91 citations · 382 across the 40 of their papers we have counts for
6 papers · 2 filters
Emergence of coherent localized structures in shear deformations of temperature dependent fluids
Theodoros Katsaounis, Julien Olivier, Athanasios E. Tzavaras
Shear localization occurs in various instances of material instability in solid mechanics and is typically associated with Hadamard-instability for an underlying model. While Hadam…
Convergence of Variational Approximation Schemes for Elastodynamics with Polyconvex Energy
Alexey Miroshnikov, Athanasios E. Tzavaras
We consider a variational scheme developed by S. Demoulini, D. M. A. Stuart and A. E. Tzavaras [Arch. Ration. Mech. Anal. 157 (2001)] that approximates the equations of three dimen…
A variational approximation scheme for radial polyconvex elasticity that preserves the positivity of Jacobians
Alexey Miroshnikov, Athanasios E. Tzavaras
We consider the equations describing the dynamics of radial motions for isotropic elastic materials; these form a system of non-homogeneous conservation laws. We construct a variat…
The problem of dynamic cavitation in nonlinear elasticity
Jan Giesselmann, Alexey Miroshnikov, Athanasios E. Tzavaras
The notion of singular limiting induced from continuum solutions (slic-solutions) is applied to the problem of cavitation in nonlinear elasticity, in order to re-assess an example…
Stress relaxation models with polyconvex entropy in Lagrangean and Eulerian coordinates
Athanasios E. Tzavaras
The embedding of the equations of polyconvex elastodynamics to an augmented symmetric hyperbolic system provides in conjunction with the relative entropy method a robust stability…
On the construction and properties of weak solutions describing dynamic cavitation
Alexey Miroshnikov, Athanasios E. Tzavaras
We consider the problem of dynamic cavity formation in isotropic compressible nonlinear elastic media. For the equations of radial elasticity we construct self-similar weak solutio…