On a general balance law for continua with an interface

Francesco Dell'Isola (1, 2) , A. Romano (3)

1 Dipartimento di Ingegneria Strutturale e Geotecnica
2 Laboratorio Strutture e Materiali Intelligenti - Fondazione Tullio Levi-Civita
3 Dipartimento di Matematica ed Applicazioni

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 (we used in [1]) starts with an integral balance equations valid only for the whole system. (see also [2], [3]). In this case it is seen in a simple way that the general balance equation is equivalent to a local volume equation and a surface jump condition where the so-called localization residual appears. This residual is usually interpreted as describing a non local interaction and therefore is neglected when this interaction does not need to be taken into account. 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 (see [4], [5]).

Domaines: Mécanique [physics.med-ph]

Francesco Dell'Isola, A. Romano. On a general balance law for continua with an interface. Ricerche di matematica, 1986, pp.13. ⟨hal-00502393⟩