By Jean A. Dieudonne
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Extra resources for A Panorama of Pure Mathematics (Pure and Applied Mathematics (Academic Pr))
Néer. Sci. , Sér. II 6, 1–24 (1901) 40. : Kontinuumstheorie der Versetzungen und Eigenspannungen. Springer, Berlin (1958) 41. Kröner, E. ): Generalized Continua. Proc. IUTAM Symp. Freudenstadt. A. Maugin 42. : Nichtlokal Elastostatik: Ableitung aus der Gittertheorie. Z. Phys. 196(3), 203–211 (1966) 43. : Model of elastic medium with simple structure and space dispersion. Prikl. Mat. Mekh. 30, 542–550 (1966) 44. : Elastic Media with Microstructure I & II. Springer, Berlin (1982). Translated from the 1975 Russian edition 45.
Dyskin ( ) · E. au E. A. V. V. Dyskin and E. Pasternak in such a modeling even if all distances are equally accessible in the continuum. When the higher order continua such as Cosserat continuum are employed, they bring their own characteristic lengths. Then the interplay between the characteristic lengths of the continuum and the scale of averaging becomes important and in some cases can control the results of the modeling. This paper investigates crack propagation in the Cosserat continua whose characteristic lengths commensurate with the microstructural length of the material (the particle size or the layer thickness).
Proof. 21). As a direct corollary of this proposition, we can propose the following definition. 1. A non-holonomic Cosserat medium is said to be semi-holonomic at X if its constitutive law at X is independent of the deformation gradient of the macro-medium. From the mathematical standpoint, it is necessary to note that this definition does not imply the existence of a canonical projection of a non-holonomic jet onto a semi-holonomic part. In fact, such a canonical projection does not exist. 21).
A Panorama of Pure Mathematics (Pure and Applied Mathematics (Academic Pr)) by Jean A. Dieudonne