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

Entropic Elasticity of Polymers and Their Networks

The elastic energy for many biopolymer systems is comparable to the thermal energy at room temperature. Therefore, biopolymers and their networks are constantly under thermal fluctuations. From the point of view of thermodynamics, this suggests that entropy plays a crucial role in determining the mechanical behaviors of these filamentous biopolymers. One of the main goals of this thesis is to understand how thermal fluctuations affect the mechanical properties and behaviors of filamentous networks, and also how stress affects the thermal fluctuations. Filaments and filamentous networks are viewed as mechanical structures, whose static equilibrium states under the action of loads or kinematic constraints are determined in the first step of the investigation. Typically, a system is discretized and represented by a finite set of kinematic variables that characterizes the configuration space. In the next step, we apply statistical mechanics to study the thermo-mechanical properties of the system. We approximate the local minimum energy well to quadratic order. Such a quadratic approximation for a discrete system gives rise to a stiffness matrix that characterizes the flexibility of the system around the ground state. Using the multidimensional Gaussian integral technique, the partition function is efficiently evaluated, provided that the energy well around the ground state is steep. In this case, the dominant contribution to the partition function is from the states that are close to the equilibrium state, whose energies are well approximated by the quadratic energy expression. All thermodynamic properties of the system can be further evaluated from the partition function. Fluctuation of the system, in particular, scales linearly with the temperature and inversely with the stiffness matrix. Therefore, the stiffness matrix governs the statistical mechanical behavior of the system near its ground state. We also show that a system with constraints on its kinematic variables can be converted into an effective non-constrained system. Using the above theoretical framework, we study the thermo-mechanical properties of filaments and filamentous networks under different loadings and confinement conditions. The filaments need not be homogeneous in the mechanical properties, and they can be subjected to non-uniform distributed loads or non-uniform confinements. Under compression, a filament can buckle. Buckling in a filament network can reduce the stiffness of the structure, which leads to significant thermal fluctuations around the buckling point. Properties of a triangular network under pure expansion, simple shear and uniaxial tension are also investigated in this thesis. As further applications, we discuss the protein forced unfolding problem. We show that different unfolding behaviors of a protein chain can be understood using a system of three equations. We also discuss the internal fluctuations of DNA under confinement and show a length-dependent transition between the de Gennes and Odijk regimes. We also show that entropy plays a role in driving the motion of a piece of DNA along a non-uniform channel. We derive the entropic force on the DNA in this thesis and discuss the coupled migration and deformation of the polymer under non-uniform confinement

Coupled approach to modelling damage in bonded composite structures

A fully coupled global-local approach for structural analysis has been developed. It is motivated by the need to use a range of scales and modelling techniques when designing a structure in composite materials. These range from the microscale at which the interfaces between fibres and matrix, or buckling of fibres themselves may play a role in the material behaviour, through intermediate scales where delamination and debonding may have an influence up to the macroscale where entire structures may be modelled with service loads directly applied. The method is based on passing boundary conditions from larger to smaller length scale models while passing information about damage and stiffness degradation up through the scales. By using nested levels of submodel, a greater range of length scales may be included in a single set of coupled analyses. Here an explanation of the methods of coupling two scales of solid models as well as coarse shell models to relatively refined solid models is presented. Each of these methods is validated against equivalent models using established modelling techniques, and are shown to produce results comparable to a complete model at the refined scale and preferable to other global-local approaches. Experimental tests have also been carried out on a stiffened panel with two stiffener runouts undergoing debonding. Not only did the coupling method model these tests accurately, but it was also shown to be more appropriate than simple submodelling in this case. A further demonstration of the techniques is included. The largest scale consisting of a shell element mesh is coupled with an intermediate scale with a continuum shell mesh, which in turn is coupled to a refined scale solid model. This demonstration shows how the methods developed here could be used to unify various analyses in the composites design process which until now have remained separate.Open Acces

Application of Local Approaches Based on NSIFs Calculated with the PSM on a Steel Tube-Tube Joint Under Combined Loading

The aim of this thesis is to verify the effectiveness of the Peak Stress Method (PSM) on a welded steel tube-tube joint under combined loading. The experimental data, provided by Vormwald in terms of applied loads and cycles to failure, have been evaluated in terms of equivalent peak stress and compared with PSM design scatter bands

Feasible Form Parameter Design of Complex Ship Hull Form Geometry

This thesis introduces a new methodology for robust form parameter design of complex hull form geometry via constraint programming, automatic differentiation, interval arithmetic, and truncated hierarchical B- splines. To date, there has been no clearly stated methodology for assuring consistency of general (equality and inequality) constraints across an entire geometric form parameter ship hull design space. In contrast, the method to be given here can be used to produce guaranteed narrowing of the design space, such that infeasible portions are eliminated. Furthermore, we can guarantee that any set of form parameters generated by our method will be self consistent. It is for this reason that we use the title feasible form parameter design. In form parameter design, a design space is represented by a tuple of design parameters which are extended in each design space dimension. In this representation, a single feasible design is a consistent set of real valued parameters, one for every component of the design space tuple. Using the methodology to be given here, we pick out designs which consist of consistent parameters, narrowed to any desired precision up to that of the machine, even for equality constraints. Furthermore, the method is developed to enable the generation of complex hull forms using an extension of the basic rules idea to allow for automated generation of rules networks, plus the use of the truncated hierarchical B-splines, a wavelet-adaptive extension of standard B-splines and hierarchical B-splines. The adaptive resolution methods are employed in order to allow an automated program the freedom to generate complex B-spline representations of the geometry in a robust manner across multiple levels of detail. Thus two complementary objectives are pursued: ensuring feasible starting sets of form parameters, and enabling the generation of complex hull form geometry

Applications of Finite Element Modeling for Mechanical and Mechatronic Systems

Modern engineering practice requires advanced numerical modeling because, among other things, it reduces the costs associated with prototyping or predicting the occurrence of potentially dangerous situations during operation in certain defined conditions. Thus far, different methods have been used to implement the real structure into the numerical version. The most popular uses have been variations of the finite element method (FEM). The aim of this Special Issue has been to familiarize the reader with the latest applications of the FEM for the modeling and analysis of diverse mechanical problems. Authors are encouraged to provide a concise description of the specific application or a potential application of the Special Issue

Radio observations of active galactic nuclei with mm-VLBI

Over the past few decades, our knowledge of jets produced by active galactic nuclei (AGN) has greatly progressed thanks to the development of very-long-baseline interferometry (VLBI). Nevertheless, the crucial mechanisms involved in the formation of the plasma flow, as well as those driving its exceptional radiative output up to TeV energies, remain to be clarified. Most likely, these physical processes take place at short separations from the supermassive black hole, on scales which are inaccessible to VLBI observations at centimeter wavelengths. Due to their high synchrotron opacity, the dense and highly magnetized regions in the vicinity of the central engine can only be penetrated when observing at shorter wavelengths, in the millimeter and sub-millimeter regimes. While this was recognized already in the early days of VLBI, it was not until the very recent years that sensitive VLBI imaging at high frequencies has become possible. Ongoing technical development and wide band observing now provide adequate imaging fidelity to carry out more detailed analyses. In this article we overview some open questions concerning the physics of AGN jets, and we discuss the impact of mm-VLBI studies. Among the rich set of results produced so far in this frequency regime, we particularly focus on studies performed at 43 GHz (7 mm) and at 86 GHz (3 mm). Some of the first findings at 230 GHz (1 mm) obtained with the Event Horizon Telescope are also presented.Comment: Published in The Astronomy & Astrophysics Review. Open access: https://link.springer.com/article/10.1007/s00159-017-0105-

Mechanics of Materials: Mechanics of Interfaces and Evolving Microstructure

Emphasis in modern day efforts in mechanics of materials is increasingly directed towards integration with computational materials science, which itself rests on solid physical and mathematical foundations in thermodynamics and kinetics of processes. Practical applications demand attention to length and time scales which are sufficiently large to preclude direct application of quantum mechanics approaches; accordingly, there are numerous pathways to mathematical modelling of the complexity of material structure during processing and in service. The conventional mathematical machinery of energy minimization provides guidance but has limited direct applicability to material systems evolving away from equilibrium. Material response depends on driving forces, whether arising from mechanical, electromagnetic, or thermal fields. When microstructures evolve, as during plastic deformation, progressive damage and fracture, corrosion, stress-assisted diffusion, migration or chemical/thermal aging, the associated classical mathematical frameworks are often ad hoc and heuristic. Advancing new and improved methods is a major focus of 21st century mechanics of materials of interfaces and evolving microstructure

Life prediction of materials exposed to monotonic and cyclic loading: A new technology survey

Reviewed and evaluated technical abstracts for about 100 significant documents are reported relating primarily to life prediction for structural materials exposed to monotonic and cyclic loading, particularly in elevated temperature environments. The abstracts in the report are mostly for publications in the period April 1962 through April 1974. The purpose of this report is to provide, in quick reference form, a dependable source for current informatio