晶体位错尺寸效应的多尺度分析

本文采用准连续介质多尺度方法，分析了面心立方（fcc）晶体铝阶梯孪晶界在不同尺寸情况下（试件尺寸长高比从1：1到8：1）受剪切作用的晶界变形。了解在不同尺寸下，晶界结构位错的成核过程，得到了大试件比值与小试件比值下作用力与应变的关系曲线及不同试件尺寸下应变能的变化曲线。其中随着试件比值的增加，作用力在应变比较小的时候变化情况相似，但当应变达到3％以后，呈现出明显的不同；应变能随试件长高比的增大而减小，各个试件在各自不同的加载阶段，应变能变化趋势同作用力变化趋势相一致。本计算揭示了不同尺寸下阶梯孪晶界在剪切作用下的微观机理，证实其尺寸效应性质。     

Multi-scale and multi-order singularity approach to non-equilibrium mechanics: Coupling of atomic-micro-macro damage

Offered in this work is the development of a macro/meso/micro model that covers the lineal scale of 10⁻¹¹ to 10⁰ by application of the volume energy density function. Boundary constraints and defect geometries are shown to play a role at the smaller scale in the same way as those at the macroscopic scale. Different orders of stress (or energy density) singularities are used to describe the defect geometry and prevailing constraint via the boundary conditions in a way similar to singularity adopted in classical fracture mechanics. Two classes of singularities have been identified in addition to classical one without violating the finiteness conditions of the local displacement and energy density. Still the connection of results from the different scales is no small task and is made possible by application of a scale multiplier. It is determined by considering the interactive effects of the parameters at the different scales from the atomic to the macroscopic. Unlike the classical boundary value problem approach, application of the scale multiplier has led to closed-form asymptotic multiscale solutions that otherwise would not have been made possible. The procedure is demonstrated for the anti-plane shear of a macro-micro-atomic model that accounts for imperfection at the different scales Published in Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 3–22, January 2006.     

Intelligent Fault Identification for Rolling Bearings Fusing Average Refined Composite Multiscale Dispersion Entropy-Assisted Feature Extraction and SVM with Multi-Strategy Enhanced Swarm Optimization

Rolling bearings act as key parts in many items of mechanical equipment and any abnormality will affect the normal operation of the entire apparatus. To diagnose the faults of rolling bearings effectively, a novel fault identification method is proposed by merging variational mode decomposition (VMD), average refined composite multiscale dispersion entropy (ARCMDE) and support vector machine (SVM) optimized by multistrategy enhanced swarm optimization in this paper. Firstly, the vibration signals are decomposed into different series of intrinsic mode functions (IMFs) based on VMD with the center frequency observation method. Subsequently, the proposed ARCMDE, fusing the superiorities of DE and average refined composite multiscale procedure, is employed to enhance the ability of the multiscale fault-feature extraction from the IMFs. Afterwards, grey wolf optimization (GWO), enhanced by multistrategy including levy flight, cosine factor and polynomial mutation strategies (LCPGWO), is proposed to optimize the penalty factor C and kernel parameter g of SVM. Then, the optimized SVM model is trained to identify the fault type of samples based on features extracted by ARCMDE. Finally, the application experiment and contrastive analysis verify the effectiveness of the proposed VMD-ARCMDE-LCPGWO-SVM method.     

Accelerated quasicontinuum: a practical perspective on hyper-QC with application to nanoindentation

Abstract

Hyper-QC is a multiscale method based on the quasicontinuum (QC) method in which time is accelerated using hyperdynamics through the addition of a suitable bias potential. This paper describes the practical details of implementing and carrying out hyper-QC simulations and introduces a novel mechanism-based bias potential for deformation processes in face-centred cubic (fcc) systems. The factors limiting the maximum achievable acceleration are discussed. The method is demonstrated for nanoindentation into a thin film of single crystal fcc nickel at near experimental loading rates. Speed up factors as high as 10,000 are achieved. The simulations reveal a thermally activated dislocation nucleation mechanism with a logarithmic dependence on temperature and indenter velocity in agreement with a theoretical model.     

Residual‐based stabilization of the finite element approximation to the acoustic perturbation equations for low Mach number aeroacoustics

The acoustic perturbation equations (APE) are suitable to predict aerodynamic noise in the presence of a non‐uniform mean flow. As for any hybrid computational aeroacoustics approach, a first computational fluid dynamics simulation is carried out from which the mean flow characteristics and acoustic sources are obtained. In a second step, the APE are solved to get the acoustic pressure and particle velocity fields. However, resorting to the finite element method (FEM) for that purpose is not straightforward. Whereas mixed finite elements satisfying an appropriate inf–sup compatibility condition can be built in the case of no mean flow, that is, for the standard wave equation in mixed form, these are difficult to implement and their good performance is yet to be checked for more complex wave operators. As a consequence, strong simplifying assumptions are usually considered when solving the APE with FEM. It is possible to avoid them by resorting to stabilized formulations. In this work, a residual‐based stabilized FEM is presented for the APE at low Mach numbers, which allows one to deal with the APE convective and reaction terms in its full extent. The key of the approach resides in the design of the matrix of stabilization parameters. The performance of the formulation and the contributions of the different terms in the equations are tested for an acoustic pulse propagating in sheared‐solenoidal mean flow, and for the aeolian tone generated by flow past a two‐dimensional cylinder. Copyright © 2016 John Wiley & Sons, Ltd.     

Design and analysis of a Schwarz coupling method for a dimensionally heterogeneous problem

In the present work, we propose and analyse an efficient iterative coupling method for a dimensionally heterogeneous problem. We consider the case of a 2D Laplace equation with non‐symmetric boundary conditions coupled with a corresponding 1D Laplace equation. We first show how to obtain the 1D model from the 2D one by integration along one direction, by analogy with the link between shallow water equations and the Navier–Stokes system. Then we focus on the design of a Schwarz‐like iterative coupling method. We discuss the choice of boundary conditions at coupling interfaces. We prove the convergence of such algorithms and give some theoretical results related to the choice of the location of the coupling interface, and to the control of the difference between a global 2D reference solution and the 2D coupled solution. These theoretical results are illustrated numerically. Copyright © 2014 John Wiley & Sons, Ltd.     

Coarse‐grained A‐graft‐B model of poly(lactic acid) for molecular dynamics simulations

A mesoscopic model of poly(lactic acid) is developed where the polymer is represented as an A‐graft‐B chain with monomer units consisting of two covalently connected beads. A coarse‐graining algorithm is proposed to convert an atomistic model of PLA into a coarse‐grained one. The developed model is based on atomistic simulations of oligolactides to take into account terminal groups correctly. It was used for coarse‐grained simulations of polylactide. Gyration radii and end to end distances of polymer chains as well as the density of the polymer melt are shown to be in a good agreement with those obtained from atomistic simulations. The thermal expansion coefficients of the OLA melts calculated using the coarse‐grained model are in reasonable agreement with those obtained from all‐atom molecular dynamics. The model provides a 17‐fold speedup compared with atomistic calculations. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 604–612     

A mathematical and physical Study of multiscale deconvolution models of turbulence

This work presents a rigorous analysis of mathematical and physical properties for solutions of multiscale deconvolution turbulence models. We show that solutions of these models exactly conserve model quantities for the integral invariants of fundamental physical importance: kinetic energy, helicity, and (in two dimensions) enstrophy. The kinetic energy conservation is the key that allows us to next apply the phenomenology of homogeneous, isotropic turbulence to establish the existence of a model energy cascade and, in particular, that the cascade exhibits enhanced energy dissipation in a secondary accelerated cascade, which ends at the model's microscale (which we establish is larger than the Kolmogorov microscale). We also prove that the model dissipates energy at the same rate as true turbulent flow, ～ O(U³ ∕ L), independent of Reynolds number. Lastly, we prove the existence of global attractors for the model solutions; the proof of which also shows that solutions are actually one degree of regularity higher than previously known. Copyright © 2012 John Wiley & Sons, Ltd.     

Multiscale geometric modeling of macromolecules II: Lagrangian representation

Geometric modeling of biomolecules plays an essential role in the conceptualization of biolmolecular structure, function, dynamics, and transport. Qualitatively, geometric modeling offers a basis for molecular visualization, which is crucial for the understanding of molecular structure and interactions. Quantitatively, geometric modeling bridges the gap between molecular information, such as that from X‐ray, NMR, and cryo‐electron microscopy, and theoretical/mathematical models, such as molecular dynamics, the Poisson–Boltzmann equation, and the Nernst–Planck equation. In this work, we present a family of variational multiscale geometric models for macromolecular systems. Our models are able to combine multiresolution geometric modeling with multiscale electrostatic modeling in a unified variational framework. We discuss a suite of techniques for molecular surface generation, molecular surface meshing, molecular volumetric meshing, and the estimation of Hadwiger's functionals. Emphasis is given to the multiresolution representations of biomolecules and the associated multiscale electrostatic analyses as well as multiresolution curvature characterizations. The resulting fine resolution representations of a biomolecular system enable the detailed analysis of solvent–solute interaction, and ion channel dynamics, whereas our coarse resolution representations highlight the compatibility of protein‐ligand bindings and possibility of protein–protein interactions. © 2013 Wiley Periodicals, Inc.     

High–quality protein backbone reconstruction from alpha carbons using Gaussian mixture models

Coarse‐grained protein structure models offer increased efficiency in structural modeling, but these must be coupled with fast and accurate methods to revert to a full‐atom structure. Here, we present a novel algorithm to reconstruct mainchain models from C traces. This has been parameterized by fitting Gaussian mixture models (GMMs) to short backbone fragments centered on idealized peptide bonds. The method we have developed is statistically significantly more accurate than several competing methods, both in terms of RMSD values and dihedral angle differences. The method produced Ramachandran dihedral angle distributions that are closer to that observed in real proteins and better Phaser molecular replacement log‐likelihood gains. Amino acid residue sidechain reconstruction accuracy using SCWRL4 was found to be statistically significantly correlated to backbone reconstruction accuracy. Finally, the PD2 method was found to produce significantly lower energy full‐atom models using Rosetta which has implications for multiscale protein modeling using coarse‐grained models. A webserver and C++ source code is freely available for noncommercial use from: http://www.sbg.bio.ic.ac.uk/phyre2/PD2_ca2main/ . © 2013 Wiley Periodicals, Inc.