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.
Minimal surfaces and conservation laws for bidimensional structures
Eremeyev V. A.
Primo
2023-01-01
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.File | Dimensione | Formato | |
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