Maxwellian-type rheological models of inelastic effects creep type at large strains are revisited in relation to strain gradient theories. In particular, we observe that a dependence the stored energy density on gradients may lead spurious hardening effects, preventing model from accommodating slips. The main result this paper is an alternative type, where higher-order contribution provided by ...

Elastography is capable of noninvasively detecting hepatic fibrosis by imposing mechanical stress and measuring the viscoelastic response in the liver. Magnetic resonance elastography (MRE) relies on time-harmonic vibrations, while most dynamic ultrasound elastography methods employ transient stimulation methods. This study attempts to benefit from the advantages of time-harmonic tissue stimula...

We numerically model the human brain dynamics in realistic 2D cross-sections during traumatic scenarios corresponding to the Head Injury Criterion’s critical value HIC36=1000. Our simulations are based on the Kelvin-Voigt Partial Differential Equations that treat the brain tissue as a viscoelastic solid and on our nonlinear generalization of these linear PDEs that treats the tissue as an incomp...

The microscopic structure of a plant cell wall is given by cellulose microfibrils embedded in a cell wall matrix. In this paper we consider a microscopic model for interactions between viscoelastic deformations of a plant cell wall and chemical processes in the cell wall matrix. We consider elastic deformations of the cell wall microfibrils and viscoelastic Kelvin–Voigt type deformations of the...

A photonic shape memory polymer film that shows large color response (∼155 nm) in a wide temperature range has been fabricated from a semi-interpenetrating network of a cholesteric polymer and poly(benzyl acrylate). The large color response is achieved by mechanical embossing of the photonic film above its broad glass transition temperature. The embossed film, as it recovers to its original sha...

Weak solutions and blow-up for wave equations of p-Laplacian type with supercritical sources" (2015). This paper investigates a quasilinear wave equation with Kelvin-Voigt damping, u t t − ∆ p u − ∆u t = f (u), in a bounded domain Ω ⊂ R 3 and subject to Dirichlét boundary conditions. The operator ∆ p , 2 < p < 3, denotes the classical p-Laplacian. The nonlinear term f (u) is a source feedback t...

A set of wave equations with fractional loss operators in time and space are analyzed. The fractional Szabo equation, the power law wave equation and the causal fractional Laplacian wave equation are all found to be low-frequency approximations of the fractional Kelvin-Voigt wave equation and the more general fractional Zener wave equation. The latter two equations are based on fractional const...

In this paper, we apply the thermodynamic framework recently put into place by Rajagopal and co-workers, to develop rate-type models for viscoelastic fluids which do not possess instantaneous elasticity. To illustrate the capabilities of such models we make a specific choice for the specific Helmholtz potential and the rate of dissipation and consider the creep and stress relaxation response as...

This paper presents chaotic behavior of a nonlinear viscoelastic beam under a moving mass interaction. Considering the stretching effect which is modeled by the Lagrangian strain theory and using linear Kelvin-Voigt model to constitute viscoelastic behavior of the beam, the governing equations of transverse vibration is derived. Then Galerkin truncation is applied to find the ordinary different...

An adhesive unilateral contact of elastic bodies with a small viscosity in the linear Kelvin-Voigt rheology at small strains is scrutinized. The flow-rule for debonding the adhesive is considered rate-independent and unidirectional. The asymptotics for the viscosity or for external loading speed approaching zero is proved in some special cases, in particular when inertia is neglected or when de...