A Review on Mechanics and Mechanical Properties of 2D Materials - Graphene and Beyond

Since the first successful synthesis of graphene just over a decade ago, a variety of two-dimensional (2D) materials (e.g., transition metal-dichalcogenides, hexagonal boron-nitride, etc.) have been discovered. Among the many unique and attractive properties of 2D materials, mechanical properties play important roles in manufacturing, integration and performance for their potential applications. Mechanics is indispensable in the study of mechanical properties, both experimentally and theoretically. The coupling between the mechanical and other physical properties (thermal, electronic, optical) is also of great interest in exploring novel applications, where mechanics has to be combined with condensed matter physics to establish a scalable theoretical framework. Moreover, mechanical interactions between 2D materials and various substrate materials are essential for integrated device applications of 2D materials, for which the mechanics of interfaces (adhesion and friction) has to be developed for the 2D materials. Here we review recent theoretical and experimental works related to mechanics and mechanical properties of 2D materials. While graphene is the most studied 2D material to date, we expect continual growth of interest in the mechanics of other 2D materials beyond graphene

Toward Growth-Accommodating Polymeric Heart Valves with Graphene-Network Reinforcement

Graphene is a 2D material well known for its high intrinsic strength of 100 GPa and Young’s modulus of 1 TPa. Because of its 2D nature, the most promising avenues to utilize graphene as a mechanical material include incorporating it as reinforcement in a nanocomposite and creating free-standing foams and aerogels. However, the current techniques are not well-controlled – the reinforcing graphene particles are often discontinuous and randomly dispersed – making it difficult to accurately model and predict the resulting material properties. Here we aim to develop a framework for a new class of nanocomposites reinforced not by discrete nanoparticles, but by a continuous 3D graphene network. These 3D graphene networks were formed by chemical vapor deposition of graphene on periodic metallic microlattices, thereby providing mechanical reinforcement for the lattices. To assist in the lattice design, analytical models were derived for the mechanical properties of core/shell composite lattices and experimentally validated through compression testing of polymer lattices coated with electroless Ni-P. The models and experiments showed good agreement at lower shell thicknesses, while there was divergence at higher thicknesses, likely due to fabrication imperfections. The analytical models were also applied to hollow metallic lattices coated with graphene and compared to experimental data. The results showed that the models are plausible and suggest that graphene has a significant strengthening effect on the microlattices. These studies represent a paradigm shift in the design and fabrication of nanocomposites as one may now precisely prescribe the placement of the reinforcing nanomaterials. On a broader scale, this work also lays the framework for using a 2D material to span 3D space, enabling further exploration of 2D material properties and applications. One potential application area for a graphene-reinforced polymer composite is in prosthetic heart valves. The tissue of a human heart valve leaflet is heavily reinforced with networks of collagen and elastin fibers. One could similarly incorporate a graphene network as reinforcement within the polymeric leaflets of a prosthetic valve. One promising application of polymeric valves is in growth-accommodating implants for pediatric patients. Here we aim to develop a polymeric valved conduit that can be expanded by transcatheter balloon dilation to match a child’s growth. We designed the valve, characterized and selected materials, fabricated the devices and performed benchtop in vitro testing. The first generation of an expandable biostable valved conduit displayed excellent hydrodynamic performance before and after permanent balloon dilation from 22 to 25 mm. The second generation has shown the potential for a greater dilation from 12 to 24 mm. These results demonstrate concept feasibility and motivate further development of a polymeric balloon-expandable device to replace valves in children and avoid reoperations

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal