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IssuesArchive of Issues2023-1pp.153-160

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E.V. Murashkin and Yu.N. Radayev, "The Schouten Force Stresses in Continuum Mechanics Formulations," Mech. Solids. 58 (1), 153-160 (2023)
Year 2023 Volume 58 Number 1 Pages 153-160
DOI 10.3103/S0025654422700029
Title The Schouten Force Stresses in Continuum Mechanics Formulations
Author(s) E.V. Murashkin (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, evmurashkin@gmail.com)
Yu.N. Radayev (Ishlinsky Institute for Problems in Mechanics RAS, Moscow, 119526 Russia, radayev@ipmnet.ru)
Abstract The paper deals with the force stress pseudotensor as proposed by Schouten and a derivation of equilibrium equations in terms of the Schouten stress pseudotensor of positive weight. The definition of Schouten's force stress pseudotensor is based on the notion of a pseudoinvariant area element. Conventional and unconventional definitions of the force stress tensor are recalled and discussed. The tensor area elements of a M-manifold immersed in N-dimensional parent (outer) plane space are revisited. The notions of vector, pseudovector, invariant and pseudo-invariant elementary areas in three-dimensional plane space are thoroughly discriminated. The usability of pseudotensor elementary volume of any given integer weight is discussed. Three realizations of the covariant differentiation of pseudotensor fields are considered and compared. Equations of equilibrium and dynamics are derived in terms of the Schouten force stress pseudotensor from the virtual displacements principle.
Keywords pseudotensor, manifold, elementary volume, elementary area, Schouten force stress pseudotensor, virtual displacements principle, fundamental orienting pseudoscalar
Received 29 June 2022Revised 18 July 2022Accepted 31 August 2022
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