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.

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.

Stress Concentrations in Three-Dimensional Electrostriction

1967 ◽  
Vol 34 (2) ◽  
pp. 431-436 ◽  
Author(s):  
T. E. Smith
Keyword(s):  
Displacement Vector ◽  
Spherical Inclusion ◽  
Crack Problem ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Uniform Electric Field ◽  
Inclusion Problem ◽  
Stress Concentrations ◽  
Displacement Potential ◽  
Penny Shaped Crack

Using the techniques employed in developing a Papkovich-Neuber representation for the displacement vector in classical elasticity, a particular integral of the kinematical equations of equilibrium for the uncoupled theory of electrostriction is developed. The particular integral is utilized in conjunction with the displacement potential function approach to problems of the theory of elasticity to obtain closed-form solutions of several stress concentration problems for elastic dielectrics. Under a prescribed uniform electric field at infinity, the problems of an infinite elastic dielectric having first a spherical cavity and then a rigid spherical inclusion are solved. The rigid spheroidal inclusion problem and the penny-shaped crack problem are also solved for the case where the prescribed field is parallel to their axes of revolution.

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

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.

scholarly journals Translation of a Coated Rigid Spherical Inclusion in an Elastic Matrix: Exact Solution, and Implications for Mechanobiology

2019 ◽  
Vol 86 (5) ◽  
Author(s):  
Xin Chen ◽  
Moxiao Li ◽  
Shaobao Liu ◽  
Fusheng Liu ◽  
Guy M. Genin ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Exact Solution ◽  
Analytical Solution ◽  
Spherical Inclusion ◽  
Matrix Material ◽  
Elastic Matrix ◽  
Protein Ligands ◽  
First Case ◽  
The Matrix ◽  
Matrix Modulus

The displacement of relatively rigid beads within a relatively compliant, elastic matrix can be used to measure the mechanical properties of the matrix. For example, in mechanobiological studies, magnetic or reflective beads can be displaced with a known external force to estimate the matrix modulus. Although such beads are generally rigid compared to the matrix, the material surrounding the beads typically differs from the matrix in one or two ways. The first case, as is common in mechanobiological experimentation, is the situation in which the bead must be coated with materials such as protein ligands that enable adhesion to the matrix. These layers typically differ in stiffness relative to the matrix material. The second case, common for uncoated beads, is the situation in which the beads disrupt the structure of the hydrogel or polymer, leading to a region of enhanced or reduced stiffness in the neighborhood of the bead. To address both cases, we developed the first analytical solution of the problem of translation of a coated, rigid spherical inclusion displaced within an isotropic elastic matrix by a remotely applied force. The solution is applicable to cases of arbitrary coating stiffness and size of the coating. We conclude by discussing applications of the solution to mechanobiology.

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.

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