Variant of the Continuum Model of Effective Elastic Moduli of Transversely Isotropic Porous Materials

2016 ◽  
Vol 52 (3) ◽  
pp. 317-324
Author(s):  
A. F. Fedotov
Keyword(s):  
Porous Materials ◽  
Continuum Model ◽  
Elastic Moduli ◽  
Transversely Isotropic ◽  
Effective Elastic Moduli ◽  
The Continuum

Elastic instabilities in dry, mesoporous minerals and their relevance to geological applications

2010 ◽  
Vol 74 (2) ◽  
pp. 341-350 ◽  
Author(s):  
E. K. H. Salje ◽  
J. Koppensteiner ◽  
W. Schranz ◽  
E. Fritsch
Keyword(s):  
Bulk Modulus ◽  
Porous Materials ◽  
Power Law ◽  
Master Curve ◽  
Elastic Moduli ◽  
External Stress ◽  
Effective Elastic Moduli ◽  
Critical Porosity ◽  
Elastic Instabilities ◽  
Linear Decay

AbstractThe collapse of minerals and mineral assemblies under external stress is modelled using a master curve where the stress failure is related to the relative, effective elastic moduli which are in turn related to the porosity of the sample. While a universal description is known not to be possible, we argue that for most porous materials such as shales, silica, cement phases, hydroxyapatite, zircon and also carbonates in corals and agglomerates we can estimate the critical porosity ϕc at which small stresses will lead to the collapse of the sample. For several samples we find ϕc ~0.5 with an almost linear decay of the bulk moduli with porosity at ϕc <0.5. The second scenario involves the persistence of elasticity for porosities until almost 1 whereby the bulk modulus decreases following a power law κ ~ (1–ϕm, m>2, between ϕ = 0.5 and ϕ = 1.

Effective Elastic Moduli of Ribbon-Reinforced Composites

1990 ◽  
Vol 57 (1) ◽  
pp. 158-167 ◽  
Author(s):  
Y. H. Zhao ◽  
G. J. Weng
Keyword(s):  
Aspect Ratio ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
Transversely Isotropic ◽  
Isotropic Case ◽  
Effective Elastic Moduli ◽  
Cross Sectional ◽  
Isotropic Composite ◽  
The Matrix ◽  
The Hill

Based on the Eshelby-Mori-Tanaka theory the nine effective elastic constants of an orthotropic composite reinforced with monotonically aligned elliptic cylinders, and the five elastic moduli of a transversely isotropic composite reinforced with two-dimensional randomly-oriented elliptic cylinders, are derived. These moduli are given in terms of the cross-sectional aspect ratio and the volume fraction of the elliptic cylinders. When the aspect ratio approaches zero, the elliptic cylinders exist as thin ribbons, and these moduli are given in very simple, explicit forms as a function of volume fraction. It turns out that, in the transversely isotropic case, the effective elastic moduli of the composite coincide with Hill’s and Hashin’s upper bounds if ribbons are harder than the matrix, and coincide with their lower bounds if ribbons are softer. These results are in direct contrast to those of circular fibers. Since the width of the Hill-Hashin bounds can be very wide when the constituents have high modular ratios, this analysis suggests that the ribbon reinforcement is far more effective than the traditional fiber reinforcement.

Grain boundaries as heterogeneous systems: atomic and continuum elastic properties

1992 ◽  
Vol 339 (1655) ◽  
pp. 555-586 ◽  
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Elastic Properties ◽  
Discrete Model ◽  
Continuum Model ◽  
Elastic Moduli ◽  
Atomic Level ◽  
Upper And Lower Bounds ◽  
Effective Moduli ◽  
The Continuum

The relation between atomic structure and elastic properties of grain boundaries is investigated theoretically from both atomistic and continuum points of view. A heterogeneous continuum model of the boundary is introduced where distinct phases are associated with individual atoms and possess their atomic level elastic moduli determined from the discrete model. The effective elastic moduli for sub-blocks from an infinite bicrystal are then calculated for a relatively small number of atom layers above and below the grain boundary. These effective moduli can be determined exactly for the discrete atomistic model, while estimates from upper and lower bounds are evaluated in the framework of the continuum model. The complete fourth-order elastic modulus tensor is calculated for both the local and the effective properties. Comparison between the discrete atomistic results and those for the continuum model establishes the validity of this model and leads to criteria to assess the stability of a given grain boundary structure. For stable structures the continuum estimates of the effective moduli agree well with the exact effective moduli for the discrete model. Metastable and unstable structures are associated with a significant fraction of atoms (phases) for which the atomic-level moduli lose positive definiteness or even strong ellipticity. In those cases, the agreement between the effective moduli of the discrete and continuum systems breaks down.

Parenchymal stability

1992 ◽  
Vol 73 (2) ◽  
pp. 596-602 ◽  
Author(s):  
D. Stamenovic ◽  
T. A. Wilson
Keyword(s):  
Surface Tension ◽  
Surface Density ◽  
Continuum Model ◽  
Elastic Moduli ◽  
Micromechanical Model ◽  
Volume Ratio ◽  
Transpulmonary Pressure ◽  
Lung Parenchyma ◽  
Micromechanical Modeling ◽  
The Continuum

Both continuum and micromechanical models have been used to describe the mechanics of lung parenchyma. Different authors, using different models, have come to different conclusions about parenchymal stability. We show that the continuum model, augmented by bounds on the elastic moduli obtained from recent micromechanical modeling, yields the same conclusions about stability that have been obtained from purely micromechanical modeling: if the lung were homogeneous, it would be stable; local atelectasis would not occur at positive transpulmonary pressure. However, the same analysis yields the prediction that if the surface-to-volume ratio is not uniform throughout the lung, regions of higher surface density collapse if surface tension is large and insensitive to surface area. A micromechanical model that illustrates regional collapse is described.

Mori-Tanaka Estimates of the Overall Elastic Moduli of Certain Composite Materials

1992 ◽  
Vol 59 (3) ◽  
pp. 539-546 ◽  
Author(s):  
Tungyang Chen ◽  
George J. Dvorak ◽  
Yakov Benveniste
Keyword(s):  
Composite Materials ◽  
Elastic Moduli ◽  
Transversely Isotropic ◽  
Effective Elastic Moduli ◽  
Explicit Formulae ◽  
Cylindrically Orthotropic ◽  
Multiphase Composite

Simple, explicit formulae are derived for estimates of the effective elastic moduli of several multiphase composite materials with the Mori-Tanaka method. Specific results are given for composites reinforced by aligned or randomly oriented, transversely isotropic fibers or platelets, and for fibrous systems reinforced by aligned, cylindrically orthotropic fibers.

Phonons and Local Elastic Moduli in Symmetrical Tilt Boundaries

1992 ◽  
Vol 291 ◽  
Author(s):  
Gui Jin Wang ◽  
V. Vitek ◽  
I. Alber ◽  
J. Bassani
Keyword(s):  
Elastic Moduli ◽  
Interfacial Region ◽  
Lattice Vibrations ◽  
Effective Elastic Moduli ◽  
Many Body ◽  
Long Wavelength ◽  
Atomic Interactions ◽  
Tilt Boundaries ◽  
Symmetrical Tilt ◽  
The Continuum

ABSTRACTLattice vibrations and atomic level elastic moduli have been studied for a bicrystal containing a fully relaxed symmetrical tilt boundary in Au. Central force many body potentials have been employed to describe atomic interactions. In the long-wavelength limit the phonons localized at grain boundaries can be identified with Stoneley waves known from continuum analyses. These waves are localized at the grain boundary and their velocity agrees well with that evaluated using the local effective elastic moduli of the interfacial region. However, the usually used continuum model assuming an ideal match across the interface is not sufficient to analyze these waves fully and an explicit description of interfacial properties need to be included into the continuum models of interfaces.

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