zbMATH — the first resource for mathematics

A direct theory of affine bodies. (English) Zbl 1210.74011
Summary: A direct derivation of the theory of affine bodies is presented, with emphasis posed to the constitutive principles underlying the theory and to the role of the group of invariance of the theory (the congruences of physical space). To reconcile our abstract presentation with the standard one, an identification procedure of the constitutive relations of an affine body from that of a three-dimensional Cauchy body is also presented.

74A20 Theory of constitutive functions in solid mechanics
Full Text: DOI
[1] Capriz, G.; Podio-Guidugli, P., Discrete and continuous bodies with affine structure, Ann. math. pura appl., 111, 195-217, (1976) · Zbl 0358.73080
[2] G. Capriz, P. Podio-Guidugli, Materials with finite-dimensional structure, in: Mechanics of Structured Media, Proceedings of the International Symposium on the Mechanical Behaviour of Structured Media, Ottawa, Canada, 1981, pp. 255-268 · Zbl 0484.73002
[3] Capriz, G.; Podio-Guidugli, P., Materials with spherical structure, Arch. rat. mech. anal., 75, 269-279, (1981) · Zbl 0484.73002
[4] Cohen, H., Pseudo-rigid bodies, Utilitas math., 20, 221-247, (1981) · Zbl 0482.70002
[5] Cohen, H.; Muncaster, M.G., The theory of pseudo-rigid bodies, Springer tracts in natural philosophy, (1989), Springer Berlin
[6] A. Di Carlo, A non-standard format for continuum mechanics, in: R.C. Batra, M.F. Beatty (Eds.), Contemporary Research in the Mechanics and Mathematics of Materials, CIMNE, Barcelona, 1996, pp. 92-104
[7] Muncaster, M.G., Invariant manifolds in mechanics II: zero-dimensional elastic bodies with directors, Arch. rat. mech. anal., 84, 375-392, (1984) · Zbl 0538.73002
[8] A. Tiero, Un modello per le interfacce, Rapporti del Dipartimento di Ingegneria Civile, Università degli Studi di Roma “Tor Vergata”, 1994, no. 47
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.