Creep, recovery and vibration of an incompressible viscoelastic material of the rate type: Simple tension case. (January 2022)

• Record Type: Journal Article
• Authors: Farina, Angiolo; Fusi, Lorenzo; Rosso, Fabio; Saccomandi, Giuseppe
• Is Part Of: International journal of non-linear mechanics. Volume 138(2022)
• Publication Date: 2022-01
• Subjects: 74A99 -- 74D99; Viscoelastic materials -- Constitutive models -- Frame indifferent derivative; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2021.103851
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: We consider three-dimensional nonlinear viscoelastic models that account for both stress relaxation and creep/recovery phenomena. These models are based on different frame indifferent time derivatives: the Oldroyd (or upper-convected) derivative, the Jaumann (or co-rotational) derivative and the Cotter–Rivlin (or lower-convected) derivative. Under a simple tension creep process, these constitutive equations predict the same stress relaxation but lead to different situations. The models based on the Oldroyd and the lower-convected derivative require restrictions on the values of the material parameters as well as on the traction/compression stress. The model based on the Jaumann derivatives does not require any restriction. All the constitutive models examined are used to study the finite amplitude, horizontal oscillatory motion of a mass attached to a rate-type viscoelastic string. In this way we generalize the classical results by Beatty and Zhou (1991).