Applied PDE Group
Nonlinear Partial Differential Equations in Fluid and Solid Mechanics

AT2013

Stress relaxation models with polyconvex entropy in Lagrangean and Eulerian coordinates

‚ÄčA.E. Tzavaras, Stress relaxation models with polyconvex entropy in Lagrangian and Eulerian coordinates, Comm. in Information and Systems 13 (2013), 487-515
A.E. Tzavaras
polyconvex elasticity, relaxation limits, pressure relaxation in gases
2014
‚ÄčThe embedding of the equations of polyconvex elastodynamics to an augmented symmetric hyperbolic system provides in conjunction with the relative entropy method a robust stability framework for approximate solutions. We devise here a model of stress relaxation motivated by the format of the enlargement process which formally approximates the equations of polyconvex elastodynamics. The model is endowed with an entropy function which is not convex but rather of polyconvex type. Using the relative entropy we prove a stability estimate and convergence of the stress relaxation model to polyconvex elastodynamics in the smooth regime. As an application, we show that models of pressure relaxation for real gases in Eulerian coordinates fit into the proposed framework