Demosthenes Polyzos

BENDING AND STABILITY ANALYSIS OF GRADIENT ELASTIC BEAMS

Abstract The problems of bending and stability of Bernoulli–Euler beams are solved analytically on the basis of a simple linear theory of gradient elasticity with surface energy. The governing equations of equilibrium are obtained by both a combination of the basic equations and a variational statement. The additional boundary conditions are obtained by both variational and weighted residual approaches. Two boundary value problems (one for bending and one for stability) are solved and the gradient elasticity effect on the beam bending response and its critical (buckling) load is assessed for both cases. It is found that beam deflections decrease and buckling load increases for increasing values of the gradient coefficient, while the surface energy effect is small and insignificant for bending and buckling, respectively.

Scattering of He–Ne laser light by an average-sized red blood cell

The scattering of He-Ne laser light by an average-sized human red blood cell (RBC) is investigated numerically. The RBC is modeled as an axisymmetric, low-contrast dielectric, biconcave disk. The interaction problem is treated numerically by means of a boundary-element methodology. The differential scattering cross sections (DSCSs) corresponding to various cell orientations are calculated. The numerical results obtained for the exact RBC geometry are compared with those corresponding to a scattering problem in which the cell is assumed to be either a volume-equivalent sphere or an oblate spheroid. A parametric study demonstrating the dependence of the DSCS on the wavelength of the incident wave and the cells refractive index is presented.

Velocity dispersion of guided waves propagating in a free gradient elastic plate: Application to cortical bone

The classical linear theory of elasticity has been largely used for the ultrasonic characterization of bone. However, linear elasticity cannot adequately describe the mechanical behavior of materials with microstructure in which the stress state has to be defined in a non-local manner. In this study, the simplest form of gradient theory (Mindlin Form-II) is used to theoretically determine the velocity dispersion curves of guided modes propagating in isotropic bone-mimicking plates. Two additional terms are included in the constitutive equations representing the characteristic length in bone: (a) the gradient coefficient g, introduced in the strain energy, and (b) the micro-inertia term h, in the kinetic energy. The plate was assumed free of stresses and of double stresses. Two cases were studied for the characteristic length: h=10(-4) m and h=10(-5) m. For each case, three subcases for g were assumed, namely, g>h, g<h, and g=h. The values of g and h were of the order of the osteons size. The velocity dispersion curves of guided waves were numerically obtained and compared with the Lamb modes. The results indicate that when g was not equal to h (i.e., g not equal h), microstructure affects mode dispersion by inducing both material and geometrical dispersion. In conclusion, gradient elasticity can provide supplementary information to better understand guided waves in bones.

Multivariate Prediction of Subcutaneous Glucose Concentration in Type 1 Diabetes Patients Based on Support Vector Regression

Data-driven techniques have recently drawn significant interest in the predictive modeling of subcutaneous (s.c.) glucose concentration in type 1 diabetes. In this study, the s.c. glucose prediction is treated as a multivariate regression problem, which is addressed using support vector regression (SVR). The proposed method is based on variables concerning: 1) the s.c. glucose profile; 2) the plasma insulin concentration; 3) the appearance of meal-derived glucose in the systemic circulation; and 4) the energy expenditure during physical activities. Six cases corresponding to different combinations of the aforementioned variables are used to investigate the influence of the input on the daily glucose prediction. The proposed method is evaluated using a dataset of 27 patients in free-living conditions. Tenfold cross validation is applied to each dataset individually to both optimize and test the SVR model. In the case, where all the input variables are considered, the average prediction errors are 5.21, 6.03, 7.14, and 7.62 mg/dl for 15-, 30-, 60-, and 120-min prediction horizons, respectively. The results clearly indicate that the availability of multivariable data and their effective combination can significantly increase the accuracy of both short-term and long-term predictions.

Light scattering by aggregated red blood cells

In low flow rates, red blood cells (RBCs) fasten together along their axis of symmetry and form a so-called rouleaux. The scattering of He-Ne laser light by a rouleau consisting of n (2 < or = n < or = 8) average-sized RBCs is investigated. The interaction problem is treated numerically by means of an advanced axisymmetric boundary element--fast Fourier transform methodology. The scattering problem of one RBC was solved first, and the results showed that the influence of the RBCs membrane on the scattering patterns is negligible. Thus the rouleau is modeled as an axisymmetric, homogeneous, low-contrast dielectric cylinder, on the surface of which appears, owing to aggregated RBCs, a periodic roughness along the direction of symmetry. The direction of the incident laser light is considered to be perpendicular to the scatterers axis of symmetry. The differential scattering cross sections in both perpendicular and parallel scattering planes and for all the scattering angles are calculated and presented in detail.

An iterative effective medium approximation (IEMA) for wave dispersion and attenuation predictions in particulate composites, suspensions and emulsions

In the present work we deal with the scattering dispersion and attenuation of elastic waves in different types of nonhomogeneous media. The iterative effective medium approximation based on a single scattering consideration, for the estimation of wave dispersion and attenuation, proposed in Tsinopoulos et al., [Adv. Compos. Lett. 9, 193-200 (2000)] is examined herein not only for solid components but for liquid suspensions as well. The iterations are conducted by means of the classical relation of Waterman and Truell, while the self-consistent condition proposed by Kim et al. [J. Acoust. Soc. Am. 97, 1380-1388 (1995)] is used for the convergence of the iterative procedure. The single scattering problem is solved using the Ying and Truell formulation, which with a minor modification can accommodate the solution of scattering on inclusions in liquid. Theoretical results for several different systems of particulates and suspensions are presented being in excellent agreement with experimental data taken from the literature.

Scattering theorems for complete dyadic fields

Abstract An incident plane dyadic field is scattered by a body, on the surface of which the boundary conditions correspond to vanishing displacements, to vanishing traction, or to elastic transmission. Both longitudinal and transverse waves with all possible polarizations are embodied in the complete incident dyadic wave. We exhibit the most general reciprocity and scattering theorems for this dyadic scattering problem and we show how to recover all related known theorems as special cases. The nine scalar relations, coming out of the component analysis of each dyadic theorem, can be used as a basis for constructing many more new results for acoustic, electromagnetic and elastic scattering problems.

Application of an effective medium theory for modeling ultrasound wave propagation in healing long bones.

Quantitative ultrasound has recently drawn significant interest in the monitoring of the bone healing process. Several research groups have studied ultrasound propagation in healing bones numerically, assuming callus to be a homogeneous and isotropic medium, thus neglecting the multiple scattering phenomena that occur due to the porous nature of callus. In this study, we model ultrasound wave propagation in healing long bones using an iterative effective medium approximation (IEMA), which has been shown to be significantly accurate for highly concentrated elastic mixtures. First, the effectiveness of IEMA in bone characterization is examined: (a) by comparing the theoretical phase velocities with experimental measurements in cancellous bone mimicking phantoms, and (b) by simulating wave propagation in complex healing bone geometries by using IEMA. The original material properties of cortical bone and callus were derived using serial scanning acoustic microscopy (SAM) images from previous animal studies. Guided wave analysis is performed for different healing stages and the results clearly indicate that IEMA predictions could provide supplementary information for bone assessment during the healing process. This methodology could potentially be applied in numerical studies dealing with wave propagation in composite media such as healing or osteoporotic bones in order to reduce the simulation time and simplify the study of complicated geometries with a significant porous nature.

On the scattering amplitudes for elastic waves

Reciprocity and scattering theorems for the normalized spherical scattering amplitude for elastic waves are obtained for the case of a rigid scatterer, a cavity and a penetrable scattering region. Depending on the polarization of the two incident waves reciprocity relations of the radial-radial, radial-angular, and angular-angular type are established. Radial and angular scattering theorems, expressing the corresponding scattering amplitudes via integrals of the amplitudes over all directions of observation, as well as their special forms for scatterers with inversion symmetry are also provided. As a consequence of the stated scattering theorems the scattering cross-section for either a longitudinal, or a transverse incident wave is expressed through the forward value of the radial, or the angular amplitude, correspondingly. All the known relative theorems for acoustic scattering are trivially recovered from their elastic counterparts.

A numerical study on the propagation of Rayleigh and guided waves in cortical bone according to Mindlin’s Form II gradient elastic theory

Cortical bone is a multiscale heterogeneous natural material characterized by microstructural effects. Thus guided waves propagating in cortical bone undergo dispersion due to both material microstructure and bone geometry. However, above 0.8 MHz, ultrasound propagates rather as a dispersive surface Rayleigh wave than a dispersive guided wave because at those frequencies, the corresponding wavelengths are smaller than the thickness of cortical bone. Classical elasticity, although it has been largely used for wave propagation modeling in bones, is not able to support dispersion in bulk and Rayleigh waves. This is possible with the use of Mindlins Form-II gradient elastic theory, which introduces in its equation of motion intrinsic parameters that correlate microstructure with the macrostructure. In this work, the boundary element method in conjunction with the reassigned smoothed pseudo Wigner-Ville transform are employed for the numerical determination of time-frequency diagrams corresponding to the dispersion curves of Rayleigh and guided waves propagating in a cortical bone. A composite material model for the determination of the internal length scale parameters imposed by Mindlins elastic theory is exploited. The obtained results demonstrate the dispersive nature of Rayleigh wave propagating along the complex structure of bone as well as how microstructure affects guided waves.