Sukky Jun

Overview and applications of the reproducing Kernel Particle methods

SummaryMultiple-scale Kernel Particle methods are proposed as an alternative and/or enhancement to commonly used numerical methods such as finite element methods. The elimination of a mesh, combined with the properties of window functions, makes a particle method suitable for problems with large deformations, high gradients, and high modal density. The Reproducing Kernel Particle Method (RKPM) utilizes the fundamental notions of the convolution theorem, multiresolution analysis and window functions. The construction of a correction function to scaling functions, wavelets and Smooth Particle Hydrodynamics (SPH) is proposed. Completeness conditions, reproducing conditions and interpolant estimates are also derived. The current application areas of RKPM include structural acoustics, elastic-plastic deformation, computational fluid dynamics and hyperelasticity. The effectiveness of RKPM is extended through a new particle integration method. The Kronecker delta properties of finite element shape functions are incorporated into RKPM to develop a Cm kernel particle finite element method. Multiresolution and hp-like adaptivity are illustrated via examples.

MULTIRESOLUTION REPRODUCING KERNEL PARTICLE METHOD FOR COMPUTATIONAL FLUID DYNAMICS

Multiresolution analysis based on the reproducing kernel particle method (RKPM) is developed for computational fluid dynamics. An algorithm incorporating multiple-scale adaptive refinement is introduced. The concept of using a wavelet solution as an error indicator is also presented. A few representative numerical examples are solved to illustrate the performance of this new meshless method.

Large-scale molecular dynamics simulations of Al(111) nanoscratching

Molecular dynamics simulations of nanoscratching are performed with emphasis on the correlation between the scratching conditions and the defect mechanism in the substrate. More than six million atoms are described by the embedded atom method (EAM) potential. The scratching process is simulated by high-speed ploughing on the Al(111) surface with an atomic force microscope (AFM) tip that is geometrically modelled to be of a smoothed conical shape. A repulsive model potential is employed to represent the interaction between the AFM tip and the Al atoms. Through the visualization technique of atomic coordination number, dislocations and vacancies are identified as the two major defect types prevailing under nanoscratching. Their structures and movements are investigated for understanding the mechanisms of defect generation and evolution under various scratching conditions. The glide patterns of Shockley partial dislocation loops are obviously dependent upon the scratching directions in conjunction with the slip system of face-centred cubic (fcc) single crystals. It is shown that the shape of the AFM tip directly influences the facet formation on the scratched groove. The penetration depth into the substrate during scratching is further verified to affect both surface pile-up and residual defect generations that are important in assessing the change of material properties after scratching.

Moving least-square method for the band-structure calculation of 2D photonic crystals

The moving least-square (MLS) basis is implemented for the real-space band-structure calculation of 2D photonic crystals. A value-periodic MLS shape function is thus proposed in order to represent the periodicity of crystal lattice. Through numerical examples, this MLS method is proved to be a promising scheme for predicting band gaps of photonic crystals.

Adatom-assisted structural transformations of fullerenes

Microscopic mechanism of autocatalytic structural transformations of fullerenes is investigated by the action-derived molecular dynamics. Dynamic pathways and the corresponding activation energies are obtained for the Stone-Wales transformation in fullerene and the fullerene coalescence, under the presence of extra carbon atoms. The adatom-assisted Stone-Wales transformation is proved to be a highly probable process unit for the structural transformations and annealing treatments of carbon-based graphitic networks. The complex processes of adatom-assisted fullerene coalescence, yielding very low activation energies, are presented.

Deformation-induced bandgap tuning of 2D silicon-based photonic crystals

We address the issue of tuning the absolute bandgap in 2D silicon-based photonic crystals by mechanical deformation. The moving least-square (MLS) method, recently proposed by the authors for photonic bandgap materials, is employed for the real-space computation of band structures. The uniaxial tension mode is shown to be more effective for bandgap tuning than both pure and simple shear deformations. We verify that bandgap modifications are strongly influenced by the deformation-induced distortion of interfaces between inclusions and matrix. This result ensures the usefulness of real-space technique for the accurate calculation of strained photonic bandgap materials.

Synthesis, electromechanical characterization, and applications of graphene nanostructures

The emerging field of graphene brings together scientists and engineers as the discovered fundamental properties and effects encountered in this new material can be rapidly exploited for practical applications. There is potential for a two-dimensional graphene-based technology and recent works have already demonstrated the utility of graphene in building nanoelectromechanical systems, complex electronic circuits, photodetectors and ultrafast lasers. The state-of-the-art of substrate-suported graphene growth, and the current fundamental understanding of the electromechanical properties of graphene and graphene nanoribbons, represent important knowledge for developing new applications.

Cooperative atomic motions and core rearrangement in dislocation cross slip

Atomistic study of cross slip of a screw dislocation in copper is presented using the action-optimization numerical technique which seeks the most probable dynamic pathway on the potential-energy surface of the atomic system during the cross-slip process. The observed mechanism reveals features of both competing mechanisms postulated in literature, i.e., the Fleischer mechanism and the Friedel-Escaig mechanism. Due to cooperative atomic motions and complex core rearrangement during the process, the activation energies of the current cross-slip mechanism are around 0.5eV less than the lowest ever reported in corresponding studies using atomistic numerical techniques.

Size dependence of the nonlinear elastic softening of nanoscale graphene monolayers under plane-strain bulge tests: a molecular dynamics study

The pressure bulge test is an experimental technique to characterize the mechanical properties of microscale thin films. Here, we perform constant-temperature molecular dynamics simulations of the plane-strain cylindrical bulge test of nanosized monolayer graphene subjected to high gas pressure induced by hydrogen molecules. We observe a nonlinear elastic softening of the graphene with an increase in hydrogen pressure due to the stretching and weakening of the carbon-carbon bonds; we further observe that this softening behavior depends upon the size of the graphene monolayers. Our simulation results suggest that the traditional microscale bulge formulas, which assume constant elastic moduli, should be modified to incorporate the size dependence and elastic softening that occur in nanosized graphene bulge tests.

Axial Green's function method for steady Stokes flow in geometrically complex domains

Axial Greens function method (AGM) is developed for the simulation of Stokes flow in geometrically complex solution domains. The AGM formulation systematically decomposes the multidimensional steady-state Stokes equations into 1D forms. The representation formula for the solution variables can then be derived using the 1D Greens functions only, from which a system of 1D integral equations is obtained. Furthermore, the explicit representation formula for the pressure variable enable the unique AGM approach to facilitating the stabilization issue caused by the saddle structure between velocity and pressure. The convergence of numerical solutions, the simple axial discretization of complex solution domains, and the nature of integral schemes are demonstrated through a variety of numerical examples.