thinshell

Thinshell, or thin shell, is an idealized concept used to describe a surface with negligible thickness that carries mass, stresses, and bending moments. This abstraction replaces a three-dimensional body with a two-dimensional shell, focusing on in-plane forces and curvature effects while simplifying the analysis of complex structures or spacetimes.

In general relativity, a thin shell is a distributional source of stress-energy confined to a closed hypersurface that separates two spacetime regions. The matching of the metric and the way stress-energy jumps across the shell are governed by the Israel junction conditions, sometimes expressed through the Lanczos equations. Thin shells model objects such as domain walls, bubble universes, gravastars, and thin-shell wormholes, enabling study of their dynamics, stability, and gravitational influence.

In structural mechanics and materials science, thin-shell theory treats curved surfaces whose thickness is small compared with other dimensions. There are membrane-dominated theories, which neglect bending, and bending-dominated theories, which account for curvature and bending stiffness. Classical approaches include Kirchhoff-Love shell theory and Donnell–Mushtari–Vibak formulations, often used for domes, pressure vessels, aerospace panels, and curved architectural shells. The thin-shell assumption reduces a three-dimensional problem to a two-dimensional one but has limitations, such as the omission of through-thickness shear and challenges under large deformations or high curvature.

Applications of thin-shell methods span physics and engineering, from modeling celestial or cosmological boundaries to designing efficient curved structures. The concept also informs computational methods, such as finite element analysis, where appropriate shell elements approximate real-world shells with reduced degrees of freedom.

See also: Israel junction conditions, thin-shell wormhole, domain wall, shell theory, Love’s theory.