Mixture theory

About: Mixture theory is a research topic. Over the lifetime, 616 publications have been published within this topic receiving 19350 citations.

Transient Response in a Micropolar Mixture of Porous Media During Thermal Shock

Abstract: In this article, the micropolar mixture theory for porous media is generalized in the context of generalized L-S theory and classical C-T theory of thermoelasticity. The thermoelastic problem for a micropolar mixture of porous media is investigated in the context of the generalized micropolar mixture theory for porous media. The surface of a semi-infinite porous media is subjected to a zonal time-dependent thermal shock. The problem is solved by using the finite element method. The results, including the temperature, stresses, displacements, and microrotation are presented graphically. Comparisons are made between the results obtained by using two theories. The fluid constituting the mixture has a significant influence on the microrotation but a very slight influence on other responses.

From discrete to continuum fields in bidisperse granular mixtures

Abstract: Micro–macro transition methods can be used to, both, calibrate and validate continuum models from discrete data obtained via experiments or simulations. These methods generate continuum fields such as density, momentum, stress, etc., from discrete data, i.e. positions, velocity, orientations and forces of individual elements. Performing this micro–macro transition step is especially challenging for non-uniform or dynamic situations. Here, we present a general method of performing this transition, but for simplicity we will restrict our attention to two-component scenarios. The mapping technique, presented here, is an extension to the micro–macro transition method, called coarse-graining, for unsteady two-component flows and can be easily extended to multi-component systems without any loss of generality. This novel method is advantageous; because, by construction the obtained macroscopic fields are consistent with the continuum equations of mass, momentum and energy balance. Additionally, boundary interaction forces can be taken into account in a self-consistent way and thus allow for the construction of continuous stress fields even within one element radius of the boundaries. Similarly, stress and drag forces can also be determined for individual constituents of a multi-component mixture, which is critical for several continuum applications, e.g. mixture theory-based segregation models. Moreover, the method does not require ensemble-averaging and thus can be efficiently exploited to investigate static, steady and time-dependent flows. The method presented in this paper is valid for any discrete data, e.g. particle simulations, molecular dynamics, experimental data, etc.; however, for the purpose of illustration we consider data generated from discrete particle simulations of bidisperse granular mixtures flowing over rough inclined channels. We show how to practically use our coarse-graining extension for both steady and unsteady flows using our open-source coarse-graining tool MercuryCG. The tool is available as a part of an efficient discrete particle solver MercuryDPM (www.​MercuryDPM.​org).

Mixture theory of domain switching in ferroelectric ceramics

Abstract: A mixture model is proposed to model domain switching in polycrystalline ferroelectric ceramics. Each grain is modeled as a body of mixture consisting of distinct types of domains which are characterized by their mass fractions as internal variables. In this model, domain switching corresponds to changes of mass fractions of the corresponding domains. A thermodynamics-based criterion is proposed to govern domain switching in quasi-static processes. With the present model, one can make grain-level calculations of internal stress and electric fields to which microcracking, the primary cause of the electric fatigue, is attributed. The explicit solution to an idealized 1D polycrystalline ferroelectric system is presented in order to explore the implications of this model.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Formulation of balance laws as mixture theory for nuclei and matrix in recrystallization

Abstract: In the previous work, the authors formulated the balance laws of mass, momentum, angular momentum and energy of the lattice element used for recrystallization. These laws were summed up over a phase in a representative volume element (RVE) and averaged in the RVE so as to develop the discrete balance laws for single phase. Furthermore, the balance law of angular momentum was separated into a bulk and a lattice parts through the orderestimation with the representative lengths both in macroscopic and microscopic scales. In this paper, the RVE converges on a material point so that the laws are rewritten in the integration form. When the laws are summed up all over the phases and averaged in them, the balance laws of mass, momentum, angular momentum and energy for nuclei and matrix as mixture are formulated, using an useful theorem proposed for the mixing summation of unsteady terms. At this time, the macroscopic part of the balance law for angular momentum results in the usual equation of angular momentum, so that the stress tensor keeps symmetry even if the lattice rotation is considered. While, the microscopic one is localized as an equation of spin angular momentum for lattice, which is suggested to be equivalent to the evolution equation of crystal orientation in KWC type phase-field model. Moreover, the increase law of entropy for mixture is also formulated. During this process, the entropy flux is defined by use of relative mass flux and chemical potential of phase transformation.