On Possible Reduction of Gradient Theories of Elasticity

Авторы: Lurie Sergey A., Belov Petr A., Solyaev Yury O.
Сборник: Advanced Structured Materials
Год издания: 2023
Издательство: Springer International Publishing
Местоположение издательства: New York
Первая страница: 479
Последняя страница: 498
DOI: 10.1007/978-3-031-26186-2_30
Аннотация: Mindlin–Tupin gradient theories of elasticity are considered, and a procedure is proposed to simplify general models with five moduli of elasticity to a gradient two-parameter model. It is shown that the simplified models are related to gradient models of the vector type, for which the quadratic form of the potential energy density is a convolution of vectors, and the number of physical additional parameters corresponds to the number of scaling characteristics in the system of resolving equations. Such models, called “vector” models, provide a classic view of static boundary conditions. For vector models, despite the fourth order of the resolving equations, there are no boundary conditions on the surface edges.
Добавил в систему: Лурье Сергей Альбертович

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