The Biot model of interpenetrating continua and its role in geomechanics

Poromechanics ◽  
2020 ◽  
pp. 123-128
Author(s):  
V.N. Nikolaevskiy
Keyword(s):  
Biot Model ◽  
Interpenetrating Continua

Investigation of an anisotropic tortuosity in a Biot model of ultrasonic propagation in cancellous bone

2007 ◽  
Vol 121 (1) ◽  
pp. 568-574 ◽  
Author(s):  
Elinor R. Hughes ◽  
Timothy G. Leighton ◽  
Paul R. White ◽  
Graham W. Petley
Keyword(s):  
Cancellous Bone ◽  
Biot Model ◽  
Ultrasonic Propagation

The Biot Model and Its Application in Viscoelastic Composite Structures

2007 ◽  
Vol 129 (5) ◽  
pp. 533-540 ◽  
Author(s):  
J. Zhang ◽  
G. T. Zheng
Keyword(s):  
Mathematical Model ◽  
Dynamic Behavior ◽  
Composite Structures ◽  
Optimization Method ◽  
Noise Attenuation ◽  
Viscoelastic Materials ◽  
Numerical Techniques ◽  
Viscoelastic Composite ◽  
Biot Model ◽  
Numerical Examples

Application of viscoelastic materials in vibration and noise attenuation of complicated machines and structures is becoming more and more popular. As a result, analytical and numerical techniques for viscoelastic composite structures have received a great deal of attention among researchers in recent years. Development of a mathematical model that can accurately describe the dynamic behavior of viscoelastic materials is an important topic of the research. This paper investigates the procedure of applying the Biot model to describe the dynamic behavior of viscoelastic materials. As a minioscillator model, the Biot model not only possesses the capability of its counterpart, the GHM (Golla-Hughes-McTavish) model, but also has a simpler form. Furthermore, by removing zero eigenvalues, the Biot model can provide a smaller-scale mathematical model than the GHM model. This procedure of dimension reduction is studied in detail here. An optimization method for determining the parameters of the Biot model is also investigated. With numerical examples, these merits, the computational efficiency, and the accuracy of the Biot model are illustrated and proved.

scholarly journals On the quest for a hyperbolic effective-field model of disperse flows

2013 ◽  
Vol 731 ◽  
pp. 184-194 ◽  
Author(s):  
Daniel Lhuillier ◽  
Chih-Hao Chang ◽  
Theo G. Theofanous
Keyword(s):  
Fluid Mechanics ◽  
Field Model ◽  
Fluid Model ◽  
Effective Field ◽  
Engineering Practice ◽  
Governing Equations ◽  
Two Fluid Model ◽  
Two Fluid ◽  
Interpenetrating Continua ◽  
Final Closure

AbstractThe cornerstone of multiphase flow applications in engineering practice is a scientific construct that translates the basic laws of fluid mechanics into a set of governing equations for effective interpenetrating continua, the effective-field (or two-fluid) model. Over more than half a century of development this model has taken many forms but all of them fail in a way that was known from the very beginning: mathematical ill-posedness. The aim of this paper is to refocus awareness of this problem from a unified fundamental perspective that clarifies the manner in which such failures took place and to suggest the means for a final closure.

scholarly journals Application of the Biot model to ultrasound in bone: Direct problem

2008 ◽  
Vol 55 (7) ◽  
pp. 1508-1515 ◽  
Author(s):  
Zine E.A. Fellah ◽  
Naima Sebaa ◽  
Mohamed Fellah ◽  
Farid G. Mitri ◽  
Erick Ogam ◽  
...  
Keyword(s):  
Direct Problem ◽  
Biot Model

Mathematical Modelling of Methane-Air Combustion in a Channel with a Porous Axial Insert

2014 ◽  
Vol 698 ◽  
pp. 660-663
Author(s):  
Anastasia I. Baygulova ◽  
Aleksey M. Bubenchikov ◽  
Oleg V. Matvienko
Keyword(s):  
Turbulent Combustion ◽  
Energy Equation ◽  
Numerical Study ◽  
Particulate Material ◽  
Diffusion Equations ◽  
Stoichiometric Mixture ◽  
Axial Zone ◽  
Averaged Equations ◽  
Irreversible Chemical Reaction ◽  
Interpenetrating Continua

In the paper we construct a mathematical model of turbulent flow, combustion and heat transfer in an axisymmetric chamber with an axial zone of a compacted particulate material. The averaged equations written using the model of interacting and interpenetrating continua contain diffusion equations of individual components, the energy equation for the gas and the porous structure, the motion equation for a mixture of gaseous components, as well as the equation of the turbulence model. This system is closed by the equations of continuity and condition of the mixture. In the flow, an irreversible chemical reaction of stoichiometric mixture of methane and oxygen proceeds. Numerical study of porosity influencing the nature of turbulent combustion is conducted.

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