On the numerical integration of the stress equilibrium equations governing the ideal plastic plane deformation of a granular material

1985 ◽  
Vol 55 (3-4) ◽  
pp. 219-238 ◽  
Author(s):  
D. Harris
Keyword(s):  
Granular Material ◽  
Numerical Integration ◽  
Plane Deformation ◽  
Equilibrium Equations ◽  
Stress Equilibrium ◽  
Ideal Plastic ◽  
The Ideal

scholarly journals An ice-shelf model test based on the Ross Ice Shelf, Antarctica

1996 ◽  
Vol 23 ◽  
pp. 46-51 ◽  
Author(s):  
D. R. MacAyeal ◽  
V. Rommelaere ◽  
P. Huybrechts ◽  
C. L. Hulbe ◽  
J. Determann ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Large Scale ◽  
Finite Difference Methods ◽  
Equilibrium Equations ◽  
Ice Shelf ◽  
Ross Ice Shelf ◽  
Stress Equilibrium ◽  
Flow Features ◽  
Large Scale Flow

A standard numerical experiment featuring the Ross Ice Shelf, Antarctica, is presented as a test package for the development and intercomparison of ice-shelf models. The emphasis of this package is solution of stress-equilibrium equations for an ice-shelf velocity consistent with present observations. As a demonstration, we compare five independently developed ice-shelf models based on finite-difference and finite-element methods. Our results suggest that there is little difference between finite-element and finite-difference methods in capturing the basic, large-scale flow features of the ice shelf. We additionally show that the fit between model and observed velocity depends strongly on the ice-shelf temperature field, for which there is presently little observational control. The main differences between model results are due to the equations being solved, the boundary conditions at the ice from and the discretization method (finite element vs finite difference).

scholarly journals Large-scale rheology of the Ross Ice Shelf, Antarctica, computed by a control method

1997 ◽  
Vol 24 ◽  
pp. 43-48 ◽  
Author(s):  
Vincent Rommelaere ◽  
Douglas R. MacAyeal
Keyword(s):  
Large Scale ◽  
Control Method ◽  
Equilibrium Equations ◽  
Ice Shelf ◽  
The West ◽  
Ross Ice Shelf ◽  
Stress Equilibrium ◽  
West Antarctic ◽  
Flow Law ◽  
Basal Melting

Measurements made during the Ross Ice Shelf Geophysical and Glaciological Survey (RIGGS, 1973–78) are used to determine the large-scale rheological conditions of the Ross Ice Shelf, Antarctica. Our method includes a numerical ice-shelf model based on the stress-equilibrium equations and control theory. We additionally perform a few tests on simplified geometries to investigate the precision of our method. Our results consist of a map of the depth-averaged viscosity of the central part of the Ross Ice Shelf to within an uncertainty of 20%. We find that the viscosity variations are consistent with Glen’s flow law. Application of a more realistic flow law in our study provides little enhancement of ice-shelf model accuracy until uncertainties associated with basal melting conditions and with temperature profiles at inflow boundaries are addressed. Finally, our results suggest a strong viscosity anomaly in the west-central part of the ice shelf, which is interpreted to be associated with changes in the dynamics of Ice Stream A or B at least 1000 years ago. This feature conforms to the prevailing notion that the West Antarctic ice streams are unsteady.

Large-scale rheology of the Ross Ice Shelf, Antarctica, computed by a control method

1997 ◽  
Vol 24 ◽  
pp. 43-48 ◽  
Author(s):  
Vincent Rommelaere ◽  
Douglas R. MacAyeal
Keyword(s):  
Large Scale ◽  
Control Method ◽  
Equilibrium Equations ◽  
Ice Shelf ◽  
The West ◽  
Ross Ice Shelf ◽  
Stress Equilibrium ◽  
West Antarctic ◽  
Flow Law ◽  
Basal Melting

Measurements made during the Ross Ice Shelf Geophysical and Glaciological Survey (RIGGS, 1973–78) are used to determine the large-scale rheological conditions of the Ross Ice Shelf, Antarctica. Our method includes a numerical ice-shelf model based on the stress-equilibrium equations and control theory. We additionally perform a few tests on simplified geometries to investigate the precision of our method. Our results consist of a map of the depth-averaged viscosity of the central part of the Ross Ice Shelf to within an uncertainty of 20%. We find that the viscosity variations are consistent with Glen’s flow law. Application of a more realistic flow law in our study provides little enhancement of ice-shelf model accuracy until uncertainties associated with basal melting conditions and with temperature profiles at inflow boundaries are addressed. Finally, our results suggest a strong viscosity anomaly in the west-central part of the ice shelf, which is interpreted to be associated with changes in the dynamics of Ice Stream A or B at least 1000 years ago. This feature conforms to the prevailing notion that the West Antarctic ice streams are unsteady.

Numerical Integral in the Ideal Adsorbed Solution Theory

2011 ◽  
Vol 396-398 ◽  
pp. 1809-1812
Author(s):  
Quan Li Feng ◽  
Ming Lei Lian ◽  
Xue Qian Wang ◽  
Ping Ning
Keyword(s):  
Experimental Data ◽  
Numerical Calculation ◽  
Numerical Integration ◽  
Pure Component ◽  
Single Component ◽  
Solution Theory ◽  
Ideal Adsorbed Solution Theory ◽  
Adsorbed Solution ◽  
The Ideal ◽  
Adsorbed Solution Theory

The ideal adsorbed solution (IAS) theory has an advantage that no restriction exists for the type of pure component isotherm. One can choose the isotherm that fits the experimental data best. However, the theory requires a lot of numerical calculation, including numerical integration. This study shows that IAS needs very accurate values of numerical integration when the D-R equation is used as a single component isotherm. The error of numerical integration should be set to be no larger than 10-7. Otherwise the error of numerical calculation will occur, which may increase prediction deviation.

Mechanical Behavior of Fracture Filled with Variable Medium

2012 ◽  
Vol 472-475 ◽  
pp. 2203-2206
Author(s):  
Jin Gang Chen ◽  
Na Chen ◽  
Jun Li Yang
Keyword(s):  
Mechanical Behavior ◽  
Laboratory Experiments ◽  
Behavior Model ◽  
Flow State ◽  
Linear Elastic ◽  
Ideal Plastic ◽  
Strain Data ◽  
Variable Medium ◽  
Normal Compression ◽  
The Ideal

Filled fracture is a fracture in which sands or other materials occupy some void spaces. This study uses well-controlled laboratory experiments to investigate mechanical behavior of fracture filled with variable medium by means of normal compression and lateral restraint. A large number of stress-strain data are obtained. The mechanical behavior of filled fracture with variable medium can be divided into three phases: rheological phase, compaction phase and linear elastic phase. At the beginning of the experiment, the filled fracture is in the ideal plastic flow state. The overall strength of filled fracture increase with finite deformation and normal stress increasing, and show linear elastic characters. Based on the experiment results and characteristics, the mechanical behavior model of fracture filled with variable medium is constructed, and also its mechanism is analyzed.

scholarly journals Numerical Modeling of Water Flow in Expansive Soils with Simplified Description of Soil Deformation

2018 ◽  
Vol 65 (4) ◽  
pp. 301-313
Author(s):  
Sławomir Michalski ◽  
Adam Szymkiewicz
Keyword(s):  
Water Flow ◽  
Unsaturated Flow ◽  
Expansive Soils ◽  
Vertical Direction ◽  
Time Discretization ◽  
Soil Mass ◽  
Flow Equation ◽  
Anthropogenic Factors ◽  
Equilibrium Equations ◽  
Stress Equilibrium

AbstractIn this paper we describe a numerical model of transient water flow in unsaturated expansive soils and the resulting soil volume change. The unsaturated flow equation is solved in a 2D domain using a finite-volume method and an explicit time discretization scheme. Strains in the soil mass are calculated by two simplified approaches, assuming that the strain state is either 1D (in the vertical direction only) or 2D with equal strains in horizontal and vertical directions. The model is applied to two cases described in the literature, in which the strains were computed from the solution of the stress equilibrium equation. It is shown that the simplified methods give results which are reasonably close to the more complex approach based on the equilibrium equations. The proposed model can be used to predict time-varying soil shrinkage and swelling caused by natural and anthropogenic factors.

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