Soon after the discovery of carbon nanotubes, it was realized that the theoretically predicted mechanical properties of these interesting structures–including high strength, high stiffness, low density and structural perfection–could make them ideal for a wealth of technological applications. The experimental verification, and in some cases refutation, of these predictions, along with a number of computer simulation methods applied to their modeling, has led over the past decade to an improved but by no means complete understanding of the mechanics of carbon nanotubes. We review the theoretical predictions and discuss the experimental techniques that are most often used for the challenging tasks of visualizing and manipulating these tiny structures. We also outline the computational approaches that have been taken, including ab initio quantum mechanical simulations, classical molecular dynamics, and continuum models. The development of multiscale and multiphysics models and simulation tools naturally arises as a result of the link between basic scientific research and engineering application; while this issue is still under intensive study, we present here some of the approaches to this topic. Our concentration throughout is on the exploration of mechanical properties such as Young’s modulus, bending stiffness, buckling criteria, and tensile and compressive strengths. Finally, we discuss several examples of exciting applications that take advantage of these properties, including nanoropes, filled nanotubes, nanoelectromechanical systems, nanosensors, and nanotube-reinforced polymers. This review article cites 349 references. @DOI: 10.1115/1.1490129#

/pdf/mechanics-of-carbon-nanotubes-4eqt38eq4w.pdf

Mechanics of carbon nanotubes

The relation between atomistic chemical structure, molecular archi- tecture, molecular weight, and material properties is of basic concern in modern soft material science and includes standard properties of bulk materials and surface and interface aspects, as well as the relation between structure and function in nanoscopic objects and molecular assemblies of both synthetic and biological origin. This all implies a thorough understanding on many length and correspondingly time scales, ranging from (sub)atomistic to macroscopic. Presently, com- puter simulations play an increasingly important, if not central, role. Some problems do not require specific atomistic details, whereas others require them only locally. However, in many cases this strict separation is not sufficient for a comprehensive understanding of systems, and flexible simulation schemes are required that link the different levels of resolution. We here give a general view of the problem regarding soft matter and discuss some specific examples of linked simulation techniques at different resolution levels. We then discuss a recently developed flexible simulation scheme, the AdResS method, which allows one to adaptively change the resolution in certain regions of space on demand.

https://www.researchgate.net/profile/Luigi_Delle_Site/publication/5785059_Multiscale_Simulation_of_Soft_Matter_From_Scale_Bridging_to_Adaptive_Resolution/links/0fcfd5134e36be4806000000.pdf

Multiscale simulation of soft matter: from scale bridging to adaptive resolution.

We present a new adaptive resolution technique for efficient particle-based multiscale molecular-dynamics simulations. The presented approach is tailor-made for molecular systems where atomistic resolution is required only in spatially localized domains whereas a lower mesoscopic level of detail is sufficient for the rest of the system. Our method allows an on-the-fly interchange between a given molecule’s atomic and coarse-grained levels of description, enabling us to reach large length and time scales while spatially retaining atomistic details of the system. The new approach is tested on a model system of a liquid of tetrahedral molecules. The simulation box is divided into two regions: one containing only atomistically resolved tetrahedral molecules, and the other containing only one-particle coarse-grained spherical molecules. The molecules can freely move between the two regions while changing their level of resolution accordingly. The hybrid and the atomistically resolved systems have the same stat...

Adaptive resolution molecular-dynamics simulation: changing the degrees of freedom on the fly.

couple different length and time scales in serial fashion. By this we mean that one set of calculations at a fundamental level, and of high computational complexity, is used to evaluate constants for use in a more approximate or phenomenological computational methodology at longer length or time scales. In pioneering work of this sort in the 1980s, Clementi and coworkers1 used high-quality quantum-mechanical methods to evaluate the interaction of several water molecules. From this database they parameterized an empirical potential for use in molecular-dynamics atomistic simulations. Such a simulation was then used to evaluate the viscosity of water from the atomic autocorrelation function. Finally, the computed viscosity was used in a computational-fluid-dynamics calculation to predict tidal circulation in Buzzards Bay, MA. This tour de force of computational physics is a powerful example of the sequential coupling of length and time scales: one series of calculations is used as input to the next up the length and time hierarchy. There are many other examples in the literature. But what underlies all these schemes is that an appropriate computational methodology is used for a given scale or task, whether it be the accuracy of quantum mechanics at the shortest scales or fluid dynamics at the longest scales. In contrast, there has been comparatively little effort devoted to the parallel coupling of different computational schemes for a simultaneous attack on a given problem; in our case, our interest dictates specific attention toward issues in materials or solid-state physics. We will focus specifically on the coupling of length scales for the three mechanics describing materials phenomena: quantum mechanics, atomistic mechanics, and continuum mechanics.

Spanning the length scales in dynamic simulation

The atomic-scale finite element method

A novel multi-scale seamless model of brittle-crack propagation is proposed and applied to the simulation of fracture growth in a two-dimensional Ag plate with macroscopic dimensions. The model represents the crack propagation at the macroscopic scale as the drift-diffusion motion of the crack tip alone. The diffusive motion is associated with the crack-tip coordinates in the position space, and reflects the oscillations observed in the crack velocity following its critical value. The model couples the crack dynamics at the macroscales and nanoscales via an intermediate mesoscale continuum. The finite-element method is employed to make the transition from the macroscale to the nanoscale by computing the continuum-based displacements of the atoms at the boundary of an atomic lattice embedded within the plate and surrounding the tip. Molecular dynamics (MD) simulation then drives the crack tip forward, producing the tip critical velocity and its diffusion constant. These are then used in the Ito stochastic calculus to make the reverse transition from the nanoscale back to the macroscale. The MD-level modelling is based on the use of a many-body potential. The model successfully reproduces the crack-velocity oscillations, roughening transitions of the crack surfaces, as well as the macroscopic crack trajectory. The implications for a 3-D modelling are discussed.

A multi-scale atomistic-continuum modelling of crack propagation in a two-dimensional macroscopic plate

A novel multiscale model of brittle crack propagation in an Ag plate with macroscopic dimensions has been developed. The model represents crack propagation as stochastic drift-diffusion motion of the crack tip atom through the material, and couples the dynamics across three different length scales. It integrates the nanomechanics of bond rupture at the crack tip with the displacement and stress field equations of continuum based fracture theories. The finite element method is employed to obtain the continuum based displacement and stress fields over the macroscopic plate, and these are then used to drive the crack tip forward at the atomic level using the molecular dynamics simulation method based on many-body interatomic potentials. The linkage from the nanoscopic scale back to the macroscopic scale is established via the Ito stochastic calculus, the stochastic differential equation of which advances the tip to a new position on the macroscopic scale using the crack velocity and diffusion constan...

Multiscale numerical modelling of cracK propagation in tvvo-dimensional metal plate

A new multi-scale model of brittle fracture growth in an Ag plate with macroscopic dimensions is proposed in which the crack propagation is identified with the stochastic drift-diffusion motion of the crack-tip atom through the material. The model couples molecular dynamics simulations, based on many-body interatomic potentials, with the continuum-based theories of fracture mechanics. The Ito stochastic differential equation is used to advance the tip position on a macroscopic scale before each nano-scale simulation is performed. Well-known crack characteristics, such as the roughening transitions of the crack surfaces, as well as the macroscopic crack trajectories are obtained.

A multi-scale numerical modelling of crack propagation in a 2D metallic plate

This paper aims to explore the construction of an individualized pulmonary artery stenosis model based on computed tomography (CT) images. The stenosis model is simulated using a porous medium, and the numerical simulation is carried out by computational fluid dynamics (CFD) method to discuss non-Newtonian effects on hemodynamics. The hemodynamic parameters and quantitative pulmonary pressure ratio (QPPR) of the right pulmonary artery stenosis are obtained. The change curves of hemodynamic parameters show that the effects of non-Newtonian fluid are more significant than those of Newtonian fluid. Under the non-Newtonian condition, pressure and velocity drop more and faster when blood flow enters into the stenosis region. There is a high wall shear stress in the stenosis downstream. The margin of error between the QPPR value of the non-Newtonian fluid simulation and the clinical measurement value is not more than 10%. This work provides the evidence that the simulation of non-Newtonian fluid is closer to the reality when a porous medium model is used in a stenosis model. This contributes to assessing the severity of pulmonary stenosis behavior and is essential to guide disease treatment.

/pdf/non-newtonian-effects-of-blood-flow-on-hemodynamics-in-1gwx6jc2.pdf

Non-Newtonian Effects of Blood Flow on Hemodynamics in Pulmonary Stenosis: Numerical Simulation

BACKGROUND
The incidence rate of pulmonary artery stenosis is increasing year by year and its numerical simulation has become a key project of biomedical engineering.


OBJECTIVE
The purpose of this work is to study the changes of hemodynamic parameters in patient-specific pulmonary artery stenosis.


METHODS
A pulmonary artery stenosis model is established based on patient-specific computed tomography (CT) images. According to the actual anatomy of patient-specific pulmonary artery stenosis, the stenosis area is simulated using a porous medium to study its hemodynamic changes. The computational fluid dynamics (CFD) method is used to simulate the hemodynamic changes of pulmonary artery stenosis, and to explore the mechanical characteristics between blood flow and vessel wall.


RESULTS
The results suggest that the blood pressure of arterial branches increases and the pressure drop at both ends of the stenosis is higher. There is a high flow rate and wall shear stress at the stenosis.


CONCLUSION
This study shows that the hemodynamic model of pulmonary artery stenosis can be accurately reconstructed by achieving numerical simulation of the local stenosis through CT images, and this work has important implications for improving the confidence of clinical diagnosis and treatment of pulmonary artery diseases.

L. Hua

Papers

A multi-scale atomistic-continuum modelling of crack propagation in a two-dimensional macroscopic plate

Multiscale numerical modelling of cracK propagation in tvvo-dimensional metal plate

A multi-scale numerical modelling of crack propagation in a 2D metallic plate

Non-Newtonian Effects of Blood Flow on Hemodynamics in Pulmonary Stenosis: Numerical Simulation

Numerical simulation of hemodynamics in patient-specific pulmonary artery stenosis.