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Research Papers

Large Amplitude Oscillatory Shear From Viscoelastic Model With Stress Relaxation

[+] Author and Article Information
Alberto Garinei

Department of Sustainability Engineering,
Guglielmo Marconi University,
Via Plinio 44,
Rome 00193, Italy
e-mail: a.garinei@unimarconi.it

Francesco Castellani

Department of Engineering,
University of Perugia,
Via G. Duranti 93,
Perugia 06125, Italy
e-mail: francesco.castellani@unipg.it

Davide Astolfi

Department of Engineering,
University of Perugia,
Via G. Duranti 93,
Perugia 06125, Italy
e-mail: davide.astolfi@unipg.it

Edvige Pucci

Professor
Department of Engineering,
University of Perugia,
Via G. Duranti 93,
Perugia 06125, Italy
e-mail: edvige.pucci@unipg.it

Lorenzo Scappaticci

Department of Sustainability Engineering,
Guglielmo Marconi University,
Via Plinio 44,
Rome 00193, Italy
e-mail: l.scappaticci@unimarconi.it

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 17, 2017; final manuscript received October 10, 2017; published online October 26, 2017. Assoc. Editor: Thomas Siegmund.

J. Appl. Mech 84(12), 121008 (Oct 26, 2017) (11 pages) Paper No: JAM-17-1381; doi: 10.1115/1.4038186 History: Received July 17, 2017; Revised October 10, 2017

The analytic response for the Cauchy extra stress in large amplitude oscillatory shear (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, and fourth harmonics. In the Jaumann case, the stress components are obtained in integral form and are approximated with a Fourier series. The behavior of the coefficients is studied parametrically, as a 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 Lissajous–Bowditch (LB) plots. Sample results in the Pipkin plane are reported, and the influence of the constitutive parameters in each case is discussed.

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Figures

Grahic Jump Location
Fig. 1

Behavior of h3L′(De) and h3L″(De)

Grahic Jump Location
Fig. 2

The behavior of τ̂12(x;c,d) for some sample values of c and d

Grahic Jump Location
Fig. 3

The behavior of N̂(x;q,r) for some sample values of q and r

Grahic Jump Location
Fig. 4

The normalized elastic LB plots for β1 = 0.2, β–1 = −0.1, η = 1.5, and λ = 1

Grahic Jump Location
Fig. 5

The normalized viscous LB plots for β1 = 0.2, β−1 = −0.1, η = 1.5, and λ = 1

Grahic Jump Location
Fig. 6

The normalized elastic LB plots for the difference of normal stresses in the Pipkin plane for β1 = 0.2, β−1 = −0.1, η = 1.5, and λ = 1

Grahic Jump Location
Fig. 7

The normalized viscous LB plots for the difference of normal stresses in the Pipkin plane for β1 = 0.2, β−1 = −0.1, η = 1.5, and λ = 1

Grahic Jump Location
Fig. 8

The normalized elastic LB plots for β1 = 0.2, β−1 = −0.1, η = 1.5, and λ = 1

Grahic Jump Location
Fig. 9

The normalized viscous LB plots for β1 = 0.2, β−1 = −0.1, η = 1.5, and λ = 1

Grahic Jump Location
Fig. 10

The normalized elastic LB plots for the difference of normal stresses in the Pipkin plane for β1 = 0.2, β−1 = −0.1, η = 1.5, and λ = 1

Grahic Jump Location
Fig. 11

The normalized viscous LB plots for the difference of normal stresses in the Pipkin plane for β1 = 0.2, β−1 = −0.1, η = 1.5, and λ = 1

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