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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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Journal ArticleDOI
01 Dec 2007-Pamm
TL;DR: In this paper, the authors investigated a space-time Galerkin method applied to the dynamic analysis of fully-saturated porous material, where the governing set of equations are derived from the well-studied Theory of Porous Media (TPM).
Abstract: We investigated a space-time Galerkin method applied to the dynamic analysis of fully-saturated porous material. The governing set of equations are derived from the well-studied Theory of Porous Media (TPM). The numerical scheme consists of a coupled finite element discretization in the space-time domain. Discontinuous approximations of the primary variables in time are employed. A natural flux treatment is applied in time to impose the consistency between the adjacent time intervals. A simple space-time decoupled adaptive strategy based on the “jumps” in time and the ZZ error indicator in space is investigated. Numerical experiments demonstrate the efficiency and reliability of the proposed approach. We investigate a discontinuous space-time Galerkin method for the dynamic modeling of porous media. The physical model is based on the thermodynamically-consistent Theory of Porous Media (TPM). In contrast to the well-known Biot’s theory, which is constructed upon a lot of intuitive assumptions, the TPM is based on the rational axioms of the mixture theory extended by the concept of volume fractions. The main advantage of the TPM is that it can be extended straight forwardly to describe more complex physical situations. The physical model of the dynamic analysis has been developed in [4]. In the current work, we solved the governing set of equations with the high-order accurate time-discontinuous Galerkin (DGT) method [1]. Moreover, due to the employment of the Embedded Velocity Integration (EVI) technique [2], we are able to solve a three-fields formulation with the primary variables in the solid velocity vs, the seepage velocity wf and the pore pressure p. The solid displacement us is achieved in a post-processing step according to consistent integration of the velocities vs. The finite element variational form of the three-fields formulation solved by the DGT method has been presented in [3], which will not be repeated here. Moreover, a simple space-time adaptive strategy for the dynamical modeling within the porous material is developed. In the spatial domain, an extended error indicator of Zienkiewicz-Zhu type was developed, in which post-processed values of the characteristic quantities are considered. In the temporal domain, due to the employment of discontinuous approximations in time, a simple error indicator based on the amount of “jumps” in the primary variables is proposed.
Book
22 Jul 2013
TL;DR: Higher-level physical laws applicable to biological tissues are presented that will permit the modeling of metabolic activity at the cellular level, including variations in the mass of a tissue, as a fluid/solid mixture.
Abstract: Higher-level physical laws applicable to biological tissues are presented that will permit the modeling of metabolic activity at the cellular level, including variations in the mass of a tissue. Here the tissue is represented as a fluid/solid mixture, wherein molecular solutes transport within the fluid, and cells can migrate throughout the porous solid. Variations in mass can arise via exchanges in mass between the constituent phases within a control volume such that mass is conserved in the tissue overall. The governing balance laws for mass, momentum, energy, and entropy are a special case of those describing a chemically reacting mixture with diffusion. Thermodynamic constraints on the constitutive structure are addressed. Biophysics; Biomechanics; Brownian motion; Cell migration; Mixture theory; Thermodynamic laws; Tissue mechanics
Journal ArticleDOI
TL;DR: In this article, the behavior of unsaturated porous materials is described according to the procedure of FICK'S mixture theory, and hysteresis is included by use of the VOLTERRA'S integral form or by an approximative method using experimental results.
Abstract: Summary The behaviour of unsaturated porous materials is described according to the procedure of FICK'S mixture theory. Hysteresis is included by use of the VOLTERRA'S integral form or by an approximative method using experimental results. Several mathematical models corresponding to physically significant situations are derived from the theory.
Proceedings ArticleDOI
TL;DR: A method to determine if points were drawn from a Gaussian mixture ρQ(x) with the same shape as the template with a robust performance against type I errors, and few type II errors when the given template Gaussian mixtures are well distinguished.
Abstract: The motivating application for this research is the problem of recognizing a planar object consisting of points from a noisy observation of that object. Given is a planar Gaussian mixture model ρT (x) representing an object along with a noise model for the observation process (the template). Also given are points representing the observation of the object (the query). We propose a method to determine if these points were drawn from a Gaussian mixture ρQ(x) with the same shape as the template. The method consists in comparing samples from the distribution of distances of ρT (x )a ndρQ(x), respectively. The distribution of distances is a faithful representation of the shape of generic Gaussian mixtures. Since it is invariant under rotations and translations of the Gaussian mixture, it provides a workaround to the problem of aligning objects before recognizing their shape without sacrificing accuracy. Experiments using synthetic data show a robust performance against type I errors, and few type II errors when the given template Gaussian mixtures are well distinguished.
Proceedings ArticleDOI
01 Jan 2007
TL;DR: In this paper, a constitutive model was developed to predict the elastic response of two dimensional balsa wood material with a distribution of cell geometries, and two planar triangular grids, each assumed to represent the structural network of an open cell foam material, were superimposed to model an overall cellular structure with the distribution of cells.
Abstract: A constitutive model has been developed to predict the elastic response of two dimensional balsa wood material with a distribution of cell geometries. Two planar triangular grids, each assumed to represent the structural network of an open cell foam material, are superimposed to model an overall cellular structure with a distribution of cell geometries. The elastic mixture theory is applied in conjunction with the micropolar elasticity theory to homogenize the cellular structure and to establish the overall constitutive relationship.Copyright © 2007 by ASME

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