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Introductory remarks to the dynamics of continua with microstructure. (English) Zbl 0656.73006

Mathematical models and methods in mechanics, Banach Cent. Publ. 15, 71-95 (1985).
[For the entire collection see Zbl 0653.00013.]
These lectures were addressed to students having as a common background only a basic course in particle and continuum mechanics. Thus elementary topics were rivisited at first though with the slant of a scholar in continuum mechanics, emphasising constitutive laws, requirements of objectivity, etc.; in fact, Sections 1 to 4 could be intended as the sketch of a modest pedagogical proposal. The second part of the paper contains a succinct report on balance laws for continua with microstructure (as proposed by the author and P. Podio-Guidugli, Materials with finite-dimensional structure [in: A.P.S. Selvaduri (ed.), Mechanics of structured media, Elsevier, Amsterdam (1981); pp. 255-268]), the conciseness being in part justified by the lengthy introduction.
Section 2 contains a brief reference to the simplest representation theorems; Section 3 is devoted to some comments on the action-reaction principle and on the law of moment of momentum; system of particles subject to perfect constraints are considered in Section 4, so as to lead in the following Sections 5 and 6 to a discussion on the allowable rigid velocity distributions. Thus a necessary, central condition on the Lagrangian components of internal forces is derived, a condition which is of essence in the developments of the later sections. Section 5 contains also some examples which should render the reader familiar with the type of implications to be expected from the condition. Geometry, kinematics and dynamics of continua with general, finite-dimensional structure are discussed briefly in Section 7. In Section 8 it is finally shown how some special theories can be set within the general framework.

MSC:

74A99 Generalities, axiomatics, foundations of continuum mechanics of solids
74A60 Micromechanical theories
74M25 Micromechanics of solids

Citations:

Zbl 0653.00013