Related papers: Generalized solutions to linearized equations of T…
In this paper, we study the thermo-elastodynamics of nonlinearly viscous solids in the Kelvin-Voigt rheology where both the elastic and the viscous stress tensors comply with the frame-indifference principle. The system features a force…
The aim of this paper is to calculate the time dependence of the mean position (and orientation) of a fluid particle when a fluid system at thermodynamic equilibrium is submitted to a mechanical action. The starting point of this novel…
A thermodynamically consistent model of non-classical coupled non-linear thermoelasticity capable of accounting for thermal wave propagation is proposed. The heat flux is assumed to consist of both additive energetic and dissipative…
We consider the fluid-structure interaction problem of a viscous incompressible fluid contained in an elastic solid whose motion is not prescribed. The equations governing the motion of the solid are given by the Navier equations of linear…
We develop a continuum theory for thermoelectric bodies following the framework of continuum mechanics and conforming to general principles of thermodynamics. For steady states, the governing equations for local fields are intrinsically…
We shall consider some common models in linear thermo-elasticity within a common structural framework. Due to the flexibility of the structural perspective we will obtain well-posedness results for a large class of generalized models…
We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We…
Viscoelastic rate-type fluid models constitute a fundamental framework for the mathematical description of complex materials exhibiting coupled elastic and viscous effects, with a wide range of applications in engineering, biomaterials, and…
We develop a unified continuum modeling framework for viscous fluids and hyperelastic solids using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the…
An irreversible thermodynamical theory of solids is presented where the kinematic quantities are defined in an automatically objective way. Namely, auxiliary elements like reference frame, reference time and reference configuration are…
We present a theory that combines the framework of irreversible thermodynamics with modified integral theorems to model arbitrarily curved and deforming membranes immersed in bulk fluid solutions. We study the coupling between the mechanics…
The continuum equations of fluid mechanics are rederived with the intention of keeping certain mechanical and thermodynamic concepts separate. A new "mechanical" mass density is created to be used in computing inertial quantities, whereas…
The thermodynamical model of visco-elastic deformable solids at finite strains is formulated in a fully Eulerian way in rates. Also effects of thermal expansion or buoyancy due to evolving mass density in a gravity field are covered. The…
We study an initial and boundary value problem modelling the motion of a rigid body in a heat conducting gas. The solid is supposed to be a perfect thermal insulator. The gas is described by the compressible Navier-Stokes-Fourier equations,…
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…
Many applications of porous media research involves high pressures and, correspondingly, exchange of thermal energy between the fluid and the matrix. While the system is relatively well understood for the case of non-moving porous media,…
We consider the physical setup of a three-dimensional fluid-structure interaction problem. A viscous compressible gas or liquid interacts with a nonlinear, visco-elastic, three-dimensional bulk solid. The latter is described by a hyperbolic…
The equations governing the flow of a viscous incompressible fluid around a rigid body that performs a prescribed time-periodic motion with constant axes of translation and rotation are investigated. Under the assumption that the period and…
Classical thermodynamics describes physical systems in thermodynamic equilibrium, characterized in particular by the absence of macroscopic motion. Global non-equilibrium thermodynamics extends this framework to include physical systems in…
We propose and analyze a mathematical model of the mechanics of gels, consisting of the laws of balance of mass and linear momentum. We consider a gel to be an immiscible and incompressible mixture of a nonlinearly elastic polymer and a…