scholarly journals Continuous and discrete models in the mechanics of deformable solid bodies

2018 ◽  
Vol 184 ◽  
pp. 01004
Author(s):  
Géza Lámer
Keyword(s):  
Continuum Model ◽  
Continuous Medium ◽  
Geometric Model ◽  
Discrete Models ◽  
Deformable Solid ◽  
Medium Model ◽  
Continuous Description ◽  
Discrete Nature ◽  
Solid Bodies ◽  
Discrete Medium

The study provides an overview of modelling possibilities for the mechanical behaviour of media. The discrete, continuous or differential geometric as well as the discrete nature and continuous description grid continuum model in particular are highlighted. We point out that the differential geometric model is based on the concept of continuity and interprets a continuous medium model. We reveal that the grid continuum model is based on the application of numerical method and interprets a discrete medium model.

Instabilities in a continuous medium model for the retina

1980 ◽  
Vol 39 (1) ◽  
pp. 11-14 ◽  
Author(s):  
Hendrik J. Van Ouwerkerk ◽  
Jan H. Tulp ◽  
Hans A. L. Piceni ◽  
Jacques A. J. Roufs ◽  
Frans J. J. Blommaert
Keyword(s):  
Continuous Medium ◽  
Medium Model

Modeling Flow and Transport in Fractured Crystalline Rock using the Discrete Fracture Network Concept

1988 ◽  
Vol 127 ◽  
Author(s):  
Björn Dverstorp ◽  
Wille Nordqvist ◽  
Johan Andersson
Keyword(s):  
Discrete Model ◽  
Continuum Model ◽  
Large Scale ◽  
Flow Analysis ◽  
Flow Distribution ◽  
Crystalline Rock ◽  
Discrete Models ◽  
Large Variability ◽  
Rock Heterogeneity ◽  
Modeling Flow

ABSTRACTThe conductive properties of fractured crystalline rock vary considerably in space, which implies that the flow is very unevenly distributed in space. The large variability raises doubts on modeling the flow with a large scale continuum model. Modeling flow in fractured crystalline rock in a network of discrete fractures provides an increased understanding of the character of the rock heterogeneity. Compared to a continuum model discrete models introduce new parameters such as statistical distributions for fracture orientation, radii, density and transmissivity that need to be estimated. By analyzing the migration experiment in the Stripa research mine in Sweden it is demonstrated how to calibrate and eventually validate a discrete model on field data. The flow analysis shows that the flow distribution on the drift roof and in two out of three vertical boreholes can be modelled with the same discrete model. The properties of the third borehole differ substantially. Initial attempts of analyzing the tracer experiment are also described.

Continuum Model of Deformation of Piezoelectric Materials with Cracks

2015 ◽  
Vol 784 ◽  
pp. 161-172 ◽  
Author(s):  
Dmytro Babich ◽  
Olexander Bezverkhyi ◽  
Tatiana Dorodnykh
Keyword(s):  
Continuum Model ◽  
Continuous Medium ◽  
Piezoelectric Materials ◽  
Electric Energy ◽  
Deformation Energy ◽  
Principle Of Equivalence ◽  
Eshelby Method ◽  
The Continuum

The present paper addresses the continuum model describing deformation and accumulation of microdamages in electroelastic materials based on the generalized Eshelby principle. The microdamageability is considered as a process of appearance of flat elliptic or circular microcracks randomly dispersed over volume, the concentration of which increases with a load. The Eshelby method is based on the principle of equivalence of the deformation energy of fractured piezoelectric materials and the energy of medium, which is modeling these materials as a continuous medium. The key point of this approach is to determine the densities of the released elastic and electric energy.

scholarly journals GEODYNAMICS

GEODYNAMICS ◽  
2011 ◽  
Vol 2(11)2011 (2(11)) ◽  
pp. 138-140
Author(s):  
H.H. Kuliyev ◽  
Keyword(s):  
Phase Transitions ◽  
Equilibrium State ◽  
Linear Theory ◽  
Structural Instability ◽  
Loss Of Stability ◽  
Geometric Form ◽  
Deformable Solid ◽  
The Earth ◽  
Internal Structures ◽  
Solid Bodies

The processes of consolidation, deconsolidation, phase transitions and destructions in the terms of internal structures of the Earth аre studied on the base of non-linear theory of deformable solid bodies. It is shown that the loss of stability of equilibrium state can precede to the processes of deconsolidation, phase transitions and destructions on geometric form change (structural instability).

scholarly journals DYNAMICS OF FRACTAL SOLIDS

2005 ◽  
Vol 19 (27) ◽  
pp. 4103-4114 ◽  
Author(s):  
VASILY E. TARASOV
Keyword(s):  
Fractional Order ◽  
Experimental Test ◽  
Fractional Integral ◽  
Continuous Medium ◽  
Fractional Integrals ◽  
Generalized Equations ◽  
Moments Of Inertia ◽  
Medium Model ◽  
Mass Dimension ◽  
Euler's Equations

We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous medium model, where all characteristics and fields are defined everywhere in the volume but they follow some generalized equations which are derived by using fractional integrals of fractional order. The order of fractional integral can be equal to the fractal mass dimension of the solid. Fractional integrals are considered as an approximation of integrals on fractals. We suggest the approach to compute the moments of inertia for fractal solids. The dynamics of fractal solids are described by the usual Euler's equations. The possible experimental test of continuous medium model for fractal solids is considered.

scholarly journals Nondestructive Identification of Inhomogeneous Residual Stress State in Deformable Bodies on the Basis of the Acoustic Sounding Method

2014 ◽  
Vol 996 ◽  
pp. 409-414 ◽  
Author(s):  
Vladimir Vladimirovich Dudarev ◽  
Rostislav Dmitrievich Nedin ◽  
Alexander Ovanesovich Vatulyan
Keyword(s):  
Residual Stress ◽  
Cylindrical Tube ◽  
Surface Displacement ◽  
Iterative Regularization ◽  
Deformable Solid ◽  
Residual Stress State ◽  
Deformable Bodies ◽  
Load Types ◽  
Solid Bodies ◽  
Set Of Points

Analysis of inhomogeneous residual stress (RS) fields in bodies is one of the major problems of the mechanics of deformable solid bodies. In the present research the new techniques of identification of inhomogeneous RS in bodies are developed on the basis of surface displacement measurement in a set of points under vibrating sounding load. Corresponding nonlinear ill-posed inverse problems (IP) are formulated and solved numerically by means of iterative regularization. Based on computational experiments, the most advantageous sounding load types and frequency ranges providing the best reconstruction accuracy are revealed. The examples for a cantilever, a plate, a layer, and a cylindrical tube are presented.

scholarly journals Continuous medium model for fractal media

2005 ◽  
Vol 336 (2-3) ◽  
pp. 167-174 ◽  
Author(s):  
Vasily E. Tarasov
Keyword(s):  
Continuous Medium ◽  
Fractal Media ◽  
Medium Model

scholarly journals Study on Water Inflow Variation Law of No.1 Shaft Auxiliary Shaft in HighLiGongshan Based on Dual Medium Model

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 930
Author(s):  
Jiabin Li ◽  
Yonghong Wang ◽  
Zhongsheng Tan ◽  
Wen Du ◽  
Zhenyu Liu
Keyword(s):  
Rock Mass ◽  
Continuous Medium ◽  
Fractured Rock ◽  
Analytical Formula ◽  
Fracture Network ◽  
Discrete Fracture Network ◽  
Water Inflow ◽  
Fracture Group ◽  
Medium Model ◽  
Discrete Fracture

When the fracture is not developed and the connectivity is poor, the original single medium simulation cannot meet the accuracy requirements. Now, the seepage simulation of fractured rock mass has gradually developed from equivalent continuous medium to dual medium and multiple medium. However, it is still difficult to establish the connection between a discrete fracture network model and a continuous medium model, which makes it difficult to simulate the influence of fracture location on the seepage field of rock mass. As the excavation direction of the shaft is vertically downward, the surrounding strata are symmetrical around the plane of the shaft axis, which is different from the horizontal tunnel. Taking the auxiliary shaft of the No.1 Shaft in HighLiGongshan as the engineering background, combined with Monte Carlo methods and DFN generator built in FLAC3D5.01, a discrete fracture network is generated. Based on the dual medium theory, MIDAS is used to optimize the modeling of each fracture group. At the same time, the concept of “Fracture Weakening area” is introduced, and the simulation is carried out based on a fluid–solid coupling method. It is found that the simulation effect is close to the reality. The water inflow increases with the increase of shaft excavation depth, and the water inflow at the end of excavation is nearly three times larger than the initial value. Combined with Legendre equation, a new analytical formula of water inflow prediction is proposed. It is found that this analytical formula is more sensitive to permeability and has a greater safety reserve.

Sign in / Sign up

Export Citation Format

Share Document