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Part III Chapter 7. Elasticity
This chapter covers general models for
computing and interpreting elastic properties. The techniques used can
map out the microstructure-property relationships for the elastic properties
of composite and porous materials.
This section discusses the 3-D digital-image-based finite element algorithm
for computing the linear elastic properties of random (or non-random) materials.
Further computational details, and actual software, can be found in Part III Chapter 2,
which contains a manual for finite element and finite difference algorithms applied
to digital images.
(1)
An algorithm for computing the effective linear elastic properties of heterogeneous materials: 3-D results for composites with equal phase Poisson's ratios
(12 pages of text, 20K of figures)
This section presents a study of how well the physical properties of porous
Vycor glass can be modelled using a 2D-3D reconstruction of the microstructure
from a TEM image. Physical properties considered include: fluid permeability,
electrical and thermal conductivity, water vapor adsorption, drying shrinkage
at all relative humidities, surface area, and elastic moduli.
(2)
Modelling drying shrinkage in reconstructed porous materials: Application to
porous Vycor glass
(27 pages of text, 300K of figures)
This section applies some of the elastic techniques discussed in Chapter 3
to reconstructed models of a Tungsten-Silver composite material. Finite element
results for the effective moduli are used to judge between models of the
material.
(3)
Elastic properties of a tungsten-silver composite by reconstruction
and computation
(23 pages of text, 272K of figures)
This section computes the elastic moduli for various general models of
random porous materials and relates them to effective medium theories
of various kinds and existing elastic moduli data for ceramics.
(4)
Elastic properties of model porous ceramics
(16 pages of text, 140K of figures)
This section computes the elastic moduli for various general models of
random open-cell cellular solids and relates them to various simple
analytical theories and
existing elastic moduli data for similar materials.
(5)
Elastic properties of model random three-dimensional open-cell solids
(22 pages of text, 379K of figures)
This section computes the elastic moduli for various general models of
random closed-cell cellular solids and relates them to various simple
analytical theories and
existing elastic moduli data for similar materials.
(6)
Elastic moduli of model random three-dimensional closed-cell cellular solids
(14 pages of text, 600K of figures)
This section develops a differential effective medium theory for the linear
elastic properties for materials with composite inclusions. An example
of this is concrete, where the composite inclusion is the aggregate
plus the surrounding interfacial transition zone.
The theory is then tested with accurate finite element simulations of
random systems. The agreement is quite good.
(7)
Elastic moduli of a material containing composite inclusions: Effective medium
theory and finite element computations
(19 pages of text, 127K of figures)
This section studies the elasticity properties of simple models,
in 2-D and 3-D, of porous materials
whose solid phase is made up of elongated particles (crystals, rods, etc.).
Discussion is given of how to properly isotropically average the results
of simulations.
(8)
Linear Elastic Properties of 2-D and 3-D Models of Porous Materials Made From
Elongated Objects (18 pages of text, 299K of figures)
A finite element method is used to study the elastic properties of random three-
dimensional porous materials with highly interconnected pores. It is shown that the
Young's modulus is practically independent of the Poisson's ratio of the solid
phase over the entire solid volume fraction range. Also, the behavior of the porous
Poisson's ratio vs. the solid Poisson's ratio appears to imply that information in
the dilute (small porosity) limit can affect behavior in the percolation threshold
limit.
(9) Computation of
the linear elastic properties of random porous materials with a wide variety of microstructure (22 pages of text, 349K of figures)
Elastic property-porosity relationships are derived directly from microtomographic images. This is illustrated for a suite of four samples of Fontainebleau
sandstone with porosities ranging from 7.5% to 22%. A finite-element method
is used to derive the elastic properties of digitized images. By estimating
and minimizing several sources of numerical error, very accurate predictions
of properties are derived in excellent agreement with experimental
measurements over a wide range of the porosity. We compare the numerical
predictions to various empirical, effective medium and rigorous approximations
used to relate the elastic properties of rocks to porosity under different
saturation conditions.
(10) Computation of the linear
elastic properties from microtomographic images: Methodology and agreement
between theory and experiment
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Part III Chapter 6: Fluid flow
References
(1) E.J. Garboczi and A.R. Day, Journal of Physics and Mechanics of Solids 43, 1349-1362 (1995).
(2) D.P. Bentz, E.J. Garboczi, and D.A. Quenard, Mod. and Sim.
in Mater. Sci. and Eng. 6, 211-236 (1998).
(3) A.P. Roberts and E.J. Garboczi, Journal of the Mechanics and Physics of
Solids 47, 2029-2055 (1999).
(4) A.P. Roberts and E.J. Garboczi, Journal of the American Ceramic Society,
83 (12) 3041-3048, (2000).
(5) A.P. Roberts and E.J. Garboczi, J. Mech. Phys. Solids,
50 (1), 33-55 (2002).
(6) A.P. Roberts and E.J. Garboczi, Acta Materiala,
49 (2) 189-197 (2000).
(7) E.J. Garboczi and J.G. Berryman, Mechanics of Materials, 33 (8)
455-470 (2001).
(8) S. Meille and E.J. Garboczi, Mod. Sim. Mater. Sci. and Eng.
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(9) A.P. Roberts and E.J. Garboczi, Proc. Royal Society, 458 (2021),
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(10) C.H. Arns, M.A. Knackstedt, W. V. Pinczewski, E.J. Garboczi, Geophysics,
67 (5), 1396-1405 (2002).