Variational model of linear elasticity considering spatial nonlocality
V. S. Zarubin
Department of Fundamental Sciences, Bauman Moscow State Technical University, Moscow, Russia
Search for more papers by this authorCorresponding Author
I. Yu. Savelyeva
Department of Fundamental Sciences, Bauman Moscow State Technical University, Moscow, Russia
Correspondence
I.Yu. Savelyeva, Department of Fundamental Sciences, Bauman Moscow State Technical University, Moscow, Russia.
Email: [email protected]
Search for more papers by this authorE. A. Maksimova
Department of Fundamental Sciences, Bauman Moscow State Technical University, Moscow, Russia
Search for more papers by this authorV. S. Zarubin
Department of Fundamental Sciences, Bauman Moscow State Technical University, Moscow, Russia
Search for more papers by this authorCorresponding Author
I. Yu. Savelyeva
Department of Fundamental Sciences, Bauman Moscow State Technical University, Moscow, Russia
Correspondence
I.Yu. Savelyeva, Department of Fundamental Sciences, Bauman Moscow State Technical University, Moscow, Russia.
Email: [email protected]
Search for more papers by this authorE. A. Maksimova
Department of Fundamental Sciences, Bauman Moscow State Technical University, Moscow, Russia
Search for more papers by this authorAbstract
It is crucial to have appropriate mathematical models that take into account the interaction between the structural elements of materials at the atomic level and at the meso-level to acquire knowledge and describe the behavior of new promising structure-sensitive materials under mechanical loading. At the same time, approaches based on modifications of known models of a continuum and allowing to take into consideration the relationship between the characteristics of such materials at the macro and micro levels remain relevant. One of the options is associated with a modification of the classical variational model of linear elasticity, which provides an adequate description of the property of spatial nonlocality characteristic of the mentioned materials.
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