Related papers: On renormalised solution for thermomechanical prob…
We consider a thermodynamically consistent model for thermoviscoplasticity. For the related PDE system, coupling the heat equation for the absolute temperature, the momentum balance with viscosity and inertia for the displacement variable,…
The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental…
In this work we study a quasi-static evolution of thermo-visco-elastic model with homogeneous thermal expansion. We assume that material is subject to two kinds of mechanical deformations: elastic and inelastic. Inelastic deformation is…
We study one-dimensional viscoelastic phase transitions modeled by a Ginzburg--Landau energy with a non-convex cubic stress-strain law. Extending the isothermal model, we couple the momentum equation to a heat equation for the temperature…
We study a Cahn--Hilliard two-phase model describing the flow of two viscoelastoplastic fluids, which arises in geodynamics. A phase-field variable indicates the proportional distribution of the two fluids in the mixture. The motion of the…
A standard elasto-plasto-dynamic model at finite strains based on the Lie-Liu-Kr\"oner multiplicative decomposition, formulated in rates, is here enhanced to cope with spatially inhomogeneous materials by using the reference (called also…
The aim of this paper is to prove the existence of weak solution for a quasi-static evolution of thermo-visco-elastic model with Norton-Hoff law of plasticity. The dependence on temperature occurs both in the elastic constitutive equations…
In this paper we consider the problem of analytical continuation of solutions to the system of thermoelasticity in a bounded domain from their values and values of their strains on a part of the boundary of this domain, i.e., the Cauchy…
A theoretical and computational investigation is carried out of a dissipative model of rate-independent strain-gradient plasticity and its regularization. It is shown that the flow relation, when expressed in terms of the Cauchy stress, is…
We study the fully nonlinear heat equation $b(\partial_tu)\partial_tu=\Delta u$ posed in a bounded domain with Dirichlet boundary conditions. Here $b(s)=b^-$ if $s<0$, $b(s)=b^+$ if $s>0$, $b^-\neq b^+$ being two positive constants. This…
We prove existence of global in time strong solutions to the truncated thermo- visco-plasticity with an inelastic constitutive function of Norton-Hoff type. This result is a starting point to obtain renoramlised solutions for the considered…
We continue the study of a dynamic evolution model for perfectly plastic plates, recently derived from three-dimensional Prandtl-Reuss plasticity. We extend the previous existence result by introducing non-zero external forces in the model,…
According to the Nernst theorem or, equivalently, the third law of thermodynamics, the absolute zero temperature is not attainable. Starting with an initial positive temperature, we show that there exist solutions to a Kelvin-Voigt model…
Within the framework of continuum mechanics, the full description Of joint motion of elastic bodies and compressible viscous fluids with taking into account thermal effects is given by the system consisting of the mass, momentum, and energy…
We propose thermodynamically consistent models for viscoelastic fluids with a stress diffusion term. In particular, we derive variants of compressible/incompressible Maxwell/Oldroyd-B models with a stress diffusion term in the evolution…
We investigate the Cauchy problem for the thermoelastic plate system associated with Newton's law of cooling, where optimal growth ($n\leqslant 4$) or decay ($n\geqslant 5$) estimates and asymptotic profiles of solutions for large-time are…
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…
We consider a quasistatic nonlinear model in thermoviscoelasticity at a finite-strain setting in the Kelvin-Voigt rheology where both the elastic and viscous stress tensors comply with the principle of frame indifference under rotations.…
The general Ericksen-Leslie system for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal model is then investigated analytically. A fairly…
This work addresses the question of regularity of solutions to evolutionary (quasi-static and dynamic) perfect plasticity models. Under the assumption that the elasticity set is a compact convex subset of deviatoric matrices, with $C^2$…