Classes of ephemeral continua. (14th December 2017)

• Record Type: Journal Article
• Authors: Capriz, Gianfranco; Giovine, Pasquale
• Other Names: Barbatis Gerassimos guestEditor.; Dougalis Vassilios guestEditor.; Stratis Ioannis G. guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 3(2018)
• Page Start: 1175
• Page End: 1196
• Publication Date: 2017-12-14
• Subjects: balance equations -- granular matter -- kinetic theory -- mechanics of fluids -- multiscale models -- sparse media; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4658
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : The qualifier "ephemeral" was proposed for continuous models of bodies, such as gases, for which the generally tacit axiom of permanence of material elements fails to apply. Consequently, to their scrutiny, a Eulerian (local) approach is mandatory, such as one adopted, eg, in molecular dynamics. Within the scheme of ephemeral continua, we discuss here 3 essential subclasses of bodies: (1) those undergoing energy‐preserving processes (in this sense hyperelastic), (2) hypoelastic bodies inspired by a type proposed by Truesdell, and (3) a number of minor ones. We re‐examine the essential issues of the general format focusing on the proposal of appropriate concepts of strains and strainings.