In this paper initial boundary value problems, defined using quasilinear diffusion equations of Volterra type, are considered. These equations arise for instance to describe diffusion processes in viscoelastic media whose behaviour is represented by a Voigt-Kelvin model or a Maxwell model. We propose a finite difference discretization defined on a general nonuniform grid and we show second conv...

Generalized constitutive relationships of viscoelastic foams are investigated in which the time derivatives of integer order are replaced by derivatives of fractional order. To this point, the justification of such models has resided in the fact that they are effective in describing the behavior of real materials. In this work, the three-parameter fractional Kelvin Voigt model is compared to th...

This paper presents the implementation of a planetary rover simulation environment focused on locomotion aspects. A multibody, port-based modeling approach was taken combined with screw theory for the description of the kinematics and dynamics. Bond graphs are used as the modeling language. The contact model considers the interacting surfaces to be smooth and utilizes their differential geometr...

We investigate how a nonlinear stress-strain relation (that leads to a stiffening of the brain matter under strain) influences the brain dynamics in traumatic situations. We numerically simulate rapid rotational accelerations and decelerations of a human head using our generalization of the viscoelastic Kelvin-Voigt brain injury model that includes an experimentally established dependency of st...

In this paper we consider a natural robustness question for a model for structural acoustics. This model, which has been of great interest in recent years, is represented by a wave equation in R coupled to a Kelvin–Voigt beam; the coupling is natural physically, and is represented mathematically by highly unbounded operators. We assume that the observation consists of point evaluation of the be...

In this paper, a new mathematical model of a Kelvin-Voigt type thermo-visco-elastic, infinite thermally conducting medium has been considered in the context of a new consideration of heat conduction having a non-local fractional order due to the presence of periodically varying heat sources. Three-phase-lag thermoelastic model, Green Naghdi models II and III (i.e., the models which predicts the...

The damping vibration characteristics of magneto-electro-viscoelastic (MEV) nanobeam resting on viscoelastic foundation based on nonlocal strain gradient elasticity theory (NSGT) is studied in this article. For this purpose, by considering the effects of Winkler-Pasternak, the viscoelastic medium consists of linear and viscous layers. with respect to the displacement field in accordance with th...

u(x, 0) = u0(x) and ut(x, 0) = u1(x) for x ∈ Ω, and u(x, t)|∂Ω = 0, t ≥ 0, (1.2) where Ω is a bounded domain in R with smooth, say C-class, boundary ∂Ω and σ(|∇u|) is a function like σ = 1/ √ 1 + |∇u|2, mean curvature type nonlinearity. The viscosity term −∆ut is often called a Kelvin-Voigt type dissipation or strong dissipation which appears in phenomena of wave propagation in a viscoelastic m...