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Accounting for Quadratic and Cubic Invariants in Continuum Mechanics–An Overview

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dc.contributor.authorDmitrenko, A. V.
dc.contributor.authorOvsyannikov, V. M.
dc.contributor.authorДмитренко, Артур Владимирович
dc.date.accessioned2024-12-04T13:24:35Z
dc.date.available2024-12-04T13:24:35Z
dc.date.issued2024
dc.description.abstractThe differential equations of continuum mechanics are the basis of an uncountable variety of phenomena and technological processes in fluid-dynamics and related fields.These equations contain derivatives of the first order with respect to time.The derivation of the equations of continuum mechanics uses the limit transitions of the tendency of the volume increment and the time increment to zero.Derivatives are used to derive the wave equation.The differential wave equation is second order in time.Therefore, increments of volume and increments of time in continuum mechanics should be considered as small but finite quantities for problems of wave formation.This is important for calculating the generation of sound waves and water hammer waves.Therefore, the Euler continuity equation with finite time increments is of interest.The finiteness of the time increment makes it possible to take into account the quadratic and cubic invariants of the strain rate tensor.This is a new branch in hydrodynamics.Quadratic and cubic invariants will be used in differential wave equations of the second and third order in time.
dc.format.extentС. 1925-1939
dc.identifier.citationDmitrenko, A. V. Accounting for Quadratic and Cubic Invariants in Continuum Mechanics–An Overview / Dmitrenko, A.V., Ovsyannikov, V.M. // Fluid Dynamics and Materials Processing. - 2024. - 20. - № 9. - P. 1925-1939. - 10.32604/fdmp.2024.048389
dc.identifier.doi10.32604/fdmp.2024.048389
dc.identifier.urihttps://www.doi.org/10.32604/fdmp.2024.048389
dc.identifier.urihttps://www.scopus.com/record/display.uri?eid=2-s2.0-85202449160&origin=resultslist
dc.identifier.urihttps://openrepository.mephi.ru/handle/123456789/26249
dc.relation.ispartofFluid Dynamics and Materials Processing
dc.subjectMechanical Characterization
dc.subjectAdaptive Control
dc.subjectInput Shaping Control
dc.subjectMechanical Behavior
dc.subjectVascular Mechanics
dc.titleAccounting for Quadratic and Cubic Invariants in Continuum Mechanics–An Overview
dc.typeArticle
dspace.entity.typePublication
oaire.citation.issue9
oaire.citation.volume20
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