Variational models with Eulerian-Lagrangian formulation allowing for material failure

Abstract: We investigate the existence of minimizers of variational models with Eulerian-Lagrangian formulations. Similar models arise naturally in many multi-physics problems such as the modeling of nematic and ferromagnetic elastomers. We consider energy functionals depending on the deformation of a body, defined on its reference configuration, and an Eulerian map defined on the unknown deformed configuration in the actual space. Our existence theory moves beyond the purely elastic setting and accounts for material failure by addressing free-discontinuity problems where both deformations and Eulerian fields are allowed to jump. To do so, we build upon the work of Henao and Mora-Corral regarding the variational modeling of cavitation and fracture in nonlinear elasticity. Two main settings are considered by modeling deformations as Sobolev and SBV -maps, respectively. The regularity of Eulerian maps is specified in each of these two settings according to the geometric and topological properties of the deformed configuration. Effectiveness and limitations of the theory are illustrated by means of explicit examples. The talk is based on joint work with Manuel Friedrich (FAU Erlangen-Nuremberg) and Carlos Mora-Corral (Universidad Autonoma de Madrid).

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)