490 research outputs found
Higher order nonlocal operator method
We extend the nonlocal operator method to higher order scheme by using a
higher order Taylor series expansion of the unknown field. Such a higher order
scheme improves the original nonlocal operator method proposed by the authors
in [A nonlocal operator method for solving partial differential equations],
which can only achieve one-order convergence. The higher order nonlocal
operator method obtains all partial derivatives with specified maximal order
simultaneously without resorting to shape functions. The functional based on
the nonlocal operators converts the construction of residual and stiffness
matrix into a series of matrix multiplication on the nonlocal operator matrix.
Several numerical examples solved by strong form or weak form are presented to
show the capabilities of this method
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.Comment: 21 page
A first-principles study on the effect of oxygen content on the structural and electronic properties of silicon suboxide as anode material for Lithium Ion Batteries
Silicon suboxide is currently considered as a unique candidate for lithium
ion batteries anode materials due to its considerable capacity. However, no
adequate information exist about the role of oxygen content on its performance.
To this aim, we used density functional theory to create silicon suboxide
matrices of various Si:O ratios and investigated the role of oxygen content on
the structural, dynamic, electronic properties and lithiation behavior of the
matrices. Our study demonstrates that the O atoms interact strongly with the
inserted Li atoms resulting in a disintegration of the host matrix. We found
that higher concentration of oxygen atoms in the mixture reduces its relative
expansion upon lithiation, which is a desirable quality for anode materials. It
helps in preventing crack formation and pulverization due to large fluctuations
in volume. Our study also demonstrate that a higher oxygen content increases
the lithium storage capacity of the anode. However, it can also cause the
formation of stable complexes like lithium silicates that might result into
reversible capacity loss as indicated by the voltage-composition curves. The
study provides valuable insights into the role of oxygen in moderating the
interaction of lithium in silicon suboxide mixture in microscopic details
A nonlocal operator method for solving partial differential equations
We propose a nonlocal operator method for solving partial differential
equations (PDEs). The nonlocal operator is derived from the Taylor series
expansion of the unknown field, and can be regarded as the integral form
"equivalent" to the differential form in the sense of nonlocal interaction. The
variation of a nonlocal operator is similar to the derivative of shape function
in meshless and finite element methods, thus circumvents difficulty in the
calculation of shape function and its derivatives. {The nonlocal operator
method is consistent with the variational principle and the weighted residual
method, based on which the residual and the tangent stiffness matrix can be
obtained with ease.} The nonlocal operator method is equipped with an hourglass
energy functional to satisfy the linear consistency of the field. Higher order
nonlocal operators and higher order hourglass energy functional are
generalized. The functional based on the nonlocal operator converts the
construction of residual and stiffness matrix into a series of matrix
multiplications on the nonlocal operators. The nonlocal strong forms of
different functionals can be obtained easily via support and dual-support, two
basic concepts introduced in the paper. Several numerical examples are
presented to validate the method.Comment: 30 page
Tensile fracture behavior of short carbon nanotube reinforced polymer composites: A coarse-grained model
Short-fiber-reinforced polymer composites are increasingly used in
engineering applications and industrial products owing to their unique
combination of superior mechanical properties, and relatively easy and low cost
manufacturing process. The mechanical behavior of short carbon nanotube (CNT)
polymer composites, however, remains poorly understood due to size and time
limitations of experiments and atomistic simulations. To address this issue,
the tensile fracture behavior of short CNT reinforced poly (methyl
methacrylate) (PMMA) matrix composites is investigated using a coarse-grained
(CG) model. The reliability of the CG model is demonstrated by reproducing
experimental results on the stress-stain behavior of the polymer material. The
effect of the nanotube weight fraction on the mechanical properties, i.e. the
Young's modulus, yield strength,tensile strength and critical strain, of the
CNT/polymer composites is studied in detail. The dependence of the mechanical
properties of the composites on the orientation and length-to-diameter aspect
ratio of nanotube reinforcements is also examined.Comment: arXiv admin note: text overlap with arXiv:1704.0145
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
Coarse-grained model of the J-integral of carbon nanotube reinforced polymer composites
The J-integral is recognized as a fundamental parameter in fracture mechanics
that characterizes the inherent resistance of materials to crack growth.
However, the conventional methods to calculate the J-integral, which require
knowledge of the exact position of a crack tip and the continuum fields around
it, are unable to precisely measure the J-integral of polymer composites at the
nanoscale. This work aims to propose an effective calculation method based on
coarse-grained (CG) simulations for predicting the J-integral of carbon
nanotube (CNT)/polymer composites. In the proposed approach, the J-integral is
determined from the load displacement curve of a single specimen. The
distinguishing feature of the method is the calculation of J-integral without
need of information about the crack tip, which makes it applicable to complex
polymer systems. The effects of the CNT weight fraction and covalent
cross-links between the polymer matrix and nanotubes, and polymer chains on the
fracture behavior of the composites are studied in detail. The dependence of
the J-integral on the crack length and the size of representative volume
element (RVE) is also explored.Comment: arXiv admin note: text overlap with arXiv:1704.0145
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
Mechanical properties of carbon nanotube reinforced polymer nanocomposites: A coarse-grained model
In this work, a coarse-grained (CG) model of carbon nanotube (CNT) reinforced
polymer matrix composites is developed. A distinguishing feature of the CG
model is the ability to capture interactions between polymer chains and
nanotubes. The CG potentials for nanotubes and polymer chains are calibrated
using the strain energy conservation between CG models and full atomistic
systems. The applicability and efficiency of the CG model in predicting the
elastic properties of CNT/polymer composites are evaluated through verification
processes with molecular simulations. The simulation results reveal that the CG
model is able to estimate the mechanical properties of the nanocomposites with
high accuracy and low computational cost. The effect of the volume fraction of
CNT reinforcements on the Young's modulus of the nanocomposites is
investigated. The application of the method in the modeling of large unit cells
with randomly distributed CNT reinforcements is examined. The established CG
model will enable the simulation of reinforced polymer matrix composites across
a wide range of length scales from nano to mesoscale
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
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