On a general balance law for continua with an interface
type: Item
instance of: scholarly article
title: On a general balance law for continua with an interface
zbMATH Open document ID: 0629.76004
published in: Ricerche di Matematica
publication date: 1986-01-01T00:00:00Z
review text: In the literature two different types of reasoning are developed in order to obtain local evolution equations and jump conditions for a continuous system with an interface (C,S). The first one starts with an integral balance equation valid only for the whole system. The second one, on the other hand, starts assuming a general integral balance equation valid for all material volumes included in (C,S). The local form of this integral equation is then obtained owing to the arbitrariness of material volumes. Notwithstanding its more clear physical justification this second approach makes use of the concept of material volume, which is ambiguous when this volume includes a portion of a nonmaterial (i.e. not made up with always the same particles) and adsorbing interface (for instance in the case of phase transition). We formulate a general integral balance law (GIBL) valid for a continuously moving family of Eulerian volumes at any instant t included in the region \(C(t)\subset R^ 3\) occupied by the continuous system (C,S). We define (when the projection of velocity on S is continuous across S) a family \(\{c_ m(t)\}\) of Eulerian regions which can be regarded as a ``first order'' material volume and assume that for this \(\{c_ m(t)\}\) the GIBL holds. It results that it reads as the usually postulated integral balance law for material volumes. We deduce even when the projection of the velocity on S is discontinuous across S the local balance law by applying GIBL to a fixed arbitrary Eulerian volume included in (C,S). We finally observe that when applied to the region occupied at the instant t by the whole system (C,S), GIBL reduces to a global integral balance law.
Mathematics Subject Classification ID: 76A02
Mathematics Subject Classification ID: 82B05
zbMATH DE Number: 4024963
zbMATH Keywords: local evolution equations
zbMATH Keywords: jump conditions
zbMATH Keywords: interface
zbMATH Keywords: integral balance equation
zbMATH Keywords: Eulerian volumes
author: Francesco dell'Isola
author: A. Romano
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4024963