Erratum: Bounds for Effective Bulk Modulus of Heterogeneous Materials

1971 ◽  
Vol 12 (6) ◽  
pp. 1057-1057 ◽  
Author(s):  
Melvin N. Miller
Keyword(s):  
Bulk Modulus ◽  
Heterogeneous Materials ◽  
Effective Bulk Modulus

Bounds for Effective Bulk Modulus of Heterogeneous Materials

1969 ◽  
Vol 10 (11) ◽  
pp. 2005-2013 ◽  
Author(s):  
Melvin N. Miller
Keyword(s):  
Bulk Modulus ◽  
Heterogeneous Materials ◽  
Effective Bulk Modulus

scholarly journals Nanoscale Effect Investigation for Effective Bulk Modulus of Particulate Polymer Nanocomposites Using Micromechanical Framework

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Tien-Thinh Le ◽  
Minh Vuong Le
Keyword(s):  
Bulk Modulus ◽  
Effective Properties ◽  
Heterogeneous Materials ◽  
Characteristic Size ◽  
Surface Strength ◽  
Nanoparticle Radius ◽  
Effective Bulk Modulus ◽  
Proposed Model ◽  
Parametric Studies ◽  
Nanoscale Effect

This paper investigates the nanoscale effect on the effective bulk modulus of nanoparticle-reinforced polymer. An interface-based model is introduced in this work to study the nanoscale effects on the effective properties of heterogeneous materials. That interface model is able to capture discontinuity of mechanical fields across the surface between the nanoparticle and matrix. A generalized self-consistent scheme is then employed to determine the effective bulk modulus. It has been seen from the results that, in a certain range of limits, the influence of nanoscale effects on effective properties of heterogeneous materials is significant and needs to be taken into account. In particular, when the nanoparticle radius is smaller than 10 nm, the value of effective bulk modulus significantly increases when the characteristic size of nanofillers decreases. Besides, it is seen that the harder the inclusion, the smaller the nanoscale influence effects on the overall behaviors of composite materials. Finally, parametric studies in terms of surface strength and filler’s volume fractions are investigated and discussed, together with a comparison between the proposed model and other contributions in the literature.

Modeling and Experimental Validation of the Effective Bulk Modulus of a Mixture of Hydraulic Oil and Air

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Hossein Gholizadeh ◽  
Doug Bitner ◽  
Richard Burton ◽  
Greg Schoenau
Keyword(s):  
Experimental Data ◽  
Bulk Modulus ◽  
Theoretical Models ◽  
Operating Conditions ◽  
Air Bubbles ◽  
Pressure Sensitivity ◽  
Hydraulic Oil ◽  
Effective Bulk Modulus ◽  
Experimental Apparatus ◽  
Major Factors

It is well known that the presence of entrained air bubbles in hydraulic oil can significantly reduce the effective bulk modulus of hydraulic oil. The effective bulk modulus of a mixture of oil and air as pressure changes is considerably different than when the oil and air are not mixed. Theoretical models have been proposed in the literature to simulate the pressure sensitivity of the effective bulk modulus of this mixture. However, limited amounts of experimental data are available to prove the validity of the models under various operating conditions. The major factors that affect pressure sensitivity of the effective bulk modulus of the mixture are the amount of air bubbles, their size and the distribution, and rate of compression of the mixture. An experimental apparatus was designed to investigate the effect of these variables on the effective bulk modulus of the mixture. The experimental results were compared with existing theoretical models, and it was found that the theoretical models only matched the experimental data under specific conditions. The purpose of this paper is to specify the conditions in which the current theoretical models can be used to represent the real behavior of the pressure sensitivity of the effective bulk modulus of the mixture. Additionally, a new theoretical model is proposed for situations where the current models fail to truly represent the experimental data.

Optimal Bounds on the Effective Bulk Modulus of Polycrystals

1989 ◽  
Vol 49 (3) ◽  
pp. 824-837 ◽  
Author(s):  
Marco Avellaneda ◽  
Graeme W. Milton
Keyword(s):  
Bulk Modulus ◽  
Effective Bulk Modulus ◽  
Optimal Bounds

Stress-smoothing holes in a regularly perforated elastic plate with a given effective bulk modulus

2021 ◽  
Vol 16 (4) ◽  
pp. 511-525
Author(s):  
Shmuel Vigdergauz ◽  
Isaac Elishakoff
Keyword(s):  
Bulk Modulus ◽  
Elastic Plate ◽  
Effective Bulk Modulus ◽  
Stress Smoothing

Aerodynamic Flutter and Flight Surface Actuation

2007 ◽  
Author(s):  
S. A. Gadsden ◽  
S. Habibi
Keyword(s):  
Bulk Modulus ◽  
Small Amplitude ◽  
Mechanical Load ◽  
Impedance Control ◽  
Hydraulic Oil ◽  
Effective Bulk Modulus ◽  
Two Parameters

This paper proposes a novel form of impedance control in order to reduce the effects of aerodynamic flutter on a flight surface actuator. The forces generated by small amplitude flutter were studied on an electrohydrostatic actuator (EHA). The effects of flutter were modeled and analyzed. Through analysis, it was found that in EHA systems, two parameters would impact the response of flutter: damping (B) of the mechanical load, and the effective bulk modulus of the hydraulic oil (βe). These can be actively controlled as proposed here in order to provide variable impedance. The results of changing these variables are discussed and presented here.

Effect of the Interphase Zone on the Bulk Modulus of a Particulate Composite

1996 ◽  
Vol 63 (4) ◽  
pp. 855-861 ◽  
Author(s):  
M. P. Lutz ◽  
R. W. Zimmerman
Keyword(s):  
Exact Solution ◽  
Bulk Modulus ◽  
Spherical Inclusion ◽  
Particulate Composite ◽  
Constant Term ◽  
Stress Concentrations ◽  
Infinite Body ◽  
Effective Bulk Modulus ◽  
Random Dispersion ◽  
Frobenius Series

An exact solution is found for the problem of hydrostatic compression of an infinite body containing a spherical inclusion, with the elastic moduli varying with radius outside of the inclusion. This may represent an interphase zone in a composite, or the transition zone around an aggregate particle in concrete, for example. Both the shear and the bulk moduli are assumed to be equal to a constant term plus a power-law term that decays away from the inclusion. The method of Frobenius series is used to generate an exact solution for the displacements and stresses. The solution is then used to estimate the effective bulk modulus of a material containing a random dispersion of these inclusions. The results demonstrate the manner in which a localized interphase zone around an inclusion may markedly affect both the stress concentrations at the interface, and the overall bulk modulus of the material.

Poroelasticity of Fluid-Saturated Nanoporous Media

2009 ◽  
Vol 614 ◽  
pp. 35-40 ◽  
Author(s):  
Vincent Pensée ◽  
Qi Chang He ◽  
H. Le Quang
Keyword(s):  
Bulk Modulus ◽  
Size Effects ◽  
Solid Phase ◽  
Hollow Spheres ◽  
Pore Surface ◽  
Nanoporous Media ◽  
Surface Stresses ◽  
Effective Bulk Modulus ◽  
Nanometric Size

The purpose of this work is to extend the equations of linear poroelasticity to the case of materials with nanopores. We consider a model of microstructure which corresponds to an assemblage of hollow spheres saturated by a fluid. The solid phase is linearly elastic and isotropic; pores are assumed to be of nanometric size. To account for the pore surface stresses, the Young-Laplace model is used. The nanopore size effects on the effective bulk modulus, Biot’ modulus and coefficient are shown. When pores are sufficiently large, the classical relations of linear poroelasticity are retrieved.

Gassmann fluid substitutions: A tutorial

Geophysics ◽  
2003 ◽  
Vol 68 (2) ◽  
pp. 430-440 ◽  
Author(s):  
Tad M. Smith ◽  
Carl H. Sondergeld ◽  
Chandra S. Rai
Keyword(s):  
Bulk Modulus ◽  
Bulk Density ◽  
Pore Fluid ◽  
Direct Result ◽  
Fluid Substitution ◽  
Seismic Attribute ◽  
Amplitude Variation With Offset ◽  
Effective Bulk Modulus ◽  
Porous Frame ◽  
Insight Into

Fluid substitution is an important part of seismic attribute work, because it provides the interpreter with a tool for modeling and quantifying the various fluid scenarios which might give rise to an observed amplitude variation with offset (AVO) or 4D response. The most commonly used technique for doing this involves the application of Gassmann's equations. Modeling the changes from one fluid type to another requires that the effects of the starting fluid first be removed prior to modeling the new fluid. In practice, the rock is drained of its initial pore fluid, and the moduli (bulk and shear) and bulk density of the porous frame are calculated. Once the porous frame properties are properly determined, the rock is saturated with the new pore fluid, and the new effective bulk modulus and density are calculated. A direct result of Gassmann's equations is that the shear modulus for an isotropic material is independent of pore fluid, and therefore remains constant during the fluid substitution process. In the case of disconnected or cracklike pores, however, this assumption may be violated. Once the values for the new effective bulk modulus and bulk density are calculated, it is possible to calculate the compressional and shear velocities for the new fluid conditions. There are other approaches to fluid substitution (empirical and heuristic) which avoid the porous frame calculations but, as described in this tutorial, often do not yield reliable results. This tutorial provides the reader with a recipe for performing fluid substitutions, as well as insight into why and when the approach may fail.

On the effective viscoelastic moduli of two-phase media. I. Rigorous bounds on the complex bulk modulus

1993 ◽  
Vol 440 (1908) ◽  
pp. 163-188 ◽  
Keyword(s):  
Bulk Modulus ◽  
Complex Dielectric Constant ◽  
Effective Moduli ◽  
Two Phase ◽  
Shear Moduli ◽  
Isotropic Composite ◽  
Effective Bulk Modulus ◽  
Circular Arcs ◽  
Static Regime ◽  
Rigorous Bounds

The dynamic response of isotropic composites of two viscoelastic isotropic phases mixed in fixed proportions is considered in the frequency range where the acoustic wavelength is much larger than the inhomogeneities. The effective bulk-modulus bounds of Hashin-Shtrikman-Walpole are extended to viscoelasticity in this quasi-static régime, where the properties of the isotropic composite can be described by complex bulk and shear moduli. The effective bulk modulus is shown to be constrained to a lens-shaped region of the complex plane bounded by the outermost pair of four circular arcs (three circular arcs in the case of two-dimensional elasticity). This is proved using a new variational principle for viscoelasticity together with two established techniques for deriving bounds on effective moduli, namely the translation method and the Hashin-Shtrikman method. In this application the Hashin-Shtrikman method needs to be generalized to allow the reference tensor to have an associated quasiconvex energy. Microstructures are identified which have bulk-moduli that correspond to various points on each of the circular arcs. Thus these microstructures have extremal viscoelastic behaviour when the associated arc forms one of the outermost pair. The bounds and the extremal microstructures are similar to those obtained for the complex dielectric constant, but the methods used here are entirely different.

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