Ellipsoidal Bounds of Elastic Composites

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
X. Frank Xu
Keyword(s):  
Physical Properties ◽  
Elastic Moduli ◽  
Applied Mechanics ◽  
Explicit Formulas ◽  
Aspect Ratios ◽  
Multiphase Composites ◽  
Rigorous Bounds ◽  
Elastic Composites ◽  
Asymptotic Analyses ◽  
Properties Of Composites

The formulation of rigorous bounds for the physical properties of composites constitutes one of the most fundamental parts of applied mechanics. In this work, the so-called ellipsoidal bounds, as a generalization of the Hashin-Shtrikman spherical bounds, are formulated for elastic moduli of multiphase composites. Explicit formulas are derived to estimate the bounds for the elastic moduli of isotropic composites. Asymptotic analyses are conducted for composites containing needlelike and disklike fillers with aspect ratios approaching infinity and zero, respectively. The new bounds and estimates are expected to be useful for polycrystals and composites containing fillers, especially with large or small aspect ratios, such as nanowires, nanotubes, and nanoplatelets.

Modes of Wave Propagation and Dispersion Relations in Inclusion Reinforced Composite Plates

2010 ◽  
Author(s):  
Yu Cheng Liu ◽  
Jin Huang Huang
Keyword(s):  
Composite Plate ◽  
Elastic Moduli ◽  
Lamb Waves ◽  
Plate Thickness ◽  
Composite Plates ◽  
Dispersion Relations ◽  
Elastic Behavior ◽  
Effective Elastic Moduli ◽  
Aspect Ratios ◽  
Reinforced Composite

This paper mainly analyzes the wave dispersion relations and associated modal pattens in the inclusion-reinforced composite plates including the effect of inclusion shapes, inclusion contents, inclusion elastic constants, and plate thickness. The shape of inclusion is modeled as spheroid that enables the composite reinforcement geometrical configurations ranging from sphere to short and continuous fiber. Using the Mori-Tanaka mean-field theory, the effective elastic moduli which are able to elucidate the effect of inclusion’s shape, stiffness, and volume fraction on the composite’s anisotropic elastic behavior can be predicted explicitly. Then, the dispersion relations and the modal patterns of Lamb waves determined from the effective elastic moduli can be obtained by using the dynamic stiffness matrix method. Numerical simulations have been given for the various inclusion types and the resulting dispersions in various wave types on the composite plate. The types (symmetric or antisymmetric) of Lamb waves in an isotropic plate can be classified according to the wave motions about the midplane of the plate. For an orthotropic composite plate, it can also be classified as either symmetric or antisymmetric waves by analyzing the dispersion curves and inspecting the calculated modal patterns. It is also found that the inclusion contents, aspect ratios and plate thickness affect propagation velocities, higher-order mode cutoff frequencies, and modal patterns.

Optimal Percolation Thresholds of Two- and Three-Dimensional Engineering Composites

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
X. Frank Xu
Keyword(s):  
Thin Films ◽  
Variational Method ◽  
Theoretical Prediction ◽  
Transport Properties ◽  
Three Dimensional ◽  
Engineering Applications ◽  
Aspect Ratios ◽  
Percolation Thresholds ◽  
Work Done ◽  
Properties Of Composites

Theoretical prediction of percolation thresholds universally applicable for various composites remains a major theoretical challenge. In the work done by Xu (2011, “Ellipsoidal Bounds and Percolation Thresholds of Transport Properties of Composites,” Acta Mech., 223, pp. 765–774), a variational method is developed to predict optimal percolation thresholds for transport properties of three dimensional composites subjected to full dispersion of fillers. In this paper, simplified formulae are provided for engineering applications of 3D composites. New formulae are derived for optimal percolation thresholds of 2D composites, i.e., laminates and thin films, and for composites containing a combination of fillers with different aspect ratios. The effects of dimensionality and waviness are especially discussed.

Modeling squirt dispersion and attenuation in fluid-saturated rocks using pressure dependency of dry ultrasonic velocities

Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. WA157-WA168 ◽  
Author(s):  
Osni Bastos de Paula ◽  
Marina Pervukhina ◽  
Dina Makarynska ◽  
Boris Gurevich
Keyword(s):  
Aspect Ratio ◽  
Elastic Properties ◽  
Elastic Moduli ◽  
Pore Space ◽  
Geometrical Parameters ◽  
Laboratory Measurements ◽  
Significant Linear Trend ◽  
Aspect Ratios ◽  
Pressure Dependency ◽  
Dispersion And Attenuation

Modeling dispersion and attenuation of elastic waves in fluid-saturated rocks due to squirt flow requires the knowledge of a number of geometrical parameters of the pore space, in particular, the characteristic aspect ratio of the pores. These parameters are usually inferred by fitting measurements on saturated rocks to model predictions. To eliminate such fitting and thus make the model more predictive, we propose to recover the geometrical parameters of the pore space from the pressure dependency of elastic moduli on dry samples. Our analysis showed that the pressure dependency of elastic properties of rocks (and their deviation from Gassmann’s prediction) at ultrasonic frequencies is controlled by the squirt flow between equant, stiff, and so-called intermediate pores (with aspect ratios between [Formula: see text]). Such intermediate porosity is expected to close at confining pressures of between 200 and 2000 MPa, and thus cannot be directly obtained from ultrasonic experiments performed at pressures below 50 MPa. However, the presence of this intermediate porosity is inferred from the significant linear trend in the pressure dependency of elastic properties of the dry rock and the difference between the bulk modulus of the dry rock computed for spherical pores and the measured modulus at 50 MPa. Moreover, we can infer the magnitude of the intermediate porosity and its characteristic aspect ratio. Substituting these parameters into the squirt model, we have computed elastic moduli and velocities of the water-saturated rock and compared these predictions against laboratory measurements of these velocities. The agreement is good for a number of clean sandstones, but not unexpectedly worse for a broad range of shaley sandstones. Our predictions showed that dispersion and attenuation caused by the squirt flow between compliant and stiff pores may occur in the seismic frequency band. Confirmation of this prediction requires laboratory measurements of elastic properties at these frequencies.

scholarly journals Experimental Dental Composites Containing a Novel Methacrylate-Functionalized Calcium Phosphate Component: Evaluation of Bioactivity and Physical Properties

2021 ◽  
Author(s):  
SUNNY SKARIA ◽  
KENNETH J BERK
Keyword(s):  
Calcium Phosphate ◽  
Physical Properties ◽  
Bioactive Compound ◽  
Dental Composite ◽  
Dental Composites ◽  
Attenuated Total Reflectance ◽  
X Ray Diffraction ◽  
Ion Release ◽  
Surface Precipitation ◽  
Properties Of Composites

The aim of this study was to synthesize and characterize a novel Methacrylate- functionalized Calcium Phosphate (MCP) used as a bioactive compound for innovative dental composites. The characterization was accomplished by Attenuated Total Reflectance Fourier-Transform Infrared Spectroscopy (ATR-FTIR), X-Ray Diffraction Analysis (XRDA), Scanning Electron Microscopy (SEM), and EnergyDispersive Spectroscopy (EDS). The incorporation of MCP as a bioactive filler in esthetic dental composite formulations and the ability of MCP containing dental composites to promote precipitation of hydroxyapatite (HAp) on the surfaces of those dental composites was explored. The translucency parameter, depth of cure, degree of conversion, ion release profile, and other physical properties of composites were studied with respect to the amount of MCP added to the composites. Composites containing 3 Wt.%, 6 Wt.%, and 20 Wt.% MCP were evaluated at 7, 14, and 21 days. The progress of surface precipitation of hydroxyapatite on MCP-containing dental composites was studied by systematically increasing the MCP content in the composite and the time of specimen storage in Dulbecco’s phosphate-buffered solution with calcium and magnesium. It was found that there was a direct correlation between the percentage of MCP in a composite formulation, the amount of time the specimen was stored in PBS, and the deposition of hydroxyapatite on the composite’s surface

scholarly journals Correlation of Elastic Moduli and Serpentine Content in Ultramafic Rocks

2019 ◽  
Author(s):  
Aida Farough ◽  
Alexander Karrasch
Keyword(s):  
Physical Properties ◽  
Lower Crust ◽  
Elastic Moduli ◽  
Oceanic Lithosphere ◽  
Ultramafic Rocks ◽  
Seismic Velocities ◽  
Rock Composition ◽  
Metamorphic History ◽  
History Of ◽  
Thin Crust

Understanding the physical properties of ultramafic rocks is important for evaluating awide variety of petrologic models of the oceanic lithosphere, particularly upper mantle and lower crust. Hydration of oceanic peridotites results in increasing serpentine content, which affects lithospheric physical properties and the global bio/geochemical cycles of various elements. In understanding tectonic, magmatic and metamorphic history of the oceanic crust, interpreting seismic velocities, rock composition and elastic moduli are of fundamental importance. In this study we show that as serpentine content increases, density decreases linearly with a slope of 7.85. We also correlate increase in serpentine content with a linear decline in shear, bulk and Young’s moduli with slopes of 0.48, 0.77, 0.45 respectively. Our results show that increase in serpentine content of lower crust and forearc mantle could decrease elasticity of lithospehere and result in break-offs. Therefore tectonic processes at peridotite rich slow spreading ridges may be strongly affected by serpentine content, particularly serpentinization may be responsible for discontinuities in thin crust, and formation of weak fault zones.

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