55 citations · 238 across the 19 of their papers we have counts for
20 papers
Uniform approximation of spectra of linear second order differential operators via discrete sine transform based discretisation
Oliver Křenek, V\'ıt Průša, Rebecca Tozzi +1
We study various discretisation schemes for the regular Sturm--Liouville operator on a bounded interval and for the Laplace operator on an arbitrary planar domain, in both cases su…
Discrete versus continuous -- linear lattice models and their exact continuous counterparts
Lorenzo Fusi, Oliver Křenek, Vít Průša +3
We review and study the correspondence between discrete linear lattice/chain models of interacting particles and their continuous counterparts represented by linear partial differe…
Modeling metamaterials by second-order rate-type constitutive relations between only the macroscopic stress and strain
Vít Průša, Casey Rodriguez, Ladislav Trnka +1
We propose a thermodynamically based approach for constructing effective rate-type constitutive relations describing finite deformations of metamaterials. The effective constitutiv…
Fast construction of the discrete Green operator for a second order ordinary differential equation
Jan Blechta, Vít Průša, Ladislav Trnka +1
We consider linear second order differential equation y''= f with zero Dirichlet boundary conditions. At the continuous level this problem is solvable using the Green function, and…
The conclusion that metamaterials could have negative mass is a consequence of improper constitutive characterisation
David Cichra, Vít Průša, K. R. Rajagopal +2
The concept of "effective mass" is frequently used for the simplification of complex lumped parameter systems (discrete dynamical systems) as well as materials that have complicate…
Numerical approximation of a thermodynamically complete rate-type model for the elastic--perfectly plastic response
Pablo Alexei Gazca-Orozco, Vít Průša, Karel Tůma
We analyse a numerical scheme for a system arising from a novel description of the standard elastic--perfectly plastic response. The elastic--perfectly plastic response is describe…
A thermodynamic framework for non-isothermal phenomenological models of isotropic Mullins effect
David Cichra, Pablo Alexei Gazca-Orozco, Vít Průša +1
The Mullins effect is a common name for a family of intriguing inelastic responses of various solid materials, in particular filled rubbers. Given the importance of the Mullins eff…
Implicit type constitutive relations for elastic solids and their use in the development of mathematical models for viscoelastic fluids
Vít Průša, K. R. Rajagopal
Viscoelastic fluids are non-Newtonian fluids that exhibit both "viscous" and "elastic" characteristics in virtue of mechanisms to store energy and produce entropy. Usually the ener…
Temperature field and heat generation at the tip of a cutout in a viscoelastic solid body undergoing loading
Vít Průša, Karel Tůma
Using the finite element method we quantitatively analyse temperature field evolution in a viscoelastic solid undergoing a loading--unloading process. In particular we investigate…
On incompressible heat-conducting viscoelastic rate-type fluids with stress-diffusion and purely spherical elastic response
Miroslav Bulíček, Josef Málek, Vít Průša +1
We prove the existence of large-data global-in-time weak solutions to an evolutionary PDE system describing flows of incompressible \emph{heat-conducting} viscoelastic rate-type fl…
Unconditional finite amplitude stability of a viscoelastic fluid in a mechanically isolated vessel with spatially non-uniform wall temperature
Mark Dostalík, Vít Průša, Judith Stein
We investigate finite amplitude stability of spatially inhomogeneous steady state of an incompressible viscoelastic fluid which occupies a mechanically isolated vessel with walls k…
A thermodynamic basis for implicit rate-type constitutive relations describing the inelastic response of solids undergoing finite deformation
David Cichra, Vít Průša
Implicit rate-type constitutive relations utilizing discontinuous functions provide a novel approach to the purely phenomenological description of the inelastic response of solids…
Numerical scheme for simulation of transient flows of non-Newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient and the Cauchy stress tensor
Adam Janečka, Josef Málek, Vít Průša +1
We propose a numerical scheme for simulation of transient flows of incompressible non-Newtonian fluids characterised by a non-monotone relation between the symmetric part of the ve…
Finite amplitude stability of internal steady flows of the Giesekus viscoelastic rate-type fluid
Mark Dostalík, Vít Průša, Karel Tůma
Using a Lyapunov type functional constructed on the basis of thermodynamical arguments we investigate the finite amplitude stability of internal steady flows of viscoelastic fluids…
Motion of the vitreous humour in a deforming eye -- fluid-structure interaction between a nonlinear elastic solid and a nonlinear viscoleastic fluid
Karel Tůma, Judith Stein, Vít Průša +1
We study the motion of vitreous humour in a deforming eyeball. From the mechanical and computational perspective this is a task to solve a fluid-structure interaction problem betwe…
Thermodynamics and stability of non-equilibrium steady states in open systems
Miroslav Bulíček, Josef Málek, Vít Průša
Thermodynamical arguments are known to be useful in the construction of physically motivated Lyapunov functionals for nonlinear stability analysis of spatially homogeneous equilibr…
Thermodynamics of viscoelastic rate-type fluids with stress diffusion
Josef Málek, Vít Průša, Tomáš Skřivan +1
We propose thermodynamically consistent models for viscoelastic fluids with a stress diffusion term. In particular, we derive variants of compressible/incompressible Maxwell/Oldroy…
Viscoelastic rate type fluids with temperature dependent material parameters -- stability of the rest state
Judith Stein, Vít Průša
We study the dynamics of small perturbations to the rest state of a viscoelastic rate type fluid with temperature dependent material parameters. We show that if the material parame…
Colombeau algebra as a mathematical tool for investigating step load and step deformation of systems of nonlinear springs and dashpots
Vít Průša, Martin Řehoř, Karel Tůma
The response of mechanical systems composed of springs and dashpots to a step input is of eminent interest in the applications. If the system is formed by linear elements, then its…
On Maxwell fluid with relaxation time and viscosity depending on the pressure
Satish Karra, Vít Průša, K. R. Rajagopal
We study a variant of the well known Maxwell model for viscoelastic fluids, namely we consider the Maxwell fluid with viscosity and relaxation time depending on the pressure. Such…