Related papers: On Scott-Blair model with time-varying viscosity i…
In a recent paper, Zhou et al. [Mech Time-Depend Mater (2017) 21: 151] studied the time-dependent properties of Glass Fiber Reinforced Polymers composites by employing a new rheological model with a time-dependent viscosity coefficient.…
We develop a thermodynamically consistent, fractional visco-elasto-plastic model coupled with damage for anomalous materials. The model utilizes Scott-Blair rheological elements for both visco-elastic/plastic parts. The constitutive…
In view of the increasing attention to the time responses of complex fluids described by power-laws in association with the need to capture inertia effects that manifest in high-frequency microrheology, we compute the five basic…
Most materials age, and their properties change over time. The aging of materials is reflected in their mechanical responses to external stress and strain, which exhibit logarithmic relaxation and universal power-law creep. Those responses…
In this note we analyze a model for a unidirectional unsteady flow of a viscous incompressible fluid with time dependent viscosity. A possible way to take into account such behaviour is to introduce a memory formalism, including thus the…
We develop a fractional return-mapping framework for power-law visco-elasto-plasticity. In our approach, the fractional viscoelasticity is accounted through canonical combinations of Scott-Blair elements to construct a series of well-known…
Polymer-based plastics exhibit time-dependent deformation under constant stress, known as creep, which can lead to rupture or static fatigue. A common misconception is that materials under tolerable static loads remain unaffected over time.…
The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the…
The purpose of this paper is twofold: from one side we provide a general survey to the viscoelastic models constructed via fractional calculus and from the other side we intend to analyze the basic fractional models as far as their creep,…
In this work, we investigate a variational formulation for a time-fractional Fokker-Planck equation which arises in the study of complex physical systems involving anomalously slow diffusion. The model involves a fractional-order Caputo…
We consider a time-space fractional diffusion equation with a variable coefficient and investigate the inverse problem of reconstructing the source term, after regularizing the problem with the quasiboundary value method to mitigate the…
The fully-implicit time discretization (i.e. the backward Euler formula) is applied to compressible nonlinear dynamical models of viscoelastic solids in the Eulerian description, i.e. in the actual deforming configuration. The Kelvin-Voigt…
Fractional calculus has been proved to be very effective in representing the visco-elastic relaxation response of materials with memory such as polymers. Moreover, in modelling the temperature dependency of the material functions in…
Understanding a material's dissipative response is important for their use in many applications, such as adhesion or fracture resistance. In dispersions, the interplay between matrix and inclusions complicates any description. Fractional…
In this work, we study a new spectral Petrov-Galerkin approximation of space-time fractional reaction-diffusion equations with viscosity terms built by Riemann-Liouville fractional-order derivatives. The proposed method is reliant on…
Owing to lack of time translational invariance, aging soft glassy materials do not obey fundamental principles of linear viscoelasticity. We show that by transforming the linear viscoelastic framework from the real time domain to the…
The fully-implicit time discretization (i.e. the backward Euler formula) is applied to compressible nonlinear dynamical models of thermo-viscoelastic solids in the Eulerian description, i.e. in the actual deforming configuration, formulated…
Motivated from the need to convert time-dependent rheometry data into complex frequency response functions, this paper studies the frequency response function of the creep compliance that is coined the complex creep function. While for any…
We formulate a quasistatic nonlinear model for nonsimple viscoelastic materials at a finite-strain setting in the Kelvin's-Voigt's rheology where the viscosity stress tensor complies with the principle of time-continuous frame-indifference.…
We investigate the well-posedness of a coupled Navier-Stokes-Fokker-Planck system with a time-fractional derivative. Such systems arise in the kinetic theory of dilute solutions of polymeric liquids, where the motion of noninteracting…