Mechanics of Continuous Deformable Media

Mechanics ◽  
2012 ◽  
pp. 293-386
Author(s):  
Masud Chaichian ◽  
Ioan Merches ◽  
Anca Tureanu
Keyword(s):  
Deformable Media

scholarly journals Rockburst hazard assessment based on seismic tomography and analytical modelling - a case study

2018 ◽  
Vol 66 ◽  
pp. 01009
Author(s):  
Dariusz Chlebowski ◽  
Zbigniew Burtan
Keyword(s):  
Hazard Assessment ◽  
Seismic Tomography ◽  
Vertical Component ◽  
Rockburst Hazard ◽  
Expert Opinions ◽  
Deformable Media ◽  
Coal Deposits ◽  
Threat Level ◽  
Survey Results

In accordance with the formal regulations currently in force in Poland, the criteria for rockburst hazard assessment with respect to coal deposits include the records of seismic events and their impacts, de-stressing of the entire seam or its parts and expert opinions of mine operation engineers. Effectiveness of the de-stressing can be verified by geophysical test data whilst the expert opinions are mostly based on mathematical modelling using specialist software or dedicated simulation algorithms. This study collates and synthesises the results of tests carried out in a seam section in a colliery within the Upper Silesia Coal Basin, obtained by the outlined methods. Geophysical survey results are interpreted basing on seismic tomography procedures utilising the geo-tomography techniques for velocity field reconstruction in data processing. For comparison, the stress state modelling data are provided, based on conventional engineering solutions applicable to mechanics of deformable media. The actual assessment of the rockburst threat level is based on observations of distributions of the longitudinal wave velocity in relation to the actual value of the vertical component of stress concentration within the coal seam.

A unified procedure for construction of theories of deformable media. I. Classical continuum physics

1995 ◽  
Vol 448 (1934) ◽  
pp. 335-356 ◽  
Keyword(s):  
Energy Balance ◽  
Companion Paper ◽  
Balance Laws ◽  
Kinematic Variable ◽  
Material Behaviour ◽  
Classical Formulation ◽  
Deformable Media ◽  
Basic Equations ◽  
Basic Features ◽  
Continuum Theories

A new unified procedure for constructing continuum theories of deformable media is presented and used in this and a companion paper. The procedure starts with a balance of energy and derives from it all the relevant balance laws that may also include those that are associated with thermal, electrical and magnetic effects; the basic energetic ingredients that are included in the balance of energy depend, of course, on the nature of the particular theory of material behaviour desired. The advantage of the new procedure becomes especially apparent when one considers formulation of a new theory of material behaviour for which additional balance laws (involving new kinetic quantities) are required to accompany any additional basic kinematic and thermal variables additional to those in the classical formulation. Indeed, in the formulation of such new theories, usually little or no previous information is available concerning properties of the new kinetic quantities in the additional balance laws; and, in this connection, the unified procedure of this paper provides a simple attractive setting for deriving the basic equations that are automatically consistent with the energy balance. In this paper, first the basic features of the new procedure are illustrated in the context of classical thermomechanics. Generalizations of this thermomechanical theory are then discussed in two cases: (1) in the presence of an additional kinematic variable and (2) in the presence of full electromagnetic effects. Both of these generalizations bring out some interesting novel features when new theories are being constructed.

scholarly journals Simulation of Dynamic Processes in Deformable Medium with the Grid-Characteristic Approach

2021 ◽  
pp. 74-81
Author(s):  
И.Б. Петров
Keyword(s):  
Neural Networks ◽  
Wave Propagation ◽  
Elastic Wave ◽  
Elastic Waves ◽  
Elastic Wave Propagation ◽  
Seismic Survey ◽  
The Arctic ◽  
Dynamic Processes ◽  
Deformable Media ◽  
Direct Problems

Существует значительное количество прикладных задач, для решения которых применяется математическое моделирование динамических процессов в деформируемых средах. К таким задачам относят моделирование распространения упругих волн в геологических средах, в том числе с учетом ледовых образований, их рассеяния на зонах трещиноватости. Актуальность этих постановок обусловлена важностью решения обратных задач сейсмической разведки, обработки данных сейсмической разведки с целью уточнения запасов углеводородов и определения расположения углеводородов и других полезных ископаемых. Поэтому приобретает важность разработка высокоточных численных методов, позволяющих моделировать упругие волны в деформируемых средах. Одним из этих методов является сеточно-характеристический численный метод, примененный в данной работе. Этот численный метод применяется для решения прямых задач, то есть для расчета распространения упругих волн при известных параметрах рассматриваемой среды. А для решения обратной задачи по восстановлению параметров геологической среды по данным сейсмической разведки можно применять нейронные сети, для обучения которых можно использовать многократное решение прямых задач сеточно-характеристическим методом. В данной работе приведены примеры решения разнообразных прямых задач по распространению упругих волн в неоднородных геологических средах, в том числе в зоне Арктики, а также представлена постановка задачи по обучению нейронных сетей и графики, показывающие эффективность их обучения с использованием двух различных подходов. Many problems can be solved with the simulation of dynamic processes in deformable media. They are the simulation of elastic wave propagation in rocks including ice formations, and wave scattering on rock-fracture zones. Such studies are important for solving inverse problems of seismic exploration and seismic data processing to get a better estimation of hydrocarbon reserves, locate hydrocarbons and other minerals. Therefore, it is necessary to develop high-precision numerical methods used to simulate elastic waves in deformable media. One of such methods is the grid-characteristic approach used in this work. It is suitable for solving direct problems, i.e., to analyze the propagation of elastic waves in a medium with known properties. Neural networks can be applied to solve the inverse problem: reconstructing the geology from seismic survey data. Multiple solving of direct problems by the gridcharacteristic approach is used for network training. This paper contains some examples of solving a range of direct problems on the elastic wave propagation in heterogeneous rocks, also in the Arctic zone, and the problem statement for training neural networks and graphs is proposed to demonstrate the efficiency of training with two approaches.

Direct Validation of Active Solute Transport Induced by Dynamic Loading of Porous Hydrated Media

2009 ◽  
Author(s):  
Michael B. Albro ◽  
Roland Li ◽  
Rajan E. Banerjee ◽  
Clark T. Hung ◽  
Gerard A. Ateshian
Keyword(s):  
Dynamic Loading ◽  
Biological Tissues ◽  
Passive Diffusion ◽  
Transport Pathways ◽  
Molecular Weights ◽  
Deformable Media ◽  
Solute Uptake ◽  
Theoretical Predictions ◽  
Engineered Tissue ◽  
Novel Concept

Transport pathways play a key role in maintaining cellular metabolic activity in biological tissues. Efforts to maintain or enhance the transport of nutrients may prove beneficial to the maintenance of native or development of engineered tissue. Various studies have investigated the potential of dynamic mechanical loading to increase the uptake and desorption rates of solutes in articular cartilage [1, 2]. Recently, a novel concept has been theoretically suggested that such dynamic loading of porous deformable media may additionally yield higher steady state concentrations of solutes, beyond those achieved by passive diffusion [3]. The first experimental evidence that dynamic loading can significantly enhance solute uptake over passive diffusion was recently reported for a model system of dextran in agarose hydrogels [4]. The results of this experimental study [4] were interpreted in the context of the earlier theoretical predictions [3], though a direct validation of theory with experiments has not yet been attempted. Therefore, the current study focuses on directly validating the theoretical framework by independently measuring the mechanical and transport properties of agarose hydrogels and dextran solutions experimentally, and substituting these values into the theory to evaluate the predicted solute uptake. These predictions are then compared to the previously reported experimental measurements of uptake of dextran in agarose under dynamic loading [4], for several gel concentrations and solute molecular weights.

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