7,320 research outputs found
Interplay of phase boundary anisotropy and electro-autocatalytic surface reactions on the lithium intercalation dynamics in LiFePO platelet-like nanoparticles
Experiments on single crystal LiFePO (LFP) nanoparticles indicate
rich nonequilibrium phase behavior, such as suppression of phase separation at
high lithiation rates, striped patterns of coherent phase boundaries,
nucleation by binarysolid surface wetting and intercalation waves. These
observations have been successfully predicted (prior to the experiments) by 1D
depth-averaged phase-field models, which neglect any subsurface phase
separation. In this paper, using an electro-chemo-mechanical phase-field model,
we investigate the coherent non-equilibrium subsurface phase morphologies that
develop in the - plane of platelet-like single-crystal platelet-like
LiFePO nanoparticles. Finite element simulations are performed for 2D
plane-stress conditions in the - plane, and validated by 3D simulations,
showing similar results. We show that the anisotropy of the interfacial tension
tensor, coupled with electroautocatalytic surface intercalation reactions,
plays a crucial role in determining the subsurface phase morphology. With
isotropic interfacial tension, subsurface phase separation is observed,
independent of the reaction kinetics, but for strong anisotropy, phase
separation is controlled by surface reactions, as assumed in 1D models.
Moreover, the driven intercalation reaction suppresses phase separation during
lithiation, while enhancing it during delithiation, by electro-autocatalysis,
in quantitative agreement with {\it in operando} imaging experiments in
single-crystalline nanoparticles, given measured reaction rate constants
A new displacement-based approach to calculate stress intensity factors with the boundary element method
The analysis of cracked brittle mechanical components considering linear elastic fracture mechanics is usually reduced to the evaluation of stress intensity factors (SIFs). The SIF calculation can be carried out experimentally, theoretically or numerically. Each methodology has its own advantages but the use of numerical methods has be-come very popular. Several schemes for numerical SIF calculations have been developed, the J-integral method being one of the most widely used because of its energy-like formulation. Additionally, some variations of the J-integral method, such as displacement-based methods, are also becoming popular due to their simplicity. In this work, a simple displacement-based scheme is proposed to calculate SIFs, and its performance is compared with contour integrals. These schemes are all implemented with the Boundary Element Method (BEM) in order to exploit its advantages in crack growth modelling. Some simple examples are solved with the BEM and the calculated SIF values are compared against available solutions, showing good agreement between the different schemes
A Unified Adaptive Cartesian Grid Method for Solid-Multiphase Fluid Dynamics with Moving Boundaries
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76397/1/AIAA-2007-4576-676.pd
Comparison of five methods of computing the Dirichlet-Neumann operator for the water wave problem
We compare the effectiveness of solving Dirichlet-Neumann problems via the
Craig-Sulem (CS) expansion, the Ablowitz-Fokas-Musslimani (AFM) implicit
formulation, the dual AFM formulation (AFM*), a boundary integral collocation
method (BIM), and the transformed field expansion (TFE) method. The first three
methods involve highly ill-conditioned intermediate calculations that we show
can be overcome using multiple-precision arithmetic. The latter two methods
avoid catastrophic cancellation of digits in intermediate results, and are much
better suited to numerical computation.
For the Craig-Sulem expansion, we explore the cancellation of terms at each
order (up to 150th) for three types of wave profiles, namely band-limited,
real-analytic, or smooth. For the AFM and AFM* methods, we present an example
in which representing the Dirichlet or Neumann data as a series using the AFM
basis functions is impossible, causing the methods to fail. The example
involves band-limited wave profiles of arbitrarily small amplitude, with
analytic Dirichlet data. We then show how to regularize the AFM and AFM*
methods by over-sampling the basis functions and using the singular value
decomposition or QR-factorization to orthogonalize them. Two additional
examples are used to compare all five methods in the context of water waves,
namely a large-amplitude standing wave in deep water, and a pair of interacting
traveling waves in finite depth.Comment: 31 pages, 18 figures. (change from version 1: corrected error in
table on page 12
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