A free boundary approach to quasistatic debonding

Abstract: Debonding models describe the evolution of an adhesive membrane peeled away from a planar rigid substrate. When the process is sufficiently slow, inertial and viscous effects can be neglected, leading to a quasistatic setting. In this framework, debonding can be formulated as a variational evolution of sets. In the talk, I will present how to prove the existence of so-called energetic solutions for this formulation—based on global minimizers of a suitable functional together with an energy balance—by exploiting an equivalent rewriting of the model in terms of the celebrated one-phase Bernoulli free boundary problem. This is based on a joint work with E. Maggiorelli and E. Tolotti. If time permits, I will also discuss the dynamic version of the problem, in which inertial effects are taken into account. In this setting, a wave equation on moving domains is coupled with a suitable criterion governing the evolution of such domains. The problem, formulated in collaboration with G. Lazzaroni, R. Molinarolo, and F. Solombrino, is still open.

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)