Mixture theory

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

A Multiscale Approximation Method to Describe Diatomic Crystalline Systems: Constitutive Equations

Abstract: We model the mechanical behavior of diatomic crystals in the light of mixture theory. Use is made of an approximation method similar to one proposed by Signorini within the theory of elasticity, by supposing that the relative motion between phases is infinitesimal. The constitutive equations for a mixture of elastic bodies in the absence of diffusion are adapted to the partially linearized case considered here, and the representation theorems for constitutive fields are applied to obtain the final expression of dynamical equations in the form which appears in theories of continua with vectorial microstructure. Comparisons are made with results of lattice theories.

Multiphase Simulation Using Material Point Method

Abstract: Author(s): Pradhana, Andre | Advisor(s): Teran, Joseph M | Abstract: We present a discussion on how one can simulate sand as a continuum using elastoplasticity. We showed the efficacy of Drucker-Prager plasticity model and St. Venant Kirchhoff with Hencky strain to model sand. We discretized the continuum equation using Material Point Method (MPM). We also present a multi-species model for the simulation of gravity driven landslides and debris flows with porous sand and water interactions. We use continuum mixture theory to describe individual phases where each species individually obeys conservation of mass and momentum and they are coupled through a momentum exchange term. Water is modeled as a weakly compressible fluid and sand is modeled with an elastoplastic law whose cohesion varies with water saturation. We use Material Point Method to discretize the governing equations. We use two grids, corresponding to water and sand phase. The momentum exchange term in the mixture theory is relatively stiff and we use semi-implicit time stepping to avoid associated small time steps. Our semi-implicit treatment is explicit in plasticity and preserves symmetry of force linearizations. We develop a novel regularization of the elastic part of the sand constitutive model that better mimics plasticity during the implicit solve to prevent numerical cohesion artifacts that would otherwise have occurred. Lastly, we develop an improved return mapping for sand plasticity that prevents volume gain artifacts in the traditional Drucker-Prager model.Finally, we revisit the problem of redistancing, which is native to the level set paradigms. We used an interesting alternative view that utilizes the Hopf-Lax formulation of the solution to the eikonal equation, as proposed by \cite{lee:2017:revisiting,darbon:2016:algorithms}. In this approach, the signed distance at an arbitrary point is obtained without the need of distance information from neighboring points. We extend the work of Lee et al. \cite{lee:2017:revisiting} to redistance functions defined via interpolation over a regular grid.

Constitutive Relation of Unsaturated Soil by Use of the Mixture Theory (I)-Nonlinear Constitutive Equations and Field Equations

Abstract: The nonlinear constitutive equations and field equations of unsaturated soils were constructed on the basis of mixture theory. The soils were treated as the mixture composed of three constituents. First, from the researches of soil mechanics, some basic assumptions about the unsaturated soil mixture were made, and the entropy inequality of unsaturated soil mixture was derived. Then, with the common method usually used to deal with the constitutive problems in mixture theory, the nonlinear constitutive equations were obtained. Finally, putting the constitutive equations of constituents into the balance equations of momentum, the nonlinear field equations of constituents were set up. The balance equation of energy of unsaturated soil was also given, and thus the complete equations for solving the thermodynamic process of unsaturated soil was formed.

Pattern Recognition with Gaussian Mixture Models of Marginal Distributions

Abstract: Precise estimation of data distribution with a small number of sample patterns is an important and challenging problem in the field of statistical pattern recognition. In this paper, we propose a novel method for estimating multimodal data distribution based on the Gaussian mixture model. In the proposed method, multiple random vectors are generated after classifying the elements of the feature vector into subsets so that there is no correlation between any pair of subsets. The Gaussian mixture model for each subset is then constructed independently. As a result, the constructed model is represented as the product of the Gaussian mixture models of marginal distributions. To make the classification of the elements effective, a graph cut technique is used for rearranging the elements of the feature vectors to gather elements with a high correlation into the same subset. The proposed method is applied to a character recognition problem that requires high-dimensional feature vectors. Experiments with a public handwritten digit database show that the proposed method improves the accuracy of classification. In addition, the effect of classifying the elements of the feature vectors is shown by visualizing the distribution.