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The potential of a finite-element technique based on an egalitarian meshing of the space–time domain D of physical problems described by parabolic or hyperbolic differential equations is explored. A least-squares minimization technique is applied in the meshed domain D to obtain stiffness-like matrices associated with various linear differential operators. Applications discussed include problems of boundary growth, and diffusive coalescence, in which D cannot be regarded as the Cartesian product of two independent domains in space and time. [ABSTRACT FROM AUTHOR]

Contact resonance atomic force microscopy (CR-AFM) was used to spatially map variations in the out-of-plane elastic modulus of graphene covered surfaces of a silicon wafer having a native oxide. A modulus of 0.973 ± 0.001 TPa was measured for one layer of graphene covering the silicon substrate, consistent with many experimental and theoretical studies. A monotonic decrease in the measured contact resonance frequency with increasing layers of graphene covering the silicon substrate was observed, resulting in a decrease in the measured modulus by 4.95% with four layers of graphene covering the substrate. The interplay between the hydrophobic graphene layers covering the hydrophilic silicon substrate, the interlayer spacing of graphene, and the range of adhesion from the substrate are proposed to influence the stiffness of the graphene–graphene interaction, which was probed with the sub-Ångström displacements with CR-AFM measurements. [ABSTRACT FROM AUTHOR]

Beside their biochemical properties, the exceptional mechanical characteristics of carbon nanotubes (CNTs) suggested growing a reinforced composite material very similar to natural bone in structure and chemical composition, but significantly stronger and stiffer. This is where biomechanical considerations portray themselves to justify the need for further investigations, in order to verify the applicability of CNTs as scaffolds that may ease bone regeneration and simultaneously raise its mechanical strength and durability. This research, using several modeling approaches, attempts to look at some of the mechanical changes likely to take place in the promised artificial tissue, while considering the relationships between mechanical and living functions of bone, particularly the remodeling process. Results suggest that notwithstanding the significant improvements induced to the mechanical behavior of the artificial tissue, applications of such stiff inclusions as CNTs in reinforcing the material of bone may detrimentally change the thresholds of mechanical stimuli that are essential for the initiation and resumption of the bone remodeling process. [ABSTRACT FROM AUTHOR]

Overload has been suggested as a contributing factor for bone loss, for instance at the bone implant interface. The objective of this study is to investigate spongy bone resorption under overload using a semi-mechanistic bone remodeling theory. Since overload can cause the accumulation of microdamage in bone, in this study, it is assumed that overload will increase the osteoclastic activity, and also will reduce the osteocyte influence distance. First, a previously proposed semi-mechanistic bone remodeling theory was extended by defining a new form for the resorption probability function, which is based on experimental evidence. Then, in order to investigate the validity of our hypothesis, a three-dimensional finite element model of spongy bone was developed. The simulation results show that, first, trabeculae adapt with the mechanical stimuli placed on them. Secondly, a sharp reduction in spongy bone density will be resulted, in agreement with experimental evidence, when bone is under overload. [ABSTRACT FROM AUTHOR]

Dynamic atomic force microscopy (AFM) was employed to spatially map the elastic modulus of highly oriented pyrolytic graphite (HOPG), specifically by using force modulation microscopy (FMM) and contact resonance (CR) AFM. In both of these techniques, a variation in the amplitude signal was observed when scanning over an uncovered step edge of HOPG. In comparison, no variation in the amplitude signal was observed when scanning over a covered step on the same surface. These observations qualitatively indicate that there is a variation in the elastic modulus over uncovered steps and no variation over covered ones. The quantitative results of the elastic modulus required the use of FMM, while the CR mode better highlighted areas of reduced elastic modulus (although it was difficult to convert the data into a quantifiable modulus). In the FMM measurements, single atomic steps of graphene with uncovered step edges showed a decrease in the elastic modulus of approximately 0.5%, which is compared with no change in the elastic modulus for covered steps. The analysis of the experimental data taken under varying normal loads and with several different tips showed that the elastic modulus determination was unaffected by these parameters.