**2.8 Bending analysis of embedded nano plates using FEM**

Eringen's nonlocal elasticity theory is capable to capture small length scale effect. Hence it is widely used to explore the mechanical behavior of nanostructures [10]. Instead of using differential form, the integral form should be used to avoid inconsistency in results. Arbitrary kernel functions are used for general form. The first order [10] shear deformation theory is used to model the nanoplates. The study evaluates the first order shear deformable embedded nanoplates for bending using Erignen's nonlocal theory. Using FEM approach the maximum deflection of the structure was evaluated. The results pronounced that the clamped or simply supported boundary conditions provided same trend for the effects of non-local parameter on the bending analysis of nano plate for Erignen's integral and differential formulation. Also the results proved that the elastic foundation increased the stiffness of the structure and decreased the influence of nonlocal parameter.

## **2.9 Stresses at bone: particle reinforced nano composite interface**

The biomaterial should satisfy its bio functionality and biocompatibility. The tissue – implant interface plays a huge role in both the parameters. Nanobioceramics is a newer technology that had widened [11] range of biomedical and dental applications including increased bioactivity for tissue regeneration and engineering, drug and gene delivery, treatment of viral infections and implantable surface modified medical devices for [11] better hard and soft tissue attachments. FEA had been accepted for simulations in biomechanics for analyzing stresses and strains in dental implants and surrounding bone structures. The tissue engineering needs combining 3D scaffolds with living cells to deliver the much needed cells to damage sites in the human body. This scaffold should be capable of making cells to attach and multiply. Hence the design of scaffold is a challenging task which could be narrated by the finite element analysis. Also the nanotechnology had revolutionized nanobiomaterials, tissue engineering nano scaffold, nano – drug delivery and dental nanocomposites [11].

## **2.10 Elastic plastic analysis of ultrafine grained Si2N2O – Si3N4 composites**

The development of micro/nanotechnology [12] had led to characterization of the mechanical properties at micro- and nano- scales. The nano indentation test has a diamond indenter to produce indentation load and the penetration depth from which load – penetration curve (P-h) is obtained. The P-h curve can be used to define mechanical properties including hardness, elastic modulus and toughness [12]. Only few studies had been reported on elastic–plastic property of brittle bulk ceramics. There are two methods to derive material properties from loading and unloading indentation curves. One of the curves involves the use of unloading curves and classical elastic solution of infinite half space [12]. This method is suitable for calculating the hardness and elastic modulus of materials. Another methodology involves producing loading and unloading response curves for various parameters through finite element modeling. Stress strain relations can be produced by using the nanoindentation experiment. The ultra-fine – grained Si2 N2O – Si3N4 had been produced by hot press sintering of amorphous nano – sized silicon nitride powders at 1600, 1650 and 1700 Deg Celsius with nanosized additives. After evaluating by nano identation through finite element formulation, the elastic modulus and P-h curve are obtained. A newer theoretical methodology for evaluating stress strain relation of brittle ceramic materials had been identified. Numerous coefficients in theoretical calculation formula had been found using calculation and simulation results.
