EQUADIFF 2017

Minisymposium MS-24

PDE analysis for implicitly constituted materials

Thursday, 27th July 2017

Organisers:

Miroslav Bulíček, Josef Málek (both Charles University, Prague, Czech Republic) &
Endre Süli (University of Oxford, UK)

Speakers:

14:00-14:30 Josef Málek (Charles University, Prague, Czech Republic) Download
14:30-15:00 Laurent Chupin (University of Clermont Auvergne, Clermont-Ferrand, France) Download
15:00-15:30 Yong Lu (Nankai University, Tianjin, China) Download
15:30-16:00 Josef Žabenský (University of Würzburg, Germany) Download

16:30-17:00 Miroslav Bulíček (Charles University, Prague, Czech Republic) Download
17:00-17:30 Victor Kovtunenko (University of Graz, Austria) Download
17:30-18:00 Sebastian Schwarzacher (Charles University, Prague, Czech Republic) Download
18:00-18:30 Yasemin Şengül (Sabanci University, Istanbul, Turkey) Download

Overview:

Most physical models describing fluid flow rely on the assumption that the Cauchy stress is an explicit function of the symmetric part of the velocity gradient of the fluid. This assumption leads to the Navier-Stokes equations and its nonlinear generalizations, such as various electrorheological flow models. It is known however that the framework of classical continuum mechanics, built upon the notions of current and reference configuration and an explicit constitutive equation for the Cauchy stress is too narrow to enable one to model inelastic behavior of solid-like materials or viscoelastic properties of materials. The focus of this minisymposium is therefore a generalization of the classical framework of continuum mechanics, called implicit constitutive theory, which was proposed recently in a series of papers by Rajagopal. The underlying principle of implicit constitutive theory in the context of viscous flows is the following: instead of demanding that the Cauchy stress is an explicit function of the symmetric part of the velocity gradient, one may allow an implicit and not necessarily continuous relationship between these quantities. The second half of the minisymposion focuses on limiting strain models in elasticity theory involving implicit relations between the Cauchy stress and the strain, where the linearized strain tensor is a bounded function of the Cauchy stress.