Geodesic
The Models of Material Continuum
Mathematica Applicanda, Tome 14 (1986) no. 28, pp. 5-32.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

In this paper the essence of models of material continuum is examined and the construction of those models is presented on the example of Mechanics of Deformable Bodies. The definition of such models is formulated and the reasons for their effectiveness are discussed. The main directions of the developement of such models are indicated. The definitions of a material body, material fields and dynamic processes are formulated. Equivalent processes are considered as those which are representations of the same physical process relative to a different frame work of references. The motion of a material continuum is described. It is regarded as a one-parameter family of transformations of an abstract body into the euclidean space E. The evolutional equations of a material continuum are introduced as a local form of the principal conservation laws. General properties of constitutive equations are discussed. They result from the objectivity and stress localization assumptions. After introducing the concept of material isomorphism and isotropy group, classification of materials is carried ont.
DOI : 10.14708/ma.v14i28.1676
Classification : 73A05 (73B99)
Mots-clés : Axiomatics, foundations 
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Czesław Rymarz. The Models of Material Continuum. Mathematica Applicanda, Tome 14 (1986) no. 28, pp.  5-32. doi : 10.14708/ma.v14i28.1676. http://geodesic.mathdoc.fr/articles/10.14708/ma.v14i28.1676/

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