Calculus of Variations and Geometric Measure Theory

P. M. Mariano - D. Mucci

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

created by mucci on 28 Dec 2022
modified on 28 Sep 2023


Published Paper

Inserted: 28 dec 2022
Last Updated: 28 sep 2023

Journal: Mathematics in Engineering
Volume: 5
Pages: 1--21
Year: 2023


We consider elastic thin shells without through-the-thickness shear and depict them as Gauss graphs of parametric surfaces. (We use the term shells in a sense including plates and thin films.) We consider an energy depending on the first derivative of the Gauss map (so, it includes 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.

Keywords: Geometric measure theory, Thin films, Plates, shells, Curvature effects, Gauss graphs