Summary
A general theory of continua with microstructure is proposed, inspired by classical lagrangian dynamics. A distinctive feature of this approach is the exploitation of an appropriately formulated principle of action-reaction; as an essential premise, this requires specification of the admissible distributions of lagrangian velocities of a rigid type. A number of special theories (e.g., continua with voids, liquid crystals and bodies with affine microstructure) are shown to fit naturally into the general scheme.
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References
G.Capriz,Introductory remarks to the dynamics of continua with microstructure, N.I. CNUCE C81-8.
G. Capriz -P. Podio-Guidugli,Discrete and continuous bodies with affine structure, Ann. Mat. Pura Appl.,111 (1976), pp. 195–217.
G. Capriz -P. Podio-Guidugli,Formal structure and classification of theories of oriented materials, Ann. Mat. Pura Appl.,115 (1977), pp. 17–39.
G. Capriz -P. Podio-Guidugli,Materials with spherical structure, Arch. Rat. Mech. Analysis,75 (1981), pp. 269–279.
G.Capriz - P.Podio-Guidugli,Materials with finite-dimensional structure, in A.P.S. Selvadurai ed.,Mechanics of Structured Media, Elsevier (1981), pp. 255–268.
G. Capriz -P. Podio-Guidugli -W. Williams,On balance equations for materials with affine structure, Meccanica,17 (1982), pp. 80–84.
S. C. Cowin,On local inertia in Cosserat continua, ZAMP,26 (1975), pp. 51–59.
S. C. Cowin -F. M. Leslie,On kinetic energy and momenta in Cosserat continua, ZAMP,31 (1980), pp. 247–260.
J. L. Ericksen,On generalized momentum, Int. J. Solids Structures,18 (1982), pp. 315–317.
M. A. Goodman -S. C. Cowin,A continuum theory for granular materials, Arch. Rat. Mech. Analysis,44 (1972), pp. 249–266.
A. E.Green - R. S.Rivlin,Generalized continuum mechanics, in H. Parkus and L. I. Sedov eds., Proc. IUTAM Symp. Vienna, 1966, Springer (1967), pp. 132–145.
R. N. Hills -P. H. Roberts,Superfluid mechanics for a high density of vortex lines, Arch. Rat. Mech. Analysis,66 (1977), pp. 43–71.
E. Kröner, ed.,Mechanics of Generalized Continua, Proc. IUTAM Symp., Freudenstadt and Stuttgart, 1967, Springer (1968).
N. D. Mermin,The topological theory of defects in ordered media, Rev. Modern Physics,51 (1979), pp. 591–648.
W. Noll,Lectures on the foundations of continuum mechanics and thermodynamics, Arch. Rat. Mech. Analysis,52 (1973), pp. 62–92.
J. W. Nunziato -S. C. Cowin,A nonlinear theory of elastic materials with voids, Arch. Rat. Mech. Analysis,72 (1979), pp. 175–201.
R. A. Toupin,Stress tensors in elastic dielectrics, Arch. Rat. Mech. Analysis,5 (1960), pp. 440–452.
R. A. Toupin,Theories of elasticity with couple-stresses, Arch. Rat. Mech. Analysis,5 (1960), pp. 440–452.
C.Truesdell - W.Noll,The Nonlinear Field Theories of Mechanics, Handbuch der Physik, III/3, Springer (1965)'
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Capriz, G., Podio-Guidugli, P. Structured continua from a lagrangian point of view. Annali di Matematica pura ed applicata 135, 1–25 (1983). https://doi.org/10.1007/BF01781060
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DOI: https://doi.org/10.1007/BF01781060