Showing papers on "Mixture theory published in 1993"

A Continuum Theory of a Lubrication Problem With Solid Particles

Abstract: The governing equations for a two-dimensional lubrication problem involving the mixture of a Newtonian fluid with solid particles at an arbitrary volume fraction are developed using the theory of interacting continuua (mixture theory). The equations take the interaction between the fluid and the particles into consideration. Provision is made for the possibility of particle slippage at the boundaries. The equations are simplified assuming that the solid volume fraction varies in the sliding direction alone. Equations are solved for the velocity of the fluid phase and that of the solid phase of the mixture flow in the clearance space of an arbitrary shaped bearing. It is shown that the classical pure fluid case can be recovered as a special case of the solutions presented. Extensive numerical solutions are presented to quantify the effect of particulate solid for a number of pertinent performance parameters for both slider and journal bearings. Included in the results are discussions on the influence of particle slippage on the boundaries as well as the role of the interacting body force between the fluid and solid particles.

Hygrothermomechanical evaluation of porous media under finite deformation. Part I ‐ finite element formulations

Abstract: The coupled thermomechanical responses of fluid-saturated porous continua subjected to finite deformation are investigated. Field equations governing the transient response of the media are derived from a continuum thermodynamics mixture theory based on mass balance, momentum balance and energy balance laws as well as the Clausius-Duhem inequality. Finite element procedures for the two-dimensional response, employing updated Lagrangian formulations for the solid skeleton deformation and the weak formulations for fluid and thermal transport equations, are implemented in a fully implicit form. Temperature-dependent mechanical properties for the non-linear solid matrix, characterized by Perzyna's viscoplastic model, are assumed. An iterative scheme based on the full Newton-Raphson method is presented for simultaneously solving the coupled non-linear equations.

Hybrid and mixed‐penalty finite elements for 3‐D analysis of soft hydrated tissue

Abstract: Solution of biomechanics problems involving three-dimensional (3-D) behaviour of soft tissue on geometries representative of such tissue in vivo will require the use of numerical methods. Toward this end, a pair of tetrahedral finite elements has been developed. The equations which are used to model the tissue behaviour for both elements are those commonly known as the linear biphasic equations. This model assumes that hydrated soft tissue is a mixture of two incompressible, immiscible phases, and employs mixture theory to derive governing equations for its mechanical behaviour. The finite element techniques applied to these equations for the two elements are the mixed-penalty method and the hybrid method. Both elements are described here, and the special requirements for 3-D analysis are discussed. Results obtained by solving canonical problems in two and three dimensions using both elements are presented and compared. Both elements are found to produce excellent results. The hybrid element is also noted to have advantages for non-linear analyses involving finite deformation which will require solution in the future.