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Showing papers on "Mixture theory published in 2012"


Journal ArticleDOI
TL;DR: A thermodynamically consistent four-species model of tumor growth on the basis of the continuum theory of mixtures, unique to this model is the incorporation of nutrient within the mixture as opposed to being modeled with an auxiliary reaction-diffusion equation.
Abstract: In this paper, we develop a thermodynamically consistent four-species model of tumor growth on the basis of the continuum theory of mixtures. Unique to this model is the incorporation of nutrient within the mixture as opposed to being modeled with an auxiliary reaction-diffusion equation. The formulation involves systems of highly nonlinear partial differential equations of surface effects through diffuse-interface models. A mixed finite element spatial discretization is developed and implemented to provide numerical results demonstrating the range of solutions this model can produce. A time-stepping algorithm is then presented for this system, which is shown to be first order accurate and energy gradient stable. The results of an array of numerical experiments are presented, which demonstrate a wide range of solutions produced by various choices of model parameters.

211 citations


Journal ArticleDOI
TL;DR: In this paper, the capabilities of an interface model to predict failure behavior of steel fiber reinforced cementitious composites (SFRCCs) are evaluated at both macro and mesoscale levels of observation.
Abstract: In this work the capabilities of an interface model to predict failure behavior of steel fiber reinforced cementitious composites (SFRCCs) are evaluated at both macro and mesoscale levels of observation. The interface model is based on a hyperbolic maximum strength criterion defined in terms of the normal and shear stress components acting on the joint plane. Pre-peak regime is considered linear elastic, while the post-peak behavior is formulated in terms of the fracture energy release under failure mode I and/or II. The well-known “Mixture Theory” is adopted for modeling the interactions between fibers and the surrounding cementitious composite. The effects of both the axial forces on the fibers induced by normal relative displacements, as well as the dowel action due to tangential relative displacements in the interfaces are considered in the formulation of the interaction mechanisms between fibers and cementitious composites. After describing the interface model, this work focuses on numerical analyses of SFRCC failure behavior. Firstly, the validation analysis of the interface model is performed at the constitutive level by comparing its numerical predictions against experimental results available in scientific literature. Then, the sensitivity of the interface theory for SFRCC regarding the variation of main parameters of the composite constituents is evaluated. Finally, the attention is focused on Finite Element (FE) analysis of SFRCC failure behavior at meso and macroscopic levels of observation. The results demonstrate the capabilities of the interface theory based on the Mixture Theory to reproduce the main features of failure behavior of SRFCC in terms of fiber content and involved fracture modes.

53 citations


Journal ArticleDOI
TL;DR: A new formulation to model the mechanical behavior of high performance fiber reinforced cement composites with arbitrarily oriented short fibers is presented, in which the macroscopic model takes into account the mesostructural phenomenon associated with the fiber-matrix interface bond/slip process.

50 citations


Journal ArticleDOI
TL;DR: The objective is to establish a basis for the development of constitutive equations for growth of tissues by transferring some poroelastic concepts developed by Maurice Biot to mixture theory.

35 citations


Journal ArticleDOI
TL;DR: The author explores the application of the derived DLD mixture model to cluster sound sources that exist in an underdetermined instantaneous sound mixture, offering a fast and stable solution.
Abstract: Directional or Circular statistics are pertaining to the analysis and interpretation of directions or rotations. In this work, a novel probability distribution is proposed to model multidimensional sparse directional data. The Generalized Directional Laplacian Distribution (DLD) is a hybrid between the Laplacian distribution and the von Mises-Fisher distribution. The distribution's parameters are estimated using Maximum-Likelihood Estimation over a set of training data points. Mixtures of Directional Laplacian Distributions (MDLD) are also introduced in order to model multiple concentrations of sparse directional data. The author explores the application of the derived DLD mixture model to cluster sound sources that exist in an underdetermined instantaneous sound mixture. The proposed model can solve the general ${K\times L~(K underdetermined instantaneous source separation problem, offering a fast and stable solution.

18 citations


Book ChapterDOI
01 Jan 2012
TL;DR: In this paper, a theoretical and numerical study of mass transport in a porous medium saturated with a fluid and characterised by an evolving internal structure is presented, where the dynamics of the porous medium and the fluid as well as their reciprocal interactions are described at a coarse scale, so that the fundamental tools of Mixture Theory and Continuum Mechanics can be used.
Abstract: We present a theoretical and numerical study of mass transport in a porous medium saturated with a fluid and characterised by an evolving internal structure. The dynamics of the porous medium and the fluid as well as their reciprocal interactions are described at a coarse scale, so that the fundamental tools of Mixture Theory and Continuum Mechanics can be used. The evolution of the internal structure of the porous medium, which is here primarily imputed either to growth or to mass exchange with the fluid, is investigated by enriching the space of kinematic variables of the mixture with a set of structural descriptors, each of which is power-conjugate to generalised forces satisfying a balance law. Establishing the influence of the structural change of the porous medium on the transport properties of the mixture and, thus, on the quantities characterising fluid flow is the crux of our contribution.

17 citations


Journal ArticleDOI
TL;DR: In this article, the authors explored the connection between the two approaches by considering the various reference configurations and material symmetries, and showed that under appropriate assumptions, the constitutive theory developed using mixture theory can coincide with the constitulative theory assuming an equivalent single material that is transversely isotropic and hyperelastic.
Abstract: There are two approaches that can be used to model the large strain mechanical response of material systems in which elastic fibers are embedded in an elastic matrix. In the first approach, a fiber reinforced material undergoing large deformation is homogenized in the sense that it is assumed to act as an equivalent single material that is transversely isotropic and hyperelastic. Both constituents then share a common reference configuration, which is typically assumed to be a natural or stress-free configuration for the equivalent single material. The stress depends on a single deformation gradient defined with respect to the natural configuration. In the second approach, the fiber/matrix system is treated as a mixture, with the matrix and the fibrous constituents having their own reference configurations and material symmetries. The total stress depends on the deformation gradients and material symmetries for both constituents, defined with respect to their reference configurations. Under appropriate assumptions, the constitutive theory developed using mixture theory can coincide with the constitutive theory assuming an equivalent single material that is transversely isotropic and hyperelastic. This paper explores the connection between the two approaches by considering the various reference configurations and material symmetries.

9 citations


Journal ArticleDOI
TL;DR: A thermodynamically consistent model for multiphase flow which allows for connected and disconnected phases in a swelling medium is developed using hybrid mixture theory with three spatial scales in this paper, which can be useful for both imbibition and drainage, including extremely dry systems.
Abstract: [1] A thermodynamically consistent model for multiphase flow which allows for connected and disconnected phases in a swelling medium is developed using hybrid mixture theory with three spatial scales The mesoscale of the medium consists of swelling particles and two bulk phases, such as liquid water and vapor The particles are a combination of a vicinal liquid and a solid, which may swell or shrink as a result of interaction with the other bulk phases; an example is a mixture of montmorillonite platelets and water The theory defines connected and disconnected bulk phases of liquid and vapor at the mesoscale to create a dual-porosity type model at the macroscale The disconnected vapor phase consists of either buoyant bubbles or confined vapor packets The incorporation of disconnected and connected phases is useful for modeling unsaturated swelling systems The macroscale solid phase volume fraction is refined from previous hybrid mixture approaches for two-phase multiscale problems and is fully utilized in the field equations and the constitutive theory Macroscale equations for each of the six phases are presented with bulk regions separated into connected and disconnected domains A constitutive theory is derived by exploiting the entropy inequality for the mixture Generalized Darcy's laws and the final set of field equations for the system are presented and compared with previous hybrid mixture theoretic results Classical parallel flow models only consider disconnected bulk regions and therefore are only appropriate for drainage; the current system can be useful for both imbibition and drainage, including extremely dry systems

6 citations


Book ChapterDOI
01 Jun 2012

5 citations


Proceedings ArticleDOI
23 Apr 2012
TL;DR: In this article, the authors present an engineering model for synthetic vascular materials that have fluid passages much smaller than a characteristic structural length such as panel thickness, and the thermomechanical characteristics of this restricted class of multifunctional materials are delineated.
Abstract: New multifunctional materials that include fluid passages are being developed. These materials hold promise for future high-performance aerospace structures. The fluid in the passages can enhance heat transfer, control deformation, provide resin for healing or remodeling, disclose damage, and modify stiffness and damping. This paper presents an engineering model for synthetic vascular materials that have fluid passages much smaller than a characteristic structural length such as panel thickness. A class of idealized materials is modeled as a two-phase continuum with a solid phase and a fluid phase occupying every volume. In order to simulate fully multifunctional synthetic vascular materials, the model permits the solid and fluid phases to exchange mass, momentum and energy. Balance equations and the entropy inequality for general mixtures are taken from existing continuum mixture theory. These are augmented with certain definite types of solid-fluid interactions in order to enable adequately general, but workable, engineering analysis. The thermomechanical characteristics of this restricted class of multifunctional materials are delineated. By demanding that the law of increase of entropy be satisfied for all processes, much is deduced about the acceptable forms of constitutive equations. The paper concludes with a study of the uniaxial tension behavior of an idealized vascular material.

4 citations


Book ChapterDOI
01 Jan 2012

01 Dec 2012
TL;DR: In this article, a new numerical model for the simulation of ASR in cement-based materials considering both the effect of temperature and moisture content is presented, and the model takes into account full coupling between hygral, thermal and chemical phenomena, as well as changes of concrete properties caused by chemical reaction.
Abstract: A new numerical model for the simulation of ASR in cement-based materials considering both the effect of temperature and moisture content is presented. A mechanistic approach, based on the mechanics of porous media, was used to obtain the governing equations by means of a hybrid mixture theory. The model equations, mass (water species and dry air), energy and momentum balances are written in terms of the chosen primary variables: gas pressure, capillary pressure, temperature and displacement vector, while the ASR evolution is described by the reaction extent being the internal variable. The model takes into account full coupling between hygral, thermal and chemical phenomena, as well as changes of concrete properties caused by chemical reaction, i.e. porosity, density, permeability. Phase changes and chemical processes, as well as the related heat and mass sources are considered. Material chemical and mechanical degradation is considered with the isotropic damage theory. The model equations are numerically solved using finite element method for discretization in space and finite differences for time integration. The model results are validated by comparison with some published experimental data concerning ASR expansion in constant and variable hygro-thermal conditions.

01 Jan 2012
TL;DR: In this article, a mesoscopic continuum multiphase model for transport and infiltration of a suspension through a porous medium is presented. But this model is not suitable for the case of a single-phase continuum model.
Abstract: This paper presents an approach for transport and infiltration of a suspension through a porous medium. The aim is to develop a mesoscopic continuum multiphase model, which takes infiltration processes into account. For this purpose, a Representative Volume Element (RVE) is considered and described by the continuum mixture theory extended by the concept of volume fractions (Theory of Porous Media - TPM). The thermodynamical-consistent TPM is a mesoscopical multiphase modelling approach, extended from classical single-phase continuum mechanics. In the present context, we further enhance the concept of volume fractions by certain distribution functions.

Journal ArticleDOI
TL;DR: In this paper, the balance laws of mass, momentum, angular momentum and energy of the lattice element used for recrystallization converges on a material point so that the laws are rewritten in the integration form.
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.

31 Jul 2012
TL;DR: In this paper, a fully coupled multiphase model for non-isothermal deformable porous media is developed within the hybrid mixture theory, where the standard Bubnov-Galerkin method is applied to the governing equations for the spatial discretization, whereas the generalized Newmark scheme is used for the time domain discretisation.
Abstract: Nowadays an increasing interest on thermo-hydro-mechanical analysis of multiphase porous media is observed because of a wide spectrum of application in civil and environmental engineering. The onset of landslides caused by rainfall or earthquake, the onset of catastrophic landslides, the seismic behaviour of deep radioactive waste disposal and concrete or earth dams are just few and challenging examples. As novel aspect, this work presents the development of a mathematical and numerical model for the analysis of the thermo-hydro-mechanical behaviour of multiphase porous materials in dynamics. The fully coupled multiphase model for non isothermal deformable porous media is developed within the hybrid mixture theory. In order to analyse the thermo-hydro-mechanical behaviour of a soil structure in the low frequency domain, e.g. under earthquake excitation, the u-p(-T) formulation is advocated for the finite element discretization, neglecting the relative fluids acceleration and their convective terms. As a consequence, the number of the independent variables is reduced to four: gas pressure, capillary pressure, temperature and solid skeleton displacements. Moreover, the dynamic seepage forcing terms in the mass and enthalpy balance equations and the compressibility of the solid grain at the microscopic level are neglected. The standard Bubnov-Galerkin method is applied to the governing equations for the spatial discretization, whereas the generalized Newmark scheme is used for the time domain discretization. The final algebraic, non linear and coupled system of equations is solved by the Newton method with a monolithic approach. The formulation and the implemented solution procedure are validated through the comparison with literature benchmarks, finite element solutions or analytical solutions when available.

Journal Article
TL;DR: In this article, a mixture graph was used to describe the relation between the general mixture state and the multiple states and multiple modes of the elements, and a mixture operator was given to give the algorithm to deduce the mixture state distribution from the multiple-state and multiple-mode distribution.
Abstract: On the basis of the mixture theory,the reliability analysis model of multiple-state and multiple-mode mechanical system was establishedAccording to the characters of different failure mechanisms and characters of different failure grades of the same failure mechanism,the mechanical system elements were classified into different failure states and modes to construct a multi-state and multi-mode mechanical systemA mixture graph was used to describe the relation between the general mixture state and the multiple-states and the multiple-modes of the elements,a mixture operator was used to give the algorithm to deduce the general mixture state distribution from the multiple-state and multiple-mode distributionThe mixture equation of series multi-state and multi-mode elements and parallel multi-state and multi-mode elements was deducedThe reliability analysis model of mixture states was established to obtain the multi-grade reliability of the system and to avoid the irrational phenomenon that the system reliability tended to reach zero in the case of independent calculation frequently done by system componentsThe reliability analysis example of high-speed pantograph components shows the effectiveness and superiority of the model

Journal ArticleDOI
TL;DR: In this article, a simple and general chemical association theory is introduced and the concept of infinite equilibrium model is re-examined and true mole fractions of associated species are calculated.
Abstract: In this study a simple and general chemical association theory is introduced. The concept of infinite equilibrium model is re-examined and true mole fractions of associated species are calculated. The theory is applied to derive the distribution function of associated species. As a severe test the application of presented theory to the van der Waals mixture model is introduced in order to perform Vapor-Liquid Equilibrium (VLE) calculations of aqueous ternary mixtures. The calculations are shown to be consistently improving the prediction over the non-associating case. Also, well known empirical models of NRTL and UNIQUAC are applied on the studied systems and their results are compared with proposed model.

Journal ArticleDOI
TL;DR: In this article, the basic boundary value problems were solved using Papkovich-Neuber representations and Fourier integral transforms when the displacement vector or stress vector values are given on the boundary.
Abstract: Abstract. For a homogeneous system of differential equations of statics of the elastic mixture theory, we solve the basic boundary value problems using Papkovich–Neuber representations and Fourier integral transforms when the displacement vector or stress vector values are given on the boundary . The solution uniqueness theorem is proved for the problems posed. Solutions are obtained in quadratures.

Proceedings ArticleDOI
TL;DR: SedMix3D as mentioned in this paper solves the Navier-Stokes equations for the fluid-sediment mixture with an additional equation describing sediment flux, treating the mixture as a single continuum with effective properties parameterizing the intraand inter-phase interactions with closure relations for the mixture viscosity, diffusion, hindered settling, and particle pressure.
Abstract: The highly turbulent, sediment-laden flow above rippled beds in the wave bottom boundary layer (WBBL) is poorly understood and difficult to quantify mainly because of our failure to understand the fundamental interaction forces driving sediment transport. However, recent advances in high performance computing allow for highly resolved simulations of fluid-sediment dynamics in the WBBL to examine the small-scale fluctuations of boundary layer processes and characterize seabed morphology. A three-dimensional mixture theory model, SedMix3D, solves the unfiltered Navier-Stokes equations for the fluid-sediment mixture with an additional equation describing sediment flux. Mixture theory treats the fluid-sediment mixture as a single continuum with effective properties parameterizing the intraand inter-phase interactions with closure relations for the mixture viscosity, diffusion, hindered settling, and particle pressure. We validate results obtained with SedMix3D using temporally and spatially resolved fluid velocity measurements acquired with a particle image velocimetry (PIV) system in a free-surface laboratory flume. Measured two-dimensional velocity fields are compared to two-dimensional vertical slices from the threedimensional simulation domain. We examine the hydrodynamics of the flow by comparing bulk flow statistics, and swirling strength. In general, results from SedMix3D were in excellent agreement with the observations. We believe SedMix3D captures the essential physics governing two–phase turbulent flow over ripples for the conditions represented by the experiments and should provide us with a powerful research tool for studying the dynamics of seafloor bedforms.