arXiv subjects

Timon Rabczuk

Publications and source records attributed to Timon Rabczuk.

At least 145 records · Page 8Linked to original sources

arXiv2017

Dual-support smoothed particle hydrodynamics for elastic mechanics

In the standard SPH method, the interaction between two particles might be not pairwise when the support domain varies, which can result in a reduction of accuracy. To deal with this problem, a modified SPH approach is presented in this paper. First of all, a Lagrangian kernel is introduced to eliminate spurious distortions of the domain of material stability, and the gradient is corrected by a linear transformation so that linear completeness is satisfied. Then, concepts of support and dual-support are defined to deal with the unbalanced interactions between the particles with different support domains. Several benchmark problems in one, two and three dimensions are tested to verify the accuracy of the modified SPH model and highlight its advantages over the standard SPH method through comparisons.

physics.comp-ph↗

arXiv2017

Strong thermal transport along polycrystalline transition metal dichalcogenides revealed by multiscale modelling for MoS2

Transition metal dichalcogenides (TMDs) represent a large family of high-quality 2D materials with attractive electronic, thermal, chemical, and mechanical properties. Chemical vapour deposition (CVD) technique is currently the most reliable route to synthesis few-atomic layer thick and large-scale TMDs films. However, the effects of grain boundaries formed during the CVD method on the properties of TMDs nanomembranes have remained less explored. In this study, we therefore aim to investigate the thermal conduction along polycrystalline molybdenum disulfide (MoS2) as the representative member of TMDs nanomembranes family. This goal was achieved by developing a combined atomistic-continuum multiscale method. In the proposed approach, reactive molecular dynamics simulations were carried out to assess thermal contact conductance of diverse grain boundaries with various defects configurations. The effective thermal conductivity along the CVD grown polycrystalline and single-layer MoS2 was finally acquired by conducting finite element modelling. Insight provided by this investigation can be useful to evaluate the effective thermal transport along a wide variety of 2D materials and structures.

cond-mat.mtrl-sci↗

arXiv2017

Volumetric parametrization from a level set boundary representation with PHT Splines

A challenge in isogeometric analysis is constructing analysis-suitable volumetric meshes which can accurately represent the geometry of a given physical domain. In this paper, we propose a method to derive a spline-based representation of a domain of interest from voxel-based data. We show an efficient way to obtain a boundary representation of the domain by a level-set function. Then, we use the geometric information from the boundary (the normal vectors and curvature) to construct a matching C1 representation with hierarchical cubic splines. The approximation is done by a single template and linear transformations (scaling, translations and rotations) without the need for solving an optimization problem. We illustrate our method with several examples in two and three dimensions, and show good performance on some standard benchmark test problems.

cs.GR↗

arXiv2017

Adaptive FEM-based nonrigid image registration using truncated hierarchical B-splines

We present an efficient approach of Finite Element Method (FEM)-based nonrigid image registration, in which the spatial transformation is constructed using truncated hierarchical B-splines (THB-splines). The image registration framework minimizes an energy functional using an FEM-based method and thus involves solving a large system of linear equations. This framework is carried out on a set of successively refined grids. However, due to the increased number of control points during subdivision, large linear systems are generated which are generally demanding to solve. Instead of using uniform subdivision, an adaptive local refinement scheme is carried out, only refining the areas of large change in deformation of the image. By incorporating the key advantages of THB-spline basis functions such as linear independence, partition of unity and reduced overlap into the FEM-based framework, we improve the matrix sparsity and computational efficiency. The performance of the proposed method is demonstrated on 2D synthetic and medical images.

math.NA↗

arXiv2017

Dual-horizon peridynamics: A stable solution to varying horizons

In this paper, we present a dual-horizon peridynamics formulation which allows for simulations with dual-horizon with minimal spurious wave reflection. We prove the general dual property for dual-horizon peridynamics, based on which the balance of momentum and angular momentum in PD are naturally satisfied. We also analyze the crack pattern of random point distribution and the multiple materials issue in peridynamics. For selected benchmark problems, we show that DH-PD is less sensitive to the spatial than the original PD formulation.

physics.comp-ph↗

arXiv2017

Mechanical properties of borophene films: A reactive molecular dynamics investigation

The most recent experimental advances could provide ways for the fabrication of several atomic thick and planar forms of boron atoms. For the first time, we explore the mechanical properties of five types of boron films with various vacancy ratios ranging from 0.1 to 0.15, using molecular dynamics simulations with ReaxFF force field. It is found that the Young's modulus and tensile strength decrease with increasing the temperature. We found that boron sheets exhibit an anisotropic mechanical response due to the different arrangement of atoms along the armchair and zigzag directions. At room temperature, 2D Young's modulus and fracture stress of these five sheets appear in the range 63 N/m and 12 N/m, respectively. In addition, the strains at tensile strength are in the ranges of 9, 11, and 10 percent at 1, 300, and 600 K, respectively. This investigation not only reveals the remarkable stiffness of 2D boron, but establishes relations between the mechanical properties of the boron sheets to the loading direction, temperature and atomic structures.

cond-mat.mtrl-sci↗

arXiv2016

The Effects of Vacancy and Oxidation on Black Phosphorus Nanoresonators

Black phosphorene is not stable at ambient conditions, so atomic defects and oxidation effects are unavoidable in black phosphorus samples in the experiment. The effects of these defects on the performance of the black phosphorus nanoresonators are still unclear. Here, we perform classical molecular dynamics to investigate the effects of the vacancy and oxidation on single-layer black phosphorus nanoresonators at different temperatures. We find that the vacancy causes strong reduction in the quality factor of the nanoresonators, while the oxidation has weaker effect on the nanoresonators. More specifically, a 2% concentration of randomly distributed single vacancies is able to reduce the quality factor by about 80% and 40% at 4.2K and 50K, respectively. We also find that the quality factor of the nanoresonator is not sensitive to the distribution pattern of the vacancy defects.

cond-mat.mtrl-sci↗

arXiv2016

Dual-support Smoothed Particle Hydrodynamics

In this paper we develop a dual-support smoothed particle hydrodynamics (DS-SPH) that naturally satisfies the conservation of momentum, angular momentum and energy when the varying smoothing length is utilized. The DS-SPH is based on the concept of dual-support, which is introduced to consider the unbalanced interactions between the particles with different smoothing lengths. Our DS-SPH formulation can be implemented in traditional SPH with little changes and improve the computational efficiency. Several numerical examples are presented to demonstrate the capability of the method.

physics.comp-ph↗

arXiv2016

A new peridynamic formulation with shear deformation for elastic solid

We propose a new peridynamic formulation with shear deformation for linear elastic solid. The key idea lies in subtracting the rigid body rotation part from the total deformation. Based on the strain energy equivalence between classic local model and non-local model, the bond force vector is derived. A new damage rule of maximal deviatoric bond strain for elastic brittle fracture is proposed in order to account for both the tensile damage and shear damage. 2D and 3D numerical examples are tested to verify the accuracy of the current peridynamics. The new damage rule is applied to simulate the propagation of Mode I, II and III cracks.

cond-mat.soft↗

arXiv2015

Dual-horizon Peridynamics

In this paper we develop a new Peridynamic approach that naturally includes varying horizon sizes and completely solves the "ghost force" issue. Therefore, the concept of dual-horizon is introduced to consider the unbalanced interactions between the particles with different horizon sizes. The present formulation is proved to fulfill both the balances of linear momentum and angular momentum. Neither the "partial stress tensor" nor the "`slice" technique are needed to ameliorate the ghost force issue in \cite{Silling2014}. The consistency of reaction forces is naturally fulfilled by a unified simple formulation. The method can be easily implemented to any existing peridynamics code with minimal changes. A simple adaptive refinement procedure is proposed minimizing the computational cost. The method is applied here to the three Peridynamic formulations, namely bond based, ordinary state based and non-ordinary state based Peridynamics. Both two- and three- dimensional examples including the Kalthof-Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method in solving wave propagation, fracture and adaptive analysis .

physics.comp-ph↗

arXiv2015

A Stillinger-Weber Potential for Single-Layer Black Phosphorus, and the Importance of Cross-Pucker Interactions for Negative Poisson's Ratio and Edge Stress-Induced Bending

The distinguishing structural feature of single-layer black phosphorus is its puckered structure, which leads to many novel physical properties. In this work, we first present a new parameterization of the Stillinger-Weber potential for single-layer black phosphorus. In doing so, we reveal the importance of a cross-pucker interaction term in capturing its unique mechanical properties, such as a negative Poisson's ratio. In particular, we show that the cross-pucker interaction enables the pucker to act as a re-entrant hinge, which expands in the lateral direction when it is stretched in the longitudinal direction. As a consequence, single-layer black phosphorus has a negative Poisson's ratio in the direction perpendicular to the atomic plane. As an additional demonstration of the impact of the cross-pucker interaction, we show that it is also the key factor that enables capturing of the edge stress-induced bending of single-layer black phosphorus that has been reported in ab initio calculations.

cond-mat.mtrl-sci↗

arXiv2014

Polar Surface Effects on the Thermal Conductivity in ZnO Nanowires: a Shell-Like Surface Reconstruction-Induced Preserving Mechanism

We perform molecular dynamics (MD) simulations to investigate the effect of polar surfaces on the thermal transport in zinc oxide (ZnO) nanowires. We find that the thermal conductivity in nanowires with free polar (0001) surfaces is much higher than in nanowires that have been stabilized with reduced charges on the polar (0001) surfaces, and also hexagonal nanowires without any transverse polar surfaces. From normal mode analysis, we show that the higher thermal conductivity is due to a shell-like reconstruction that occurs for the free polar surfaces. This shell-like reconstruction suppresses twisting motion in the nanowires such that the bending phonon modes are not scattered by the other phonon modes, and leads to substantially higher thermal conductivity in the ZnO nanowire with free polar surfaces. Furthermore, the auto-correlation function of the normal mode coordinate is utilized to extract the phonon lifetime, which leads to a concise explanation for the higher thermal conductivity in ZnO nanowires with free polar surfaces. Our work demonstrates that ZnO nanowires without polar surfaces, which exhibit low thermal conductivity, are more promising candidates for thermoelectric applications than nanowires with polar surfaces (and also high thermal conductivity).

cond-mat.mtrl-sci↗

arXiv2014

MoS2 Nanoresonators: Intrinsically Better Than Graphene?

We perform classical molecular dynamics simulations to examine the intrinsic energy dissipation in single-layer MoS$_{2}$ nanoresonators, where a point of emphasis is to compare its dissipation characteristics with those of single-layer graphene. Our key finding is that MoS$_{2}$ nanoresonators exhibit significantly lower energy dissipation, and thus higher quality (Q)-factors by at least a factor of four below room temperature, than graphene. Furthermore, this high Q-factor endows MoS$_{2}$ nanoresonators with a higher figure of merit, defined as frequency times Q-factor, despite a resonant frequency that is $50%$ smaller than graphene for the same size. By utilizing arguments from phonon-phonon scattering theory, we show that this reduced energy dissipation is enabled by the large energy gap in the phonon dispersion of MoS$_{2}$, which separates the acoustic phonon branches from the optical phonon branches, leading to a preserving mechanism for the resonant oscillation of MoS$_{2}$ nanoresonators. We further investigate the effects of tensile mechanical strain and nonlinear actuation on the Q-factors, where the tensile strain is found to counteract the reductions in Q-factor that occur with higher actuation amplitudes. Overall, our simulations illustrate the potential utility of MoS$_{2}$ for high frequency sensing and actuation applications.

cond-mat.mes-hall↗

arXiv2014

Preserving the Q-Factors of ZnO Nanoresonators via Polar Surface Reconstruction

We perform molecular dynamics simulations to investigate the effect of polar surfaces on the quality (Q)-factors of zinc oxide (ZnO) nanowire-based nanoresonators. We find that the Q-factors in ZnO nanoresonators with free polar (0001) surfaces is about one order of magnitude higher than in nanoresonators that have been stabilized with reduced charges on the polar (0001) surfaces. From normal mode analysis, we show that the higher Q-factor is due to a shell-like reconstruction that occurs for the free polar surfaces. This shell-like reconstruction suppresses twisting motion in the nanowires such that the mixing of other modes with the resonant mode of oscillation is minimized, and leads to substantially higher Q-factors in the ZnO nanoresonators with free polar surfaces.

cond-mat.mtrl-sci↗

arXiv2014

Phonon Modes in Single-Walled Molybdenum Disulphide (MoS2) Nanotubes: Lattice Dynamics Calculation and Molecular Dynamics Simulation

We study the phonon modes in single-walled MoS$_{2}$ nanotubes via the lattice dynamics calculation and molecular dynamics simulation. The phonon spectra for tubes of arbitrary chiralities are calculated from the dynamical matrix constructed by the combination of an empirical potential with the conserved helical quantum numbers $(κ, n)$. In particular, we show that the frequency ($ω$) of the radial breathing mode is inversely proportional to the tube diameter ($d$) as $ω=665.3/d$ {cm$^{-1}$}. The eigen vectors of the first twenty lowest-frequency phonon modes are illustrated. Based on these eigen vectors, we demonstrate that the radial breathing oscillation is disturbed by phonon modes of three-fold symmetry initially, and the tube is squashed by the modes of two-fold symmetry eventually. Our study provides fundamental knowledge for further investigations of the thermal and mechanical properties of the MoS$_{2}$ nanotubes.

cond-mat.mtrl-sci↗

arXiv2013

Isogeometric analysis: an overview and computer implementation aspects

Isogeometric analysis (IGA) represents a recently developed technology in computational mechanics that offers the possibility of integrating methods for analysis and Computer Aided Design (CAD) into a single, unified process. The implications to practical engineering design scenarios are profound, since the time taken from design to analysis is greatly reduced, leading to dramatic gains in efficiency. The tight coupling of CAD and analysis within IGA requires knowledge from both fields and it is one of the goals of the present paper to outline much of the commonly used notation. In this manuscript, through a clear and simple Matlab implementation, we present an introduction to IGA applied to the Finite Element (FE) method and related computer implementation aspects. Furthermore, implemen- tation of the extended IGA which incorporates enrichment functions through the partition of unity method (PUM) is also presented, where several examples for both two-dimensional and three-dimensional fracture are illustrated. The open source Matlab code which accompanies the present paper can be applied to one, two and three-dimensional problems for linear elasticity, linear elastic fracture mechanics, structural mechanics (beams/plates/shells including large displacements and rotations) and Poisson problems with or without enrichment. The Bezier extraction concept that allows FE analysis to be performed efficiently on T-spline geometries is also incorporated. The article includes a summary of recent trends and developments within the field of IGA.

math.NA↗

arXiv2013

Adsorbate Migration Effects on Continuous and Discontinuous Temperature-Dependent Transitions in the Quality Factors of Graphene Nanoresonators

We perform classical molecular dynamics simulation to investigate the mechanisms underpinning the unresolved, experimentally-observed temperature-dependent scaling transition in the quality factors of graphene nanomechanical resonators (GNMR). Our simulations reveal that the mechanism underlying this temperature scaling phenomenon is the out-of-plane migration of adsorbates on GNMRs. Specifically, the migrating adsorbate undergoes frequent collisions with the GNMR, which strongly influences the resulting mechanical oscillation, and thus the quality factors. We also predict a discontinuous transition in the quality factor at a lower critical temperature, which results from the in-plane migration of the adsorbate. Overall, our work clearly demonstrates the strong effect of adsorbate migration on the quality factors of GNMRs.

cond-mat.mtrl-sci↗

arXiv2013

Molecular Dynamics Simulations of Single-Layer Molybdenum Disulphide (MoS2): Stillinger-Weber Parametrization, Mechanical Properties, and Thermal Conductivity

We present a parameterization of the Stillinger-Weber potential to describe the interatomic interactions within single-layer MoS2 (SLMoS2). The potential parameters are fitted to an experimentally-obtained phonon spectrum, and the resulting empirical potential provides a good description for the energy gap and the crossover in the phonon spectrum. Using this potential, we perform classical molecular dynamics simulations to study chirality, size, and strain effects on the Young's modulus and the thermal conductivity of SLMoS2. We demonstrate the importance of the free edges on the mechanical and thermal properties of SLMoS2 nanoribbons. Specifically, while edge effects are found to reduce the Young's modulus of SLMoS2 nanoribbons, the free edges also reduce the thermal stability of SLMoS2 nanoribbons, which may induce melting well below the bulk melt temperature. Finally, uniaxial strain is found to efficiently manipulate the thermal conductivity of infinite, periodic SLMoS2.

cond-mat.mtrl-sci↗