SUMMARYThis paper presents a new numerical integration technique on arbitrary polygonal domains. The polygonal domain is mapped conformally to the unit disk using Schwarz-Christoffel mapping and a midpoint quadrature rule defined on this unit disk is used. This method eliminates the need for a two-level isoparametric mapping usually required. Moreover, the positivity of the Jacobian is guaranteed. Numerical results presented for a few benchmark problems in the context of polygonal finite elements show that the proposed method yields accurate results.

To date, the SFEM has only been investigated for bilinear and Wachspress approximations and is limited to linear reproducing conditions. The goal of this paper is to extend the strain smoothing to higher order elements and to investigate numerically in which condition strain smoothing is beneficial to accuracy and convergence of enriched finite element approximations. We focus on three widely used enrichment schemes, namely: (a) weak discontinuities; (b) strong discontinuities; (c) near-tip linear elastic fracture mechanics functions. The main conclusion is that strain smoothing in enriched approximation is only beneficial when the enrichment functions are polynomial (cases (a) and (b)), but that non-polynomial enrichment of type (c) lead to inferior methods compared to the standard enriched FEM (e.g. XFEM).

Developing a biodegradable scaffold remains a major challenge in bone tissue engineering. This study was aimed at developing novel alginate-chitosan-collagen (SA-CS-Col)-based composite scaffolds consisting of graphene oxide (GO) to enrich porous structures, elicited by the freeze-drying technique. To characterize porosity, water absorption, and compressive modulus, GO scaffolds (SA-CS-Col-GO) were prepared with and without Ca-mediated crosslinking (chemical crosslinking) and analyzed using Raman, Fourier transform infrared (FTIR), X-ray diffraction (XRD), and scanning electron microscopy techniques. The incorporation of GO into the SA-CS-Col matrix increased both crosslinking density as indicated by the reduction of crystalline peaks in the XRD patterns and polyelectrolyte ion complex as confirmed by FTIR. GO scaffolds showed increased mechanical properties which were further increased for chemically crosslinked scaffolds. All scaffolds exhibited interconnected pores of 10-250 μm range. By increasing the crosslinking density with Ca, a decrease in the porosity/swelling ratio was observed. Moreover, the SA-CS-Col-GO scaffold with or without chemical crosslinking was more stable as compared to SA-CS or SA-CS-Col scaffolds when placed in aqueous solution. To perform in vitro biochemical studies, mouse osteoblast cells were grown on various scaffolds and evaluated for cell proliferation by using MTT assay and mineralization and differentiation by alizarin red S staining. These measurements showed a significant increase for cells attached to the SA-CS-Col-GO scaffold compared to SA-CS or SA-CS-Col composites. However, chemical crosslinking of SA-CS-Col-GO showed no effect on the osteogenic ability of osteoblasts. These studies indicate the potential use of GO to prepare free SA-CS-Col scaffolds with preserved porous structure with elongated Col fibrils and that these composites, which are biocompatible and stable in a biological medium, could be used for application in engineering bone tissues.

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Partition of unity methods, such as the extended finite element method (XFEM) allow discontinuities to be simulated independently of the mesh [1]. This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome re-meshing, as the discontinuity evolves. However, to compute the stiffness matrix of the elements intersected by the discontinuity, a subdivision of the elements into quadrature subcells aligned with the discontinuity is commonly adopted. In this paper, we use a simple integration technique, proposed for polygonal domains [2] to suppress the need for element subdivision. Numerical results presented for a few benchmark problems in the context of linear elastic fracture mechanics and a multi-material problem, show that the proposed method yields accurate results. Owing to its simplicity, the proposed integration technique can be easily integrated in any existing code.

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An overview (with 376 refs.) is given here on the current state of methods for electrochemical sensing of glucose based on the use of advanced nanomaterials. An introduction into the field covers aspects of enzyme based sensing versus nonenzymatic sensing using nanomaterials. The next chapter cover the most commonly used nanomaterials for use in such sensors, with sections on uses of noble metals, transition metals, metal oxides, metal hydroxides, and metal sulfides, on bimetallic nanoparticles and alloys, and on other composites. A further section treats electrodes based on the use of carbon nanomaterials (with subsections on carbon nanotubes, on graphene, graphene oxide and carbon dots, and on other carbonaceous nanomaterials. The mechanisms for electro-catalysis are also discussed, and several Tables are given where the performance of sensors is being compared. Finally, the review addresses merits and limitations (such as the frequent need for working in strongly etching alkaline solutions and the need for diluting samples because sensors often have analytical ranges that are far below the glucose levels found in blood). We also address market/technology gaps in comparison to commercially available enzymatic sensors. Graphical Abstract Schematic representation of electrochemical nonenzymatic glucose sensing on the nanomaterials modified electrodes. At an applied potential, the nanomaterial-modified electrodes exhibit excellent electrocatalytic activity for direct oxidation of glucose oxidation.