Topic
Mixture theory
About: Mixture theory is a research topic. Over the lifetime, 616 publications have been published within this topic receiving 19350 citations.
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TL;DR: In this article, a nonlinear multi-field coupled model for multi-constituent three-phase soils is derived by using the hybrid mixture theory, and the balance equations with three levels (constituents, phases and the whole mixture soil) are set up under the assumption that soil is composed of multiscale elastic-plastic solid skeleton and viscous liquid and ideal gas.
Abstract: A nonlinear multi-field coupled model for multi-constituent three-phase soils is derived by using the hybrid mixture theory. The balance equations with three levels (constituents, phases and the whole mixture soil) are set up under the assumption that soil is composed of multi-constituent elastic-plastic solid skeleton (which is different from the linearization method) and viscous liquid and ideal gas. With reasonable constitutive assumptions in such restrictive conditions as the principles of determinism, equipresence, material frame-indifference and the compatible principle in continuum mechanics, a theoretical framework of constitutive relations modeling three-phase soil in both non-equilibrium and equilibrium states is established, thus the closed field equations are formed. In the theoretical framework, the concept of effective generalized thermodynamic forces is introduced, and the nonlinear coupling constitutive relations between generalized dissipation forces and generalized flows within the system at nonequilibrium state are also presented. On such a basis, four special coupling relations, i.e., solid thermal elastic-plastic constitutive relation, liquid visco-elastic-plastic constitutive relation, the generalized Fourier’s law, and the generalized Darcy’s law are put forward. The generalized or nonlinear results mentioned above can degenerate into the linear coupling results given by Bennethum and Singh. Based on a specific dissipation function, the concrete form of generalized Darcy’s law is deduced, which may degenerate into the traditional form of Darcy’s law by neglecting the influence of skeleton deformation and temperature. Without considering temperature and other coupling effects, the nonlinear coupled model in this paper can degenerate into a soil elastic-plastic constitutive model.
21 citations
TL;DR: Based on the Mixture theory and the principles of continuum mechanics, a dynamic three-phase model for partially saturated poroelasticity is established as well as the corresponding governing equations in Laplace domain this paper.
Abstract: Based on the Mixture theory and the principles of continuum mechanics, a dynamic three-phase model for partially saturated poroelasticity is established as well as the corresponding governing equations in Laplace domain. The three-dimensional fundamental solutions are deduced following Hormander's method. Based on the weighted residual method, the boundary integral equations are established. The boundary element formulation in time domain for partially saturated media is obtained after regularization by partial integration, spatial discretization, and the time discretization with the Convolution Quadrature Method. The proposed formulation is validated with the semi-analytical one-dimensional solution of a column. Studies with respect to the spatial and temporal discretization show its sensitivity on a fine enough mesh. A half-space example allows to study the wave fronts. Finally, the proposed formulation is used to compute the vibration isolation of an open trench.
21 citations
TL;DR: In this article, the authors present a simple theory which takes into account the distribution of the particles in the fluid, the applied electric field, and the relative motion of the two constituents, and study the flow of an electro-rheological material between two parallel plates under the application of an electrical field normal to the plates.
21 citations
TL;DR: In this article, the authors used the classical mixture theory approach whereby constitutive relations are proposed for the stress tensor of each phase, and the effect of different hindrance functions for the drag force is studied; moreover a generalized form of the expression for the coefficients of the interactions forces, also known as the hindrance function, is suggested.
Abstract: In this short paper we study the flow of a mixture of a fluid infused with particles in a channel. We use the classical mixture theory approach whereby constitutive relations are proposed for the stress tensor of each phase. For the interaction forces, the effect of different hindrance functions for the drag force is studied; moreover a generalized form of the expression for the coefficients of the interactions forces, also known as the hindrance functions, is suggested. For studying this two-component system numerically, a three-dimensional CFD solver based on OpenFOAM® has been developed. Applying this solver, a specific problem (blood flow) has been studied for which our numerical results and experimental data show good agreement.
21 citations