By Konstantin Naumenko, Marcus Aßmus
This quantity provides a suite of contributions on complex methods of continuum mechanics, that have been written to rejoice the sixtieth birthday of Prof. Holm Altenbach. The contributions are on subject matters concerning the theoretical foundations for the research of rods, shells and three-d solids, formula of constitutive types for complicated fabrics, in addition to improvement of latest methods to the modeling of wear and fractures.
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An extended arbitrary Lagrangian–Eulerian finite element modeling (X-ALE-FEM) in powder forming processes. J. Mater. Process. Technol. : Hydrodynamics. : Fluid Mechanics, vol. 6, 1st edn. : Mechanics of liquid and gas. : Introduction to the Mechanics of a Continuous Medium. : Theory and Problems of Continuum Mechanics. : Theoretical Hydrodynamics. Martin’s Press, Macmillan and Co. : Bilanzgleichungen offener mehrkomponentiger systeme. I. massenund impulsbilanzen. J. Non-Equilib. Thermodyn. : What Spacetime Explains: Metaphysical Essays on Space and Time.
Politechnic University Publishing House, St. Petersburg (2012) The Cosserats’ Memoir of 1896 on Elasticity Gérard A. Maugin Abstract Nowadays the Cosserat brothers are mostly cited for their work on socalled “Cosserat continua” of 1909 that practically initiated the theory of “oriented media” as generalized continua. But in 1896 they had already published a lengthy well-structured memoir on the theory of elasticity. This memoir is often considered as a foundational work on the modern approach to elasticity as it beautifully summarizes what was achieved in the nineteenth century but with original traits that will permeate further the twentieth century developments with an emphasis on finite deformations, the interest for applying the thermodynamic laws, the allied formulation of the notion of stress (internal forces), questions of stability, and the use of curvilinear coordinates, though still without using vector and/or tensor analysis.
Indeed, the displacement Δs = v(r, t)Δt on the right side of Eq. (46) cannot be expressed in terms of function arguments. This is due to a peculiarity of the spatial description in which the position vector r is unrelated to the evolution of matter and dr the velocity v(r, t) is an independent characteristic. Since = 0 and ∇r = I (I dt is the unit tensor), the equation relating the position vector and the velocity, v(r, t) ≡ dr δr r = + v(r, t) · ∇r δt dt (49) turns into an identity. Thus, the velocity v(r, t) is the primary quantity in the spatial description and all other quantities are expressed in terms of v(r, t).