On a multiweight formulation of boundary conditions for surface growth theories

V. A. Kovalev^a, E. V. Murashkin^b, N. E. Stadnik<sup>b

a</sup> Moscow City Government University of Management Moscow
^b Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow

Abstract: In this paper, we consider a method for constructing a multiweight theory of surface growth in terms of pseudotensors. The mathematical theory proposed for consideration is substantially based on the achievements of modern pseudotensor calculus. Definitions of multiweight pseudotensor elements of area and volume are given. The general multiweight form of the pseudotensor relation on a growing surface is derived, taking into account the additional selected direction. The necessary system of independent multiweight pseudotensor arguments of the defining pseudotensor function on the growing surface is determined. A complete multiweight set of joint rational pseudoinvariants of force and couple stress pseudotensors is determined. A pseudoinvariant complete formulation of the constitutive relations on the growing surface is given.

Keywords: algebraic weight, pseudotensor, nanoscale, microscale, micropolarity, pseudotensor volume element, multiweight formulation, constitutive pseudotensor function, growing surface, rational pseudoinvariant.

UDC: 539.374

Received: 03.03.2024
Revised: 05.07.2024
Accepted: 16.03.2024

DOI: 10.37972/chgpu.2024.59.1.013