Related papers: On diffusive variants of some classical viscoelast…
This paper deals with the numerical modeling of transient mechanical waves in linear viscoelastic solids. Dissipation mechanisms are described using the generalized Zener model. No time convolutions are required thanks to the introduction…
Intracrystalline diffusion is an invaluable tool for estimating timescales of geological events. Diffusion is typically modeled using gradients in chemical potential. However, chemical potential is derived for uniform pressure and…
We continue to investigate the diffusive compressible Euler (dcE) model for viscous and heat conducting compressible fluid flow, which has been proposed by M. Sv\"ard as an alternative to the Navier-Stokes-Fourier (NSF) equations. The…
In this paper we explore a possibility that all transport turbulent models are contained in a coarse-grained kinetic equation. Building on a recent work by H.Chen et al (2004), we account for fluctuations of a single -point probability…
We propose and analyse the properties of a new class of models for the electromechanics of cardiac tissue. The set of governing equations consists of nonlinear elasticity using a viscoelastic and orthotropic exponential constitutive law…
We introduce and analyze a new mixed finite element method with reduced symmetry for the standard linear model in viscoelasticity. Following a previous approach employed for linear elastodynamics, the present problem is formulated as a…
This article deals with a viscoplastic material model of overstress type. The model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part. An additional multiplicative decomposition of…
This paper deals with the rigorous study of the diffusive stress relaxation in the multidimensional system arising in the mathematical modeling of viscoelastic materials. The control of an appropriate high order energy shall lead to the…
In this study, we formulate a thermodynamically consistent rheological model for yield stress fluids by introducing an internal dynamic variable and extending the framework established by Kamani et al (2021) and the classical Oldroyd-B…
The thermodynamical model of viscoelastic deformable solids at finite strains with Kelvin-Voigt rheology with a higher-order viscosity (using the concept of multipolar materials) is formulated in a fully Eulerian way in rates. Assumptions…
In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…
Viscoelastic fluids are a class of fluids that exhibit both viscous and elastic nature. Modelling such fluids requires constitutive equations for the stress, and choosing the most appropriate constitutive relationship can be difficult. We…
Viscoelastic rate-type fluids are popular models of choice in many applications involving flows of fluid-like materials with complex micro-structure. A well-developed mathematical theory for the most of these classical fluid models is…
Simulating turbulent flows is crucial for a wide range of applications, and machine learning-based solvers are gaining increasing relevance. However, achieving temporal stability when generalizing to longer rollout horizons remains a…
A general thermodynamic treatment of dissipative relativistic fluids is introduced, where the temperature four vector is not parallel to the velocity field of the fluid. Generic stability and kinetic equilibrium points out a particular…
Various spatial-gradient extensions of standard viscoelastic rheologies of the Kelvin-Voigt, Maxwell's, and Jeffreys' types are analyzed in linear one-dimensional situations as far as the propagation of waves and their dispersion and…
Recently linear dissipative models of the Boltzmann equation have been introduced. In this work, we consider the problem of constructiing suitable hydrodynamic approximations for such models where the mean velocity and the temperature of…
Among the numerous anomalies of water, the acceleration of dynamics under pressure is particularly puzzling. Whereas the diffusivity anomaly observed in experiments has been reproduced in several computer studies, the parallel viscosity…
Kinetically-constrained models are lattice-gas models that are used for describing glassy systems. By construction, their equilibrium state is trivial and there are no equal-time correlations between the occupancy of different sites. We…
Elastic turbulence is a chaotic regime that emerges in polymer solutions at low Reynolds numbers. A common way to ensure stability in numerical simulations of polymer solutions is to add artificially large polymer-stress diffusion. In order…