Minimal surfaces and conservation laws for bidimensional structures

Autor:	Victor Eremeyev
Rok vydání:	2022
Předmět:	Mechanics of Materials General Mathematics General Materials Science
Zdroj:	Mathematics and Mechanics of Solids. 28:380-393
ISSN:	1741-3028 1081-2865
DOI:	10.1177/10812865221108374
Popis:	We discuss conservation laws for thin structures which could be modeled as a material minimal surface, i.e., a surface with zero mean curvatures. The models of an elastic membrane and micropolar (six-parameter) shell undergoing finite deformations are considered. We show that for a minimal surface, it is possible to formulate a conservation law similar to three-dimensional non-linear elasticity. It brings us a path-independent J-integral which could be used in mechanics of fracture. So, the class of minimal surfaces extends significantly a possible geometry of two-dimensional structures which possess conservation laws.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::309ee9ad67eabfa5bc1d685332177ba6 https://doi.org/10.1177/10812865221108374 Zobrazit plný text záznamu