A derivation of the time dependent von Kármán equations from atomistic models

Abstract: We derive the time-dependent von Kármán plate equations from three dimensional, purely atomistic particle models. In particular, we prove that a thin structure of interacting particles whose dynamics is governed by Newton's laws of motion is effectively described by the von Kármán equations in the limit of vanishing interatomic distance $\eps$ and vanishing plate thickness h. While the classical plate equations are obtained for $\eps \ll h \ll 1$, we find new plate equations for finitely many layers in the ultrathin case $\eps\sim h$.

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. Unless stated otherwise, we will meet on Mondays at 15:40 in the lecture hall K3 (2nd floor)