Band 21, Heft 5-6

Mathematical modeling of blood flows in the arteries is an important and challenging problem. This study compares several non-Newtonian blood models with the Newtonian model in simulating pulsatile blood flow through two three-dimensional models of an arterial stenosis and an aneurysm. Four non-Newtonian blood models, namely the Power Law, the Casson, the Carreau, and the Generalized Power Law, as well as the Newtonian model of blood viscosity, are used to investigate the flow effects induced by these different blood constitutive equations. The aim of this study is three-fold: firstly, to investigate the variation in wall shear stress in an artery with a stenosis or aneurysm at different flow rates and degrees of severity; secondly, to compare the various blood models and hence quantify the differences between the models and judge their significance; and lastly, to determine whether the use of the Newtonian blood model is appropriate over a wide range of shear rates.

Damped vibrations of elastic thin bodies, such as plates and circular cylindrical shells, embedded into a viscoelastic medium, the rheological features of which are described by fractional derivatives, are considered in the present article. Besides the forces of viscous friction, a thin body is subjected to the action of external forces dependent on the coordinates of the middle surface and time. The boundary conditions are proposed in such a way that the governing equations allow the Navier-type solution. The Laplace integral transform method and the method of expansion of all functions entering into the set of governing equations in terms of the eigenfunctions of the given problem are used as the methods of solution. It is shown that as a result of such a procedure, the systems of equations in the generalized coordinates could be reduced to infinite sets of uncoupled equations, each of which describes damped vibrations of a mechanical oscillator based on the fractional derivative Kelvin-Voigt model.

The determination of the interstitial sites and saddle points corresponding to the diffusion of an interstitial atom in ultrathin face-centered cubic (fcc) film is of particular interest. The outcome is strongly influenced not only by the orientation of the free surface but also by the location of the defect with respect to the free surface and film-rigid substrate interface. In this article, an atomic-scale simulation is conducted to analyze the effects of depth on the out-of-plane interstitial mechanism of diffusion. To ensure reasonable accuracy and numerical convergence, the atomic interaction up to the second-nearest neighbor is considered. The ab initio examination of the above-mentioned problem associated with thin films requires a large supercell and is computationally time consuming. However, for the sake of demonstration, the values of the barrier height energy pertinent to a diffusing self-interstitial atom in the bulk material are computed using both the first principles density functional theory (DFT) and the developed technique, indicating reasonable correspondence.

This study utilizes instrumented nanoindentation to compare the mechanical response of a transformation-induced plasticity (TRIP) steel to that of a quench and partition steel (QP). The nanoindenter was operated using continuous stiffness mode, and the microstructure under the indent revealed by chemical etching was examined. Examination of the microstructure in the indents by scanning electron microscopy allows a direct correlation with nanoindentation properties. It is found that the hardness measured at an indentation depth of 1.1 μm is, on average, significantly greater in the QP steel than in the TRIP steel. The continuous hardness measurement also allows the microstructure observed at the center of the indent to be correlated with the hardness values when indentation depths are <0.1 μm. This high-resolution hardness measurement allows for a direct comparison of mechanical response for the individual retained austenite phase particles in the TRIP steel with the strengthening microconstituent in the QP steel. With this methodology, the surprising result is that the TRIP retained austenite particles have a higher hardness than the QP hardening microconstituent. It is proposed that the resolution of the apparent disagreement between the hardness measurements obtained at 1.1 μm depth (QP has the higher hardness) and the 0.1-μm depth hardness measurements of the microconstituents containing retained austenite (TRIP has the higher hardness) lies in the volume fraction of the microconstituent as the QP has a two- to threefold higher volume fraction of hardening phase as compared to TRIP.

Temporal scaling in mechanical strength of materials is vital for long-term effects such as fatigue. The fatigue crack length α is related to the change in the stress intensity factor Δ K by the omnipresent Paris’s law, which works well for cyclic fatigue of specific frequency and amplitude. The paper considers time scaling in fatigue and through it incorporates the effects of temporal events such as unexpected or accidental loads, impact loads, and rare events such as earthquake loads. This is achieved by theoretically incorporating the effects of delta-function type loads into fatigue. Since the time-scale decomposition of such a load contains information at all scales, the theoretical framework is easily extended to include general types of loads.

Bending deformations are reviewed in the context of strain gradient linear elasticity, considering the complete set of strain gradient components. It is well understood that conventional bending deformations depend on the collective uniaxial extension of axial fibers resulting in the dependence on the curvature of the neutral geometry of various (linear or surface) structures. Nevertheless, the deformation of each fiber depends not only on the local curvature of the neutral geometry but also on the distance of the fiber from the neutral axis. Hence, the strain gradient tensor of the conventional bending strain should include not only components along the neutral axis but also those on the transverse direction. The problems of bending and buckling, along with geometrically non-linear and post-critical behavior, are reviewed in the context of strain gradient elasticity considering not only conventional bending strain but also the complete components of the strain gradient.

The modest aim of this short article is to provide some new results for a screw dislocation in a functionally graded material within the theory of gradient elasticity. These results, based on a displacement formulation and the Fourier transform technique, complete earlier findings obtained with the stress function method and extends them to the case of the second strain gradient elasticity. Rigorous and easy-to-use analytical expressions for the displacements, strains, and stresses are obtained, which are free from singularities at the dislocation line.