By Gérard A. Maugin (auth.), Gérard A. Maugin, Andrei V. Metrikine (eds.)
In their 1909 booklet Théorie des corps déformables, Eugène and François Cosserat made a old contribution to fabrics technology via developing the elemental rules of the mechanics of generalized continua. The chapters accrued during this quantity exhibit the numerous components of continuum mechanics that grew out of the foundational paintings of the Cosserat brothers.
The integrated contributions offer an in depth survey of the latest theoretical advancements within the box of generalized continuum mechanics. the various issues coated contain: the houses of Cosserat media, micromorphic our bodies, micropolar solids and fluids, weakly- and strongly-nonlocal theories, gradient theories of elasticity and plasticity, disorder conception, everywhere-defective fabrics, our bodies with fractal constitution, in addition to different similar subject matters.
- makes a speciality of fresh advancements in continuum mechanics and fabrics layout, together with numerical examples and newly constructed models.
- provides numerical examples to illustrate the potency of assorted answer techniques.
- presents a distinct evaluate of generalized continuum mechanics, illustrating the $64000 functions of this thought in a number of different medical disciplines.
- incorporates a foreword written via popular physicist and fabrics scientist A.C. Eringen.
Mechanics of Generalized Continua can function an invaluable reference for graduate scholars and researchers in mechanical engineering, fabrics technology, utilized physics and utilized mathematics.
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Additional info for Mechanics of Generalized Continua: One Hundred Years After the Cosserats
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).
Mechanics of Generalized Continua: One Hundred Years After the Cosserats by Gérard A. Maugin (auth.), Gérard A. Maugin, Andrei V. Metrikine (eds.)