Papers by Keyword: Navier-Lamé

Abstract: In this work we show that the volume velocity, ρυ , rather than the local centre of mass velocity should be used in continua. We use the volume continuity equation to define the volume frame of reference in the multicomponent, compressible continua. The volume velocity (material velocity) is a unique frame of reference for all internal forces and processes, e.g., the mass diffusion. No basic changes are required in the foundations of linear irreversible thermodynamics except recognizing the need to add volume to the usual list of extensive physical properties undergoing transport in every continuum. The volume fixed frame of reference allows the translation of the Newton’s discrete mass-point molecular mechanics into continuum mechanics and the use of the Cauchy linear momentum equation of fluid mechanics and Navier-Lamé equation of mechanics of solids. Our proposed modifications of Navier-Lamé and energy conservation equations are selfconsistent with the literature for solid-phase continua dating back to the classical interdiffusion experiments of Kirkendall and their subsequent interpretation by Darken in terms of diffusive volume transport. We do show that the local diffusion processes do not change the centre of mass of the system and that the internal stress depends on the gradient of the local volume velocity only.

Abstract: The mass transport in the presence of stress, electrical, mechanical and chemical potential gradients in multicomponent solid solution is analyzed. The method bases on the Darken concept and the calorimetric equation of state. We effectively coupled the conservation of the mass (continuity equations), energy, momentum and Gauss equations. The diffusion fluxes of the components are given by the Nernst-Planck formulae and take into account the electro-chemical and mechanical potentials. We simulate the deformation field during the diffusion caused by the gradients of the chemical potential of all elements in non-ideal Fe-Cu-Ni alloy. The simulations show that the model is compatible with experimental results, and can be effectively used for modelling the energy, momentum and mass transport problems in compressible multicomponent solid solutions. The numerical problems and methods of solution are presented.