Equilibrium of thin shells under large strains without through-the-thickness shear and self-penetration of matter

Abstract

<abstract><p>We consider elastic thin shells without through-the-thickness shear and depict them as Gauss graphs of parametric surfaces. (We use the term <italic>shells</italic> to include plates and thin films therein.) We consider an energy depending on the first derivative of the Gauss map (so, it involves curvatures) and its second-rank minors. For it we prove existence of minimizers in terms of currents carried by Gauss graphs. In the limiting process we adopt sequences of competitors that satisfy a condition that prevents self-penetration of matter.</p></abstract>