We investigate existence and stability of viscoelastic shock profiles for a class of planar models including the incompressible shear case studied by Antman and MalekMadani. We establish that the resulting equations fall into the class of symmetrizable hyperbolic–parabolic systems, hence spectral stability implies linearized and nonlinear stability with sharp rates of decay. The new contributio...

We consider a novel asymptotic limit of model equations proposed to describe the formation of localised states in a vertically vibrated layer of granular material or viscoelastic fluid. In physical terms, the asymptotic limit is motivated by experimental observations that localised states (‘oscillons’) arise when regions of weak excitation are nevertheless able to expel material rapidly enough ...

A compressively strained film on a substrate can wrinkle into intricate patterns. This Rapid Communication studies the evolution of the wrinkle patterns. The film is modeled as an elastic nonlinear plate and the substrate a viscoelastic foundation. A spectral method is developed to evolve the nonlinear system. When the initial film strains are isotropic, the wrinkles evolve into a pattern with ...

Starting from stationary bifurcations in Couette-Dean flow, we compute nontrivial stationary solutions in inertialess viscoelastic circular Couette flow. These solutions are strongly localized vortex pairs, exist at arbitrarily large wavelengths, and show hysteresis in the Weissenberg number, similar to experimentally observed "diwhirl" patterns. Based on the computed velocity and stress fields...

Variational iteration method VIM is applied to solve linear and nonlinear boundary value problems with particular significance in structural engineering and fluid mechanics. These problems are used as mathematical models in viscoelastic and inelastic flows, deformation of beams, and plate deflection theory. Comparison is made between the exact solutions and the results of the variational iterat...

As is well known, the extrusion rate of polymers from a cylindrical tube or slit (a "die") is in practice limited by the appearance of "melt fracture" instabilities which give rise to unwanted distortions or even fracture of the extrudate. We present the results of a weakly nonlinear analysis which gives evidence for an intrinsic generic route to melt fracture via a weakly nonlinear subcritical...

We consider numerical approximations of a quasistatic problem modeling the sliding frictional contact with wear between a viscoelastic body and a rigid moving foundation. The contact is modeled with the Coulomb's law of dry friction and the wear is described by a version of Archard's law. The variational formulation of the problem consists of a nonlinear evolutionary equation coupled with a tim...

where J(t) is the creep compliance as it depends on time t, and E(t) is the relaxation modulus. Many constitutive models have been developed to describe the nonlinear viscoelastic behavior of materials; see Schapery (1969) and Findley et al. (1976). Models described by Johnson et al. (1996) are for large deformations and Pioletti et al. (1998) take into account the strain rate. In the present s...

This paper offers a reappraisal of Fung's model for quasi-linear viscoelasticity. It is shown that a number of negative features exhibited in other works, commonly attributed to the Fung approach, are merely a consequence of the way it has been applied. The approach outlined herein is shown to yield improved behaviour and offers a straightforward scheme for solving a wide range of models. Resul...

We present special Newton-multigrid techniques for stationary incompressible nonlinear flow models discretised by the high order LBB-stable Q2P1 element pair. We treat the resulting nonlinear and the corresponding linear discrete systems by a fully coupled monolithic approach to maintain high accuracy and robustness, particularly with respect to different rheological behaviour but also regardin...