Showing papers on "Elasticity (economics) published in 2007"

Capillary origami: spontaneous wrapping of a droplet with an elastic sheet.

Abstract: The interaction between elasticity and capillarity is used to produce three-dimensional structures through the wrapping of a liquid droplet by a planar sheet. The final encapsulated 3D shape is controlled by tailoring the initial geometry of the flat membrane. Balancing interfacial energy with elastic bending energy provides a critical length scale below which encapsulation cannot occur, which is verified experimentally. This length is found to depend on the thickness as ${h}^{3/2}$, a scaling favorable to miniaturization which suggests a new way of mass production of 3D micro- or nanoscale objects.

Microstructural Randomness and Scaling in Mechanics of Materials

Abstract: PREFACE BASIC RANDOM MEDIA MODELS Probability Measure of Geometric Objects Basic Point Fields Directional Data Random Fibers, Random Line Fields, Tessellations Basic Concepts and Definitions of Random Microstructures RANDOM PROCESSES AND FIELDS Elements of One-Dimensional Random Fields Mechanics Problems on One-Dimensional Random Fields Elements of Two- and Three-Dimensional Random Fields Mechanics Problems on Two- and Three-Dimensional Random Fields Ergodicity The Maximum Entropy Method PLANAR LATTICE MODELS: PERIODIC TOPOLOGIES AND ELASTOSTATICS One-Dimensional Lattices Planar Lattices: Classical Continua Applications in Mechanics of Composites Planar Lattices: Nonclassical Continua Extension-Twist Coupling in a Helix LATTICE MODELS: RIGIDITY, RANDOMNESS, DYNAMICS, AND OPTIMALITY Rigidity of Networks Spring Network Models for Disordered Topologies Particle Models Michell Trusses: Optimal Use of Material TWO- VERSUS THREE-DIMENSIONAL CLASSICAL ELASTICITY Basic Relations The CLM Result and Stress Invariance Poroelasticity TWO- VERSUS THREE-DIMENSIONAL MICROPOLAR ELASTICITY Micropolar Elastic Continua Classical vis-a-vis Nonclassical (Elasticity) Models Planar Cosserat Elasticity The CLM Result and Stress Invariance Effective Micropolar Moduli and Characteristic Lengths of Composites MESOSCALE BOUNDS FOR LINEAR ELASTIC MICROSTRUCTURES Micro-, Meso-, and Macroscales Volume Averaging Spatial Randomness Hierarchies of Mesoscale Bounds Examples of Hierarchies of Mesoscale Bounds Moduli of Trabecular Bone RANDOM FIELD MODELS AND STOCHASTIC FINITE ELEMENTS Mesoscale Random Fields Second-Order Properties of Mesoscale Random Fields Does There Exist a Locally Isotropic, Smooth Elastic Material? Stochastic Finite Elements for Elastic Media Method of Slip-Lines for Inhomogeneous Plastic Media Michell Trusses in the Presence of Random Microstructure HIERARCHIES OF MESOSCALE BOUNDS FOR NONLINEAR AND INELASTIC MICROSTRUCTURES Physically Nonlinear Elastic Microstructures Finite Elasticity of Random Composites Elastic-Plastic Microstructures Rigid-Perfectly Plastic Microstructures Viscoelastic Microstructures Stokes Flow in Porous Media Thermoelastic Microstructures Scaling and Stochastic Evolution in Damage Phenomena Comparison of Scaling Trends MESOSCALE RESPONSE IN THERMOMECHANICS OF RANDOM MEDIA From Statistical Mechanics to Continuum Thermodynamics Extensions of the Hill Condition Legendre Transformations in (Thermo)Elasticity Thermodynamic Orthogonality on the Mesoscale Complex versus Compound Processes: The Scaling Viewpoint Toward Continuum Mechanics of Fractal Media WAVES AND WAVEFRONTS IN RANDOM MEDIA Basic Methods in Stochastic Wave Propagation Toward Spectral Finite Elements for Random Media Waves in Random 1D Composites Transient Waves in Heterogeneous Nonlinear Media Acceleration Wavefronts in Nonlinear Media BIBLIOGRAPHY INDEX

Imaging and estimation of tissue elasticity by ultrasound.

Abstract: Ultrasound (US) elasticity imaging is an extension of the ancient art of palpation and of earlier US methods for viewing tissue stiffness such as echopalpation. Elasticity images consist of either an image of strain in response to force or an image of estimated elastic modulus. There are 3 m

Dynamics of Consumer Demand for New Durable Goods

Abstract: Most new consumer durable goods experience rapid declines in prices and improvements in qual- ity, suggesting the importance of modeling dynamics. This paper estimates a dynamic model of consumer preferences for new durable goods with persistent heterogeneous consumer tastes, rational expectations and repeat purchases over time. We estimate the model on the digital camcorder in- dustry using panel data on prices, sales and characteristics. We nd that standard COLIs overstate welfare gain in later periods due to a changing composition of buyers. The one-year industry elas- ticity in response to a transitory industry-wide price shock is about 25% less than the one-month elasticity.

Mixed finite element methods for linear elasticity with weakly imposed symmetry

Abstract: In this paper, we construct new finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approxima- tions to both stresses and displacements. The methods are based on a modified form of the Hellinger-Reissner variational principle that only weakly imposes the symmetry condition on the stresses. Although this approach has been previously used by a number of authors, a key new ingredient here is a constructive derivation of the elasticity complex starting from the de Rham complex. By mimicking this construction in the discrete case, we derive new mixed finite elements for elasticity in a systematic manner from known discretizations of the de Rham complex. These elements appear to be simpler than the ones previously derived. For example, we construct stable discretizations which use only piecewise linear elements to approximate the stress field and piecewise constant functions to approximate the displacement field.

A novel atomistic approach to determine strain-gradient elasticity constants: Tabulation and comparison for various metals, semiconductors, silica, polymers and the (Ir) relevance for nanotechnologies

Abstract: Strain-gradient elasticity is widely used as a suitable alternative to size-independent classical continuum elasticity to, at least partially, capture elastic size effects at the nanoscale. In this work, borrowing methods from statistical mechanics, we present mathematical derivations that relate the strain-gradient material constants to atomic displacement correlations in a molecular dynamics computational ensemble. Using the developed relations and numerical atomistic calculations, the strain-gradient constants are explicitly determined for some representative semiconductor, metallic, amorphous and polymeric materials. This method has the distinct advantage that amorphous materials can be tackled in a straightforward manner. For crystalline materials we also employ and compare results from both empirical and ab initio based lattice dynamics. Apart from carrying out a systematic tabulation of the relevant material parameters for various materials, we also discuss certain subtleties of strain-gradient elasticity, including: the paradox associated with the sign of the strain-gradient constants, physical reasons for low or high characteristic length scales associated with the strain-gradient constants, and finally the relevance (or the lack thereof) of strain-gradient elasticity for nanotechnologies.

Three-dimensional cross-linked F-actin networks : Relation between network architecture and mechanical behavior

Abstract: Numerical simulations are reported for the response of three-dimensional cross-linked F-actin networks when subjected to large deformations. In addition to the physiological parameters such as actin and cross-linker concentration, the model explicitly accounts for filament properties and network architecture. Complementary to two-dimensional studies, we find that the strain-stiffening characteristics depend on network architecture through the local topology around cross-links.

Length scales at which classical elasticity breaks down for various materials.

Abstract: At what characteristic length scale does classical continuum elasticity cease to accurately describe small deformation mechanical behavior? The two dominant physical mechanisms that lead to size dependency of elastic behavior at the nanoscale are surface energy effects and nonlocal interactions. The latter arises due to the discrete structure of matter and the fluctuations in the interatomic forces that are smeared out within the phenomenological elastic modulus at coarser sizes. While surface energy effects have been well characterized in the literature, little is known about the length scales at which nonlocal effects manifest for different materials. Using a combination of empirical molecular dynamics and lattice dynamics (empirical and ab initio), we provide estimates of nonlocal elasticity length scales for various classes of materials: semiconductors, metals, amorphous solids, and polymers.

Determination of the modulus of elasticity of the human cornea.

Abstract: Purpose To determine the material behavior of the human cornea in the form of simple relationships between the modulus of elasticity and intraocular pressure (IOP) and to establish the effect of age on the material behavior. Methods Human corneal specimens with age between 50 and 95 years were tested under inflation conditions to determine their behavior. The corneas were subjected to two extreme load rates to represent dynamic and static loading conditions. The pressure-deformation results were analyzed using shell theory to derive the relationship between the modulus of elasticity and IOP. Results The corneas demonstrated a nonlinear hyperelastic behavior pattern with an initial low stiffness stage and a final high stiffness stage. Despite the nonlinearity of the pressure deformation results, the relationship between the modulus of elasticity and the applied pressure was almost linear. A considerable increase was noted in the values of the modulus of elasticity associated with both age and load rate. General equations were derived to calculate the values of the secant and tangent moduli of elasticity in terms of IOP for any age greater than 50 years, and these equations are presented in a simple form suitable for use in numerical simulations. Conclusions Adequate representation of corneal material behavior is essential for the accurate predictive modeling of corneal biomechanics. The material models developed in this work could be implemented in numerical simulations of refractive surgery procedures, corneal shape changes due to contact lens wear, and other applications.

Analytical Solution for Size-Dependent Elastic Field of a Nanoscale Circular Inhomogeneity

Abstract: Two-dimensional elastic field of a nanoscale circular hole/inhomogeneity in an infinite matrix under arbitrary remote loading and a uniform eigenstrain in the inhomogeneity is investigated. The Gurtin-Murdoch surface/interface elasticity model is applied to take into account the surface/interface stress effects. A closed-form analytical solution is obtained by using the complex potential function method of Muskhelishvili. Selected numerical results are presented to investigate the size dependency of the elastic field and the effects of surface elastic moduli and residual surface stress. Stress state is found to depend on the radius of the inhomogeneity/hole, surface elastic constants, surface residual stress, and magnitude of far-field loading.

Elasticity of Olivine (α), Beta(β), and Spinel (γ) Polymorphs of Germanates and Silicates

Abstract: Summary Ultrasonic data for the velocities of germanate and silicate compounds in the olivine (a), beta (8) and spinel (y) crystal structures have been determined as a function of pressure to 7-5 kbar at room temperature for polycrystalline specimens hot-pressed at pressures up to 65 kbar. The a-y phase transformations are characterized by the following velocity (u)-density (p) relationships: (a) the velocity jumps are twice the percentage magnitude of the density jumps; (b) the ratio (vp/v,) of the compressional to shear velocity is either approximately constant or increases slightly across the transitions; and (c) the slopes (linear or logarithmic) on v-p diagrams for the a-y transition are comparable to those produced by isothermal compression or isobaric expansion of the low-pressure olivine phase. The behaviour of up/u, is a feature common to many phase transformations. However, the observed relationships (a) and (c), while similar to those for the quartz-coesite transition in Si02, are in marked contrast with those for the coesite-rutile, pyroxene-garnet and pyroxeneilmenite transformations. These latter transitions involve increases in cation-anion co-ordination and nearest-neighbour distances whereas the olivine-spinel and olivine-beta phase transformations do not. Such crystallographic details may be diagnostic for interpretations of the composition and mineralogy of the Earth’s transition zone. Systematic trends in the elastic properties for isostructural sequences support the concept of germanates as models for the elasticity of their silicate analogues; this scheme is applied to estimate the bulk modulus of the spinel polymorph of Mg, Si04 (K, = 2-06 0.05 Mbar). Comparison of the new elasticity data with recent Earth models in the vicinity of the 400-km discontinuity reveals that only model 1066B of Gilbert & Dziewonski is compatible with the experimental data for the u-y and a-8 transformations.

Nonaffine rubber elasticity for stiff polymer networks

Abstract: We present a theory for the elasticity of cross-linked stiff polymer networks. Stiff polymers, unlike their flexible counterparts, are highly anisotropic elastic objects. Similar to mechanical beams, stiff polymers easily deform in bending, while they are much stiffer with respect to tensile forces ("stretching"). Unlike in previous approaches, where network elasticity is derived from the stretching mode, our theory properly accounts for the soft bending response. A self-consistent effective medium approach is used to calculate the macroscopic elastic moduli starting from a microscopic characterization of the deformation field in terms of "floppy modes"-low-energy bending excitations that retain a high degree of nonaffinity. The length scale characterizing the emergent nonaffinity is given by the "fiber length" lf, defined as the scale over which the polymers remain straight. The calculated scaling properties for the shear modulus are in excellent agreement with the results of recent simulations obtained in two-dimensional model networks. Furthermore, our theory can be applied to rationalize bulk rheological data in reconstituted actin networks.

Nonlinear finite-element analysis of nanoindentation of viral capsids.

Abstract: Recent atomic force microscope (AFM) nanoindentation experiments measuring mechanical response of the protein shells of viruses have provided a quantitative description of their strength and elasticity To better understand and interpret these measurements, and to elucidate the underlying mechanisms, this paper adopts a course-grained modeling approach within the framework of three-dimensional nonlinear continuum elasticity Homogeneous, isotropic, elastic, thick-shell models are proposed for two capsids: the spherical cowpea chlorotic mottle virus (CCMV), and the ellipsocylindrical bacteriophage phi29 As analyzed by the finite-element method, these models enable parametric characterization of the effects of AFM tip geometry, capsid dimensions, and capsid constitutive descriptions The generally nonlinear force response of capsids to indentation is shown to be insensitive to constitutive particulars, and greatly influenced by geometric and kinematic details Nonlinear stiffening and softening of the force response is dependent on the AFM tip dimensions and shell thickness Fits of the models capture the roughly linear behavior observed in experimental measurements and result in estimates of Young's moduli of approximately 280-360 MPa for CCMV and approximately 45 GPa for phi29

Dynamics of viscoelastic fluid filaments in microfluidic devices

Abstract: The effects of fluid elasticity and channel dimension on polymeric droplet formation in the presence of a flowing continuous Newtonian phase are investigated systematically by using different molecular weight (MW) poly(ethylene oxide) (PEO) solutions and varying microchannel dimensions with constant orifice width (w) to depth (h) ratio (w∕h=1∕2) and w=25μm, 50μm, 100μm, and 1mm. The flow rate is varied so that the mean shear rate is practically identical for all cases considered. Relevant times scales include inertia-capillary Rayleigh time τR=(Rmax3ρ∕σ)1∕2, viscocapillary Tomotika time τT=η0Rmax∕σ, and the polymer relaxation time λ, where ρ is the fluid density of the dispersed phase, σ is the interfacial tension, η0 is the zero shear viscosity of the dispersed polymer phase, and Rmax is the maximum filament radius. Dimensionless numbers include the elasticity number E=λν∕Rmax2, elastocapillary number Ec=λ∕τT, and Deborah number, De=λ∕τR, where ν=η0∕ρ is the kinematic shear viscosity of the fluids. Exper...

Using the bending beam model to estimate the elasticity of diphenylalanine nanotubes.

Abstract: The core recognition motif of the amyloidogenic β-amyloid polypeptide, diphenylalanine peptide, has previously been shown to self-assemble into discrete, well-ordered, stiff nanotubes under mild conditions. The nanotubes keep the same morphology from room temperature up to 100 °C. In the presented study, we applied the bending beam model to atomic force microscopy images of diphenylalanine nanotubes suspended across cavities and obtained the Young’s modulus 27 ± 4 GPa and the shear modulus 0.21 ± 0.03 GPa. We also showed that the elasticity of these nanotubes is stable within the same temperature range and at relative humidity from 0% to 70%. This study furthers our understanding of the structure and properties of these nanotubes, which are important for their potential applications in biotechnology.

Effective properties of elastic periodic composite media with fibers

Abstract: A series solution to obtain the effective properties of some elastic composites media having periodically located heterogeneities is described. The method uses the classical expansion along Neuman series of the solution of the periodic elasticity problem in Fourier space, based on the Green's tensor, and exact expressions of factors depending on the shape of the inclusions. Some properties of convergence of the solution are presented, more specifically concerning the elasticity tensor of the reference medium, showing that the convergence occurs even for empty fibers. The solution is extended for rigid inclusions. A comparison is made with previous exact solutions for a fiber composite made of cylindrical fibers with circular cross-sections and with previous estimates. Different examples are presented for new situations concerning the study of fiber composites: composites with elliptic cross-sections and multi-phase fibrous composites.

Correlation between a Cutometer and quantitative evaluation using Moire topography in age-related skin elasticity.

Abstract: Background/purpose: As aging occurs, our skin gets more wrinkles, becomes drier and loses its elasticity. Validating the evaluation of skin elasticity is especially important, because it is not as visible as other signs of aging such as wrinkles. So it is needed that the method for measuring skin elasticity is able to reflect perception about the change of the skin state. Methods: Here, the correlation between age and the parameters given by a Cutometer® is identified and the main parameters that reflect the decreases in skin elasticity in terms of ages are presented. Also, Moire's system, an evaluation method to quantify the sensory value of viewing, is developed. A five-grade standard of Moire topographic photo scale on the face is used to evaluate the state of skin elasticity and lifting 20- to 61-year-old women. Based on this photo standard, scoring is performed using a five-grade system by three specialists to obtain the consensus score. The score is compared with the result of a Cutometer®. Results: Significant negative correlations between age and results of a Cutometer® (r=−0.687−0.725), Moire's topography scores (r=−938), were found. Some Cutometer® parameters and the decreases in skin elasticity in terms of ages were highly correlated (r=−0.687−0.725). The results from Moire system and flexibility as sensory evaluation also had a very high correlation with age (r=−0.765−0.932). Finally, we have shown the significance of the correlation between the result of a Cutometer® and the score of Moire topography (r=0.711). Conclusions: It is considered that Cutometer® parameters R7 and R2 are used as main parameters to assess skin elasticity and aging. And our studies using Moire topography on the face have confirmed that instrumental measurements reflect the decrease in skin elasticity, which is perceived visually.

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Ab-initio simulation of elastic constants for some ceramic materials

Abstract: Athermal elasticity for some ceramic materials (α-Al2O3, SiC (α and β phases), TiO2 (rutile and anatase), hexagonal AlN and TiB2, cubic BN and CaF2, and monoclinic ZrO2) have been investigated via density functional theory. Energy-volume equation-of-state computations to obtain the zero pressure equilibrium volume and bulk modulus as well as computations of the full elastic constant tensor of these ceramics at the experimental zero pressure volume have been performed. The present results for the single crystal elasticity are in good agreement with experiments both for the aggregate properties (bulk and shear modulus) and the elastic anisotropy. In contrast, a considerable discrepancy for the zero pressure bulk modulus of some ceramics evaluated from the energy-volume fit to the computational zero pressure volume has been observed.

Estimation of tissue’s elasticity with surface wave speed

Abstract: The mechanical response of tissues to external forces has gained considerable interest in medical diagnosis. One approach to imaging tissue elastic properties is to apply an external force on the surface of the body. Another approach is to generate a localized force inside the tissue with the radiation force of ultrasound. In this paper, a new method is developed to estimate tissue’s elasticity based on surface wave speed measurement. The theory of surface wave speed is developed for estimating tissue’s elasticity. Experiments are carried out on a tissue-mimicking ultrasound phantom. An amplitude modulated ultrasound signal of a few hundred hertz is used to generate a localized force in the phantom. The surface wave fields are measured with a laser vibrometer. It shows that the surface wave speed can be used for inversely estimating tissue’s elastic properties based on tissue’s surface measurement.

Elastic moduli of anisotropic clay

Abstract: Claymineralsareimportantcomponentsinshales,controlling their elastic properties and anisotropy. The elasticity of crystalline clay minerals differs significantly from that of clay in situ because of the ability of clay particles to bind water. In the majority of published works, only isotropic moduli for in situ clays are reported. However, anisotropy is inherent in the clay elasticity. We develop an inversion technique for determination of thestiffnesstensorofinsituclayfromtheshale’sstiffnesstensor. As an example, we obtain the stiffness tensor of a “water-clay” composite from the data on the water-saturated Greenhorn shale sample, whose clay composition consists of almost equal amounts of illite and smectite and comparable amounts of kaolinite and chlorite. The stiffness tensor of the water-clay composite is found for the Greenhorn shale with step-by-step inversion based upon an effective medium theory. The inversion uses a nonlinear optimization technique with bounds imposed on the estimated parameters. In the inversion, we apply different approaches of the effective medium theory using a published method referred to here as the generalized singular approximation GSA. The GSA method makes it possible to take into account the microstructure of shales. The resulting elasticity constants of the anisotropic transversely isotropic in situ clay composite are C11 = 23.7, C33 = 8.5, C44 = 0.8, C66 = 5.7, and C13 = 3.1 in GPa; and the density equals 2.17 g/cm 3 . The Thomsen parameters for the clay composite are = 0.89, = 3.10, and = 0.34. The elasticity constants found for this clay composite can be used in the theoretical analysis of shales that have a similar composition of clay but with different mineral compositions. The inversion technique developed can be used for general shale water-clay composites when the mineral composition and orientation of the clay platelets are known.

Size, temperature, and bond nature dependence of elasticity and its derivatives on extensibility, Debye temperature, and heat capacity of nanostructures

Abstract: With the miniaturization of a solid down to nanometer scale, the elasticity, extensibility, Debye temperature, and specific heat capacity of the solid are no longer constant but change with variation of size. These quantities also change with the temperature of the measurement and the nature of the chemical bond involved. The mechanism behind the intriguing tunability and the interdependence of these quantities remain yet a high challenge. A set of analytical solutions is presented herewith showing that the observed trends could be reproduced by taking the fact of bond order deficiency into consideration. Agreement between predictions and observations clarifies that the shortened and strengthened surface bonds dictate intrinsically the observed tunability, yet atoms in the core interior remain as they are in the bulk. The thermally softening of a specimen arises from bond expansion and bond vibration due to the internal energy increases.