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Nanoscience and Technology: An International Journal
ESCI SJR: 0.228 SNIP: 0.484 CiteScore™: 0.37

ISSN Print: 2572-4258
ISSN Online: 2572-4266

Nanoscience and Technology: An International Journal

Formerly Known as Nanomechanics Science and Technology: An International Journal

DOI: 10.1615/NanoSciTechnolIntJ.2018028673
pages 1-20


Alexey I. Shveykin
Perm National Research Polytechnic University, 29 Komsomolsky Ave., Perm, 614990, Russian Federation
Peter V. Trusov
Perm National Research Polytechnic University, 29 Komsomolsky Ave., Perm, 614990, Russian Federation


Multilevel models of materials give an explicit description of the physical mechanisms, evolution of material structure, and physical and mechanical properties in inelastic deformation. This allows one to apply such models to improve the existing technologies of mechanical treatment (including the ones for submicrocrystalline and nanocrystalline materials) and develop some new ones. A key point in multilevel modeling of polycrystalline metals and alloys is the formulation of kinematic and constitutive relations at the mesolevel (the level of individual crystallites), which would apply to large displacement gradients peculiar to most processes of thermomechanical treatment of metals and alloys. Various formulations of the constitutive mesolevel models used in multilevel models of polycrystalline metals and alloys are considered. These are the relations in the unloaded configuration in the finite form, which are based on the motion decomposition with an explicit separation of the motion of the moving coordinate system, and the relations written in the rate form in the current configuration. The relationships used in these formulations to describe the rotations of the crystallite lattices are analyzed and compared. The analysis reveals the equivalence or closeness (in the sense of the response to be estimated) of the spins under consideration (with the exception of the logarithmic spin). The results of numerical calculations carried out for a polycrystal under arbitrarily chosen kinematic impacts lend support to the analytical conclusions.


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