arXiv subjects

Timon Rabczuk

Publications and source records attributed to Timon Rabczuk.

157 records · Page 9Linked to original sources

arXiv2013

Elastic Bending Modulus of Single-Layer Molybdenum Disulphide (MoS2): Finite Thickness Effect

We derive, from an empirical interaction potential, an analytic formula for the elastic bending modulus of single-layer MoS2 (SLMoS2). By using this approach, we do not need to define or estimate a thickness value for SLMoS2, which is important due to the substantial controversy in defining this value for two-dimensional or ultrathin nanostructures such as graphene and nanotubes. The obtained elastic bending modulus of 9.61 eV in SLMoS2 is significantly higher than the bending modulus of 1.4 eV in graphene, and is found to be within the range of values that are obtained using thin shell theory with experimentally obtained values for the elastic constants of SLMoS2. This increase in bending modulus as compared to monolayer graphene is attributed, through our analytic expression, to the finite thickness of SLMoS2. Specifically, while each monolayer of S atoms contributes 1.75 eV to the bending modulus, which is similar to the 1.4 eV bending modulus of monolayer graphene, the additional pairwise and angular interactions between out of plane Mo and S atoms contribute 5.84 eV to the bending modulus of SLMoS2.

cond-mat.mtrl-sci↗

arXiv2013

Orientation Dependent Thermal Conductance in Single-Layer MoS2

We investigate the thermal conductivity in the armchair and zigzag MoS$_{2}$ nanoribbons, by combining the non-equilibrium Green's function approach and the first-principles method. A strong orientation dependence is observed in the thermal conductivity. Particularly, the thermal conductivity for the armchair MoS$_{2}$ nanoribbon is about 673.6 Wm$^{-1}$K$^{-1}$ in the armchair nanoribbon, and 841.1 Wm$^{-1}$K$^{-1}$ in the zigzag nanoribbon at room temperature. By calculating the Caroli transmission, we disclose the underlying mechanism for this strong orientation dependence to be the fewer phonon transport channels in the armchair MoS$_{2}$ nanoribbon in the frequency range of [150, 200] {cm$^{-1}$}. Through the scaling of the phonon dispersion, we further illustrate that the thermal conductivity calculated for the MoS$_{2}$ nanoribbon is esentially in consistent with the superior thermal conductivity found for graphene.

cond-mat.mtrl-sci↗

arXiv2013

Why twisting angles are diverse in graphene Moire patterns?

The interlayer energy of the twisting bilayer graphene is investigated by the molecular mechanics method using both the registry-dependent potential and the Lennard-Jones potential. Both potentials show that the interlayer energy is independent of the twisting angle $θ$, except in the two boundary regions $θ\approx 0$ or $60^{\circ}$, where the interlayer energy is proportional to the square of the twisting arc length. The calculation results are successfully interpreted by a single atom model. An important information from our findings is that, from the energy point of view, there is no preference for the twisting angle in the experimental bilayer graphene samples, which actually explains the diverse twisting angles in the experiment.

cond-mat.mtrl-sci↗

arXiv2013

A Surface Stacking Fault Energy Approach to Predicting Defect Nucleation in Surface-Dominated Nanostructures

We present a surface stacking fault (SSF) energy approach to predicting defect nucleation from the surfaces of surface-dominated nanostructure such as FCC metal nanowires. The approach leads to a criteria that predicts the initial yield mechanism via either slip or twinning depending on whether the unstable twinning energy or unstable slip energy is smaller as determined from the resulting SSF energy curve. The approach is validated through a comparison between the SSF energy calculation and low-temperature classical molecular dynamics simulations of copper nanowires with different axial and transverse surface orientations, and cross sectional geometries. We focus on the effects of the geometric cross section by studying the transition from slip to twinning previously predicted in moving from a square to rectangular cross section for $\ <100\ > /\{100\}$ nanowires, and also for moving from a rhombic to truncated rhombic cross sectional geometry for $\ <110\ >$ nanowires. \hsp{We also provide the important demonstration that the criteria is able to predict the correct deformation mechanism when full dislocation slip is considered concurrently with partial dislocation slip and twinning. This is done in the context of rhombic aluminum nanowires which do not show a tensile reorientation due to full dislocation slip.} We show that the SSF energy criteria successfully predicts the initial mode of surface-nucleated plasticity at low temperature, while also discussing the effects of strain and temperature on the applicability of the criterion.

cond-mat.mtrl-sci↗

arXiv2013

Modulation of Thermal Conductivity in Kinked Silicon Nanowires: Phonon Interchanging and Pinching Effects

We perform molecular dynamics simulations to investigate the reduction of the thermal conductivity by kinks in silicon nanowires. The reduction percentage can be as high as 70% at room temperature. The temperature dependence of the reduction is also calculated. By calculating phonon polarization vectors, two mechanisms are found to be responsible for the reduced thermal conductivity: (1) the interchanging effect between the longitudinal and transverse phonon modes and (2) the pinching effect, i.e a new type of localization, for the twisting and transverse phonon modes in the kinked silicon nanowires. Our work demonstrates that the phonon interchanging and pinching effects, induced by kinking, are brand new and effective ways in modulating heat transfer in nanowires, which enables the kinked silicon nanowires to be a promising candidate for thermoelectric materials.

cond-mat.mtrl-sci↗

arXiv2013

Superior thermal conductivity and extremely high mechanical strength in polyethylene chains from {\it ab initio} calculation

The upper limit of the thermal conductivity and the mechanical strength are predicted for the polyethylene chain, by performing the {\it ab initio} calculation and applying the quantum mechanical non-equilibrium Green's function approach. Specially, there are two main findings from our calculation: (1). the thermal conductivity can reach a high value of 310 W/K/m in a 100 nm polyethylene chain at room temperature; (2). the Young's modulus in the polyethylene chain is as high as 374.5 GPa, and the polyethylene chain can sustain $32.85% \pm 0.05%$ (ultimate) strain before undergoing structural phase transition into gaseous ethylene.

cond-mat.mtrl-sci↗

arXiv2013

Mechanical Oscillation of Kinked Silicon Nanowires: a Natural Nanoscale Spring

We perform classical molecular dynamics simulations to demonstrate the application of kinked silicon nanowires (KSiNWs) as nanoscale springs. The spring-like oscillation in gigahertz frequency range is successfully actuated using a similar procedure as the actuation of a classical mass spring oscillator. We detect the spring-like mechanical oscillation and some other low-frequency oscillations by the energy spectrum analysis, where a dimensional crossover phenomenon is observed for the transverse mode in KSiNWs with decreasing aspect ratio. Our findings shed light on the elastic properties of the KSiNW and open a way for its application in nanomechanical devices.

cond-mat.mes-hall↗

arXiv2013

Size-Sensitive Young's modulus of Kinked Silicon Nanowires

We perform both classical molecular dynamics simulations and beam model calculations to investigate the Young's modulus of kinked silicon nanowires (KSiNWs). The Young's modulus is found to be highly sensitive to the arm length of the kink and is essentially inversely proportional to the arm length. The mechanism underlying the size dependence is found to be the interplay between the kink angle potential and the arm length potential, where we obtain an analytic relationship between the Young's modulus and the arm length of the KSiNW. Our results provide insight into the application of this novel building block in nanomechanical devices.

cond-mat.mtrl-sci↗

arXiv2012

A partitioned model order reduction approach to rationalise computational expenses in multiscale fracture mechanics

We propose in this paper an adaptive reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order reduction permits to focus the numerical effort where it is most needed: around the zones where damage propagates. No \textit{a priori} knowledge of the damage pattern is required, the extraction of the corresponding spatial regions being based solely on algebra. The efficiency of the proposed approach is demonstrated numerically with an example relevant to engineering fracture.

physics.class-ph↗

arXiv2012

Enhancing the Mass Sensitivity of Graphene Nanoresonators Via Nonlinear Oscillations: The Effective Strain Mechanism

We perform classical molecular dynamics simulations to investigate the enhancement of the mass sensitivity and resonant frequency of graphene nanomechanical resonators that is achieved by driving them into the nonlinear oscillation regime. The mass sensitivity as measured by the resonant frequency shift is found to triple if the actuation energy is about 2.5 times the initial kinetic energy of the nanoresonator. The mechanism underlying the enhanced mass sensitivity is found to be the effective strain that is induced in the nanoresonator due to the nonlinear oscillations, where we obtain an analytic relationship between the induced effective strain and the actuation energy that is applied to the graphene nanoresonator. An important implication of this work is that there is no need for experimentalists to apply tensile strain to the resonators before actuation in order to enhance the mass sensitivity. Instead, enhanced mass sensitivity can be obtained by the far simpler technique of actuating nonlinear oscillations of an existing graphene nanoresonator.

cond-mat.mes-hall↗

arXiv2012

NURBS-based finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter

In this paper, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates. The material properties are assumed to be graded only in the thickness direction and the effective properties are computed either using the rule of mixtures or by Mori-Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation plate theory (FSDT). The shear correction factors are evaluated employing the energy equivalence principle and a simple modification to the shear correction factor is presented to alleviate shear locking. Static bending, mechanical and thermal buckling, linear free flexural vibration and supersonic flutter analysis of FGM plates are numerically studied. The accuracy of the present formulation is validated against available three-dimensional solutions. A detailed numerical study is carried out to examine the influence of the gradient index, the plate aspect ratio and the plate thickness on the global response of functionally graded material plates.

math.NA↗

arXiv2012

A comparative study of two molecular mechanics models based on harmonic potentials

We show that the two molecular mechanics models, the stick-spiral and the beam models, predict considerably different mechanical properties of materials based on energy equivalence. The difference between the two models is independent of the materials since all parameters of the beam model are obtained from the harmonic potentials. We demonstrate this difference for finite width graphene nanoribbons and a single polyethylene chain comparing results of the molecular dynamics (MD) simulations with harmonic potentials and the finite element method with the beam model. We also find that the difference strongly depends on the loading modes, chirality and width of the graphene nanoribbons, and it increases with decreasing width of the nanoribbons under pure bending condition. The maximum difference of the predicted mechanical properties using the two models can exceed 300% in different loading modes. Comparing the two models with the MD results of AIREBO potential, we find that the stick-spiral model overestimates and the beam model underestimates the mechanical properties in narrow armchair graphene nanoribbons under pure bending condition.

cond-mat.mtrl-sci↗

arXiv2012

Statistical extraction of process zones and representative subspaces in fracture of random composite

We propose to identify process zones in heterogeneous materials by tailored statistical tools. The process zone is redefined as the part of the structure where the random process cannot be correctly approximated in a low-dimensional deterministic space. Such a low-dimensional space is obtained by a spectral analysis performed on pre-computed solution samples. A greedy algorithm is proposed to identify both process zone and low-dimensional representative subspace for the solution in the complementary region. In addition to the novelty of the tools proposed in this paper for the analysis of localised phenomena, we show that the reduced space generated by the method is a valid basis for the construction of a reduced order model.

physics.class-ph↗