS is computed from a constitutive model for isotropic incompressible materials, including viscoelastic contributions and relaxation time. Three cases of frame invariant derivatives are considered: lower, upper and Jaumann. In the first two cases, the shear stress at steady state includes the first and third harmonics and the difference of normal stresses includes the zeroth, second, fourth harmonics. In the Jaumann case, the stress components are obtained in integral form and are approximated with a Fouries series. The behavior of the coefficients is studied parametrically, as function of relaxation time and constitutive parameters. Further, the shear stress and the difference of normal stresses are studied as functions of shear strain and shear rate and are visualized by means of the elastic and viscous LB-plots. Sample results in the Pipkin plane are reported and the influence of the constitutive parameters in each case is discussed.

Copyright (c) 2017 by ASME
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