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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 paper, the authors compare and contrast the fundamental basis upon which these continuum models have been formulated and illustrate the difference in these models including the incompatible nomenclature which impedes direct comparison.
Abstract: Over the last 12 years, numerous new theoretical continuum models have been formulated to predict particle segregation in the size-based bidisperse granular flows over inclined channels. Despite their presence, to our knowledge, no attempts have been made to compare and contrast the fundamental basis upon which these continuum models have been formulated. In this paper, firstly, we aim to illustrate the difference in these models including the incompatible nomenclature which impedes direct comparison. Secondly, we utilise (i) our robust and efficient in-house particle solver MercuryDPM, and (ii) our accurate micro–macro (discrete to continuum) mapping tool called coarse-graining, to compare several proposed models. Through our investigation involving size-bidisperse mixtures, we find that (i) the proposed total partial stress fraction expressions do not match the results obtained from our simulation, and (ii) the kinetic partial stress fraction dominates over the total partial stress fraction and the contact partial stress fraction. However, the proposed theoretical total stress fraction expressions do capture the kinetic partial stress fraction profile, obtained from simulations, very well, thus possibly highlighting the reason why mixture theory segregation models work for inclined channel flows. However, further investigation is required to strengthen the basis upon which the existing mixture theory segregation models are built upon.

56 citations

Journal ArticleDOI
TL;DR: In this paper, a binary mixture theory with microstructure is constructed for unidirectionally fiber-reinforced elastic composites, based on a asymptotic scheme with multiple scales and the application of Reissner's new mixed variational principle.
Abstract: : A binary mixture theory with microstructure is constructed for unidirectionally fiber-reinforced elastic composites. Model construction is based on a asymptotic scheme with multiple scales and the application of Reissner's new mixed variational principle (1984). In order to assess the accuracy of the model, comparison of the mixture model predictions with available experimental data on dispersion of harmonic waves is made for boron/epoxy and tungusten/aluminum composites. Formulas for the effective moduli are also presented, and the results are compared with the test data and other available predictions.

56 citations

Journal ArticleDOI
TL;DR: In this article, a non-linear theory of drying is constructed based on the concept of mixture theory and the thermodynamics of irreversible processes, which is concerned with deformations and drying-induced stresses of moistened capillary-porous medium during intensive drying.

56 citations

Journal ArticleDOI
TL;DR: A novel algorithm for learning mixture models from multivariate data using TRUST-TECH to compute neighborhood local maxima on the likelihood surface using stability regions and can be easily generalized to any other parametric finite mixture model.
Abstract: The expectation maximization (EM) algorithm is widely used for learning finite mixture models despite its greedy nature. Most popular model-based clustering techniques might yield poor clusters if the parameters are not initialized properly. To reduce the sensitivity of initial points, a novel algorithm for learning mixture models from multivariate data is introduced in this paper. The proposed algorithm takes advantage of TRUST-TECH (TRansformation Under STability-reTaining Equilibria CHaracterization) to compute neighborhood local maxima on the likelihood surface using stability regions. Basically, our method coalesces the advantages of the traditional EM with that of the dynamic and geometric characteristics of the stability regions of the corresponding nonlinear dynamical system of the log-likelihood function. Two phases, namely, the EM phase and the stability region phase, are repeated alternatively in the parameter space to achieve local maxima with improved likelihood values. The EM phase obtains the local maximum of the likelihood function and the stability region phase helps to escape out of the local maximum by moving toward the neighboring stability regions. Though applied to Gaussian mixtures in this paper, our technique can be easily generalized to any other parametric finite mixture model. The algorithm has been tested on both synthetic and real data sets and the improvements in the performance compared to other approaches are demonstrated. The robustness with respect to initialization is also illustrated experimentally.

55 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


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202311
20228
20219
20208
201913
201811