Publications (8)
Non-isothermal multicomponent flows with mass diffusion and heat conduction
Stefanos Georgiadis, Ansgar Jüngel, Athanasios Tzavaras
A type-I model of non-isothermal multicomponent systems of gases describing mass diffusive and heat conductive phenomena is presented. The derivation of the model and a convergence…
Existence of localizing solutions in plasticity via geometric singular perturbation theory
Min-Gi Lee, Athanasios Tzavaras
Shear bands are narrow zones of intense shear observed during plastic deformations of metals at high strain rates. Because they often precede rupture, their study attracted attenti…
Conservation of energy for the Euler-Korteweg equations
Tomasz DÄbiec, Piotr Gwiazda, Agnieszka Åwierczewska-Gwiazda +1
In this article we study the principle of energy conservation for the Euler-Korteweg system. We formulate an Onsager-type sufficient regularity condition for weak solutions of the…
Localization in inelastic rate dependent shearing deformations
Theodoros Katsaounis, Min-Gi Lee, Athanasios Tzavaras
Metals deformed at high strain rates can exhibit failure through formation of shear bands, a phenomenon often attributed to Hadamard instability and localization of the strain into…
Equilibration versus Localization in a Diffusion-Relaxation System
Aseel AlNajjar, Hoyoun Kim, Athanasios Tzavaras
We consider a diffusion-relaxation system and investigate the conditions on parameters leading to equilibration versus localization. When the diffusion is dominant, solutions conve…
Weak-strong uniqueness of dissipative measure-valued solutions for polyconvex elastodynamics
Sophia Demoulini, David Stuart, Athanasios Tzavaras
For the equations of elastodynamics with polyconvex stored energy, and some related simpler systems, we define a notion of dissipative measure-valued solution and show that such a…
Localization in adiabatic shear flow via geometric theory of singular perturbations
Min-Gi Lee, Theodoros Katsaounis, Athanasios Tzavaras
We study localization occurring during high speed shear deformations of metals leading to the formation of shear bands. The localization instability results from the competition am…
Relative entropy for hyperbolic-parabolic systems and application to the constitutive theory of thermoviscoelasticity
Cleopatra Christoforou, Athanasios Tzavaras
We extend the relative entropy identity to the class of hyperbolic-parabolic systems whose hyperbolic part is symmetrizable. The resulting identity, in the general theory, is usefu…