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Abstract
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.
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- Publication version
- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1177/10812865221108374
- License
- Copyright (2022 The Authors)
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
-
MATHEMATICS AND MECHANICS OF SOLIDS
no. 28,
pages 1 - 14,
ISSN: 1081-2865 - Language:
- English
- Publication year:
- 2022
- Bibliographic description:
- Eremeev V.: Minimal surfaces and conservation laws for bidimensional structures// MATHEMATICS AND MECHANICS OF SOLIDS -Vol. 28,iss. 1 (2022), s.1-14
- DOI:
- Digital Object Identifier (open in new tab) 10.1177/10812865221108374
- Sources of funding:
-
- COST_FREE
- Verified by:
- Gdańsk University of Technology
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