Invariant line integrals in the theory of defective crystals
Parry, Gareth P. ; Šilhavý, Miroslav
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 11 (2000), p. 111-140 / Harvested from Biblioteca Digitale Italiana di Matematica

In a continuum theory of crystals with defects, invariant line integrals measure the line defects of the lattice structure. It is shown that the integrands of invariant line integrals can always be taken to have the transformation properties of covariant vector-valued functions.

Invarianti integrali di linea in una teoria dei cristalli difettivi. In una teoria che modellizza i cristalli con difetti come mezzi continui, gli invarianti integrali di linea quantificano proprio i difetti di linea nella struttura cristallina. Si mostra in questo lavoro che le integrande di tali invarianti integrali possono sempre essere scelte in modo da avere la proprietà di transformazione di un vettore covariante.

Publié le : 2000-06-01
@article{RLIN_2000_9_11_2_111_0,
     author = {Gareth P. Parry and Miroslav \v Silhav\'y},
     title = {Invariant line integrals in the theory of defective crystals},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {11},
     year = {2000},
     pages = {111-140},
     zbl = {0967.74021},
     mrnumber = {1797515},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_2000_9_11_2_111_0}
}
Parry, Gareth P.; Šilhavý, Miroslav. Invariant line integrals in the theory of defective crystals. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 11 (2000) pp. 111-140. http://gdmltest.u-ga.fr/item/RLIN_2000_9_11_2_111_0/

[1] Davini, C., A proposal for a continuum theory of defective crystals. Arch. Rational Mech. Anal., 96, 1986, 295-317. | MR 855751 | Zbl 0623.73002

[2] Davini, C., Elastic invariants in crystal theory. In: J. M. Ball (ed.), Material instabilities in continuum mechanics and related mathematical problems. Clarendon Press, Oxford 1988, 85-105. | MR 970520 | Zbl 0659.73001

[3] Davini, C. - Parry, G. P., On defect-preserving deformations in crystals. Int. J. Plasticity, 5, 1989, 337-369. | Zbl 0697.73036

[4] Davini, C. - Parry, G. P., A complete list of invariants for defective crystals. Proc. R. Soc. Lond. A, 432, 1991, 341-365. | MR 1116537 | Zbl 0726.73032

[5] Davini, C. - Parry, G. P., Uniform rearrangement in defective crystals. Proc. R. Soc. Lond. A, 439, 1992, 247-256. | MR 1193002 | Zbl 0766.73057

[6] Fonseca, I. - Parry, G. P., Equilibrium configurations of defective crystals. Arch. Rational Mech. Anal., 120, 1992, 245-283. | MR 1183552 | Zbl 0785.73007

[7] Fonseca, I. - Parry, G. P., On a class of invariant functionals. Proc. R. Soc. Lond. A, 436, 1992, 317-329. | MR 1177132 | Zbl 0767.73095

[8] Olver, P. J., Conservation laws and null divergences. Math. Proc. Camb. Phil. Soc., 94, 1983, 529-540. | MR 720804 | Zbl 0556.35021

[9] Olver, P. J., Applications of Lie groups to partial differential equations. Springer-Verlag, New York1986. | MR 836734 | Zbl 0588.22001

[10] Olver, P. J., Equivalence, invariants, and symmetry. Cambridge University Press, Cambridge1996. | MR 1337276 | Zbl 0837.58001

[11] Parry, G. P., Defects and rearrangements in crystals. In: L. M. Brock (ed.), Defects and anelasticity in the characterization of crystalline solids. ASME, New York 1992, 117-132.

[12] Parry, G. P., Elastic-plastic decompositions of defect-preserving changes of state in solid crystals. In: M. D. P. Monteiro Marques - J. F. Rodrigues (eds.), Trends in applications of mathematics to mechanics. Longman, Harlow, Essex 1994, 154-163. | MR 1475480 | Zbl 0865.73051

[13] Parry, G. P., Material symmetry in solid crystals. In: D. F. Parker - A. H. England (eds.), IUTAM Symposium on Anisotropy, inhomogeneity and nonlinearity in solid mechanics. Kluwer Academic Publishers, Amsterdam 1995, 229-234. | MR 1367108 | Zbl 0900.73054

[14] Parry, G. P., On defective crystalography. Arch. Mech., 50, 1998, 567-575. | Zbl 0955.74016

[15] Parry, G. P. - Šilhavý, M., Elastic invariants in the theory of defective crystals. Proc. R. Soc. Lond. A, 455, 1999, 4333-4346. | MR 1809363 | Zbl 0954.74013