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1.
Ton Tran-Cong 《Archive of Applied Mechanics (Ingenieur Archiv)》1996,67(1-2):96-104
Summary A variational principle for fluid mechanics is derived without calling for any additional postulates in any ad hoc way. In the principle derived here, the Lagrangian is essentially the sum of kinetic and heat energy transferred to the fluid, less the sum of its internal and potential energy, less the work done on its exterior (similar to the enthalpy concept), rather than the difference between only kinetic energy and internal energy, as obtained previously by Seliger and Whitham [1] for a more restricted mode of variation. 相似文献
2.
F. dell'Isola M. Guarascio K. Hutter 《Archive of Applied Mechanics (Ingenieur Archiv)》2000,70(5):323-337
Summary The principle of virtual power is used to derive the equilibrium field equations of a porous solid saturated with a fluid,
including second density-gradient effects; the intention is the elucidation and extension of the effective stress principle
of Terzaghi and Fillunger. In the context of a first density-gradient theory for a saturated solid we interpret the porewater
pressure as a Lagrange multiplier in the expression for the deformation energy, assuring that the saturation constraint is
verified. We prove that this saturation pressure is distributed among the constituents according to their respective volume
fraction (Delesse law) only if they are both true density-preserving. We generalize the Delesse law to the case of compressible
constituents. If a material-dependent effective stress contribution is to arise, it is, in general, nonvanishing simultaneously
in both the solid and fluid constituents. Moreover, saturation pressure, effective stresses and compressibility constitutive
equations determine the exchange volume forces. In a theoretical formulation without non-isotropic strain measures, second
density-gradient effects must be incorporated, not only to accommodate for the equilibrium-solid-shear stress and the interaction
among neighboring solid-matrix pores, but also to describe internal capillarity effects. The earlier are accounted for by
a dependence of the thermodynamic energy upon the density-gradient of the solid, while the latter derives from a mixed density-gradient
dependence. Examples illustrate the necessity of these higher gradient effects for properly posed boundary value problems
describing the mechanical behaviour of the disturbed rock zone surrounding salt caverns. In particular, we show that solid
second-gradient strains allow for the definition of the concept of static permeability, which is distinct from the dynamic
Darcy permeability.
Received 1 February 1999; accepted for publication 9 March 1999 相似文献