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A FEniCS implementation of the phase field method for quasi-static brittle fracture

HIRSHIKESH, Sundararajan NATARAJAN, Ratna Kumar ANNABATTULA

《结构与土木工程前沿(英文)》 2019年 第13卷 第2期   页码 380-396 doi: 10.1007/s11709-018-0471-9

摘要: In the recent years, the phase field method for simulating fracture problems has received considerable attention. This is due to the salient features of the method: 1) it can be incorporated into any conventional finite element software; 2) has a scalar damage variable is used to represent the discontinuous surface implicitly and 3) the crack initiation and subsequent propagation and branching are treated with less complexity. Within this framework, the linear momentum equations are coupled with the diffusion type equation, which describes the evolution of the damage variable. The coupled nonlinear system of partial differential equations are solved in a ‘staggered’ approach. The present work discusses the implementation of the phase field method for brittle fracture within the open-source finite element software, FEniCS. The FEniCS provides a framework for the automated solutions of the partial differential equations. The details of the implementation which forms the core of the analysis are presented. The implementation is validated by solving a few benchmark problems and comparing the results with the open literature.

关键词: phase field method     FEniCS     brittle fracture     crack propagation     variational theory of fracture    

Implementation aspects of a phase-field approach for brittle fracture

G. D. HUYNH, X. ZHUANG, H. NGUYEN-XUAN

《结构与土木工程前沿(英文)》 2019年 第13卷 第2期   页码 417-428 doi: 10.1007/s11709-018-0477-3

摘要: This paper provides a comprehensive overview of a phase-field model of fracture in solid mechanics setting. We start reviewing the potential energy governing the whole process of fracture including crack initiation, branching or merging. Then, a discretization of system of equation is derived, in which the key aspect is that for the correctness of fracture phenomena, a split into tensile and compressive terms of the strain energy is performed, which allows crack to occur in tension, not in compression. For numerical analysis, standard finite element shape functions are used for both primary fields including displacements and phase field. A staggered scheme which solves the two fields of the problem separately is utilized for solution step and illustrated with a segment of Python code.

关键词: phase-field modeling     FEM     staggered scheme     fracture    

High-order phase-field model with the local and second-order max-entropy approximants

Fatemeh AMIRI

《结构与土木工程前沿(英文)》 2019年 第13卷 第2期   页码 406-416 doi: 10.1007/s11709-018-0475-5

摘要: We approximate the fracture surface energy functional based on phase-field method with smooth local maximum entropy (LME) and second-order maximum entropy (SME) approximants. The higher-order continuity of the meshfree methods such as LME and SME approximants allows to directly solve the fourth-order phase-field equations without splitting the fourth-order differential equation into two second-order differential equations. We will first show that the crack surface functional can be captured more accurately in the fourth-order model with smooth approximants such as LME, SME and B-spline. Furthermore, smaller length scale parameter is needed for the fourth-order model to approximate the energy functional. We also study SME approximants and drive the formulations. The proposed meshfree fourth-order phase-field formulation show more stable results for SME compared to LME meshfree methods.

关键词: second-order maximum entropy     local maximum entropy     second- and fourth-order phase-field models     B-spline    

A MATLAB code for the material-field series-expansion topology optimization method

《机械工程前沿(英文)》 2021年 第16卷 第3期   页码 607-622 doi: 10.1007/s11465-021-0637-3

摘要: This paper presents a MATLAB implementation of the material-field series-expansion (MFSE) topo-logy optimization method. The MFSE method uses a bounded material field with specified spatial correlation to represent the structural topology. With the series-expansion method for bounded fields, this material field is described with the characteristic base functions and the corresponding coefficients. Compared with the conventional density-based method, the MFSE method decouples the topological description and the finite element discretization, and greatly reduces the number of design variables after dimensionality reduction. Other features of this method include inherent control on structural topological complexity, crisp structural boundary description, mesh independence, and being free from the checkerboard pattern. With the focus on the implementation of the MFSE method, the present MATLAB code uses the maximum stiffness optimization problems solved with a gradient-based optimizer as examples. The MATLAB code consists of three parts, namely, the main program and two subroutines (one for aggregating the optimization constraints and the other about the method of moving asymptotes optimizer). The implementation of the code and its extensions to topology optimization problems with multiple load cases and passive elements are discussed in detail. The code is intended for researchers who are interested in this method and want to get started with it quickly. It can also be used as a basis for handling complex engineering optimization problems by combining the MFSE topology optimization method with non-gradient optimization algorithms without sensitivity information because only a few design variables are required to describe relatively complex structural topology and smooth structural boundaries using the MFSE method.

关键词: MATLAB implementation     topology optimization     material-field series-expansion method     bounded material field     dimensionality reduction    

Applying the spectral stochastic finite element method in multiple-random field RC structures

Abbas YAZDANI

《结构与土木工程前沿(英文)》 2022年 第16卷 第4期   页码 434-447 doi: 10.1007/s11709-022-0820-6

摘要: This paper uses the spectral stochastic finite element method (SSFEM) for analyzing reinforced concrete (RC) beam/slab problems. In doing so, it presents a new framework to study how the correlation length of a random field (RF) with uncertain parameters will affect modeling uncertainties and reliability evaluations. It considers: 1) different correlation lengths for uncertainty parameters, and 2) dead and live loads as well as the elasticity moduli of concrete and steel as a multi-dimensional RF in concrete structures. To show the SSFEM’s efficiency in the study of concrete structures and to evaluate the sensitivity of the correlation length effects in evaluating the reliability, two examples of RC beams and slabs have been investigated. According to the results, the RF correlation length is effective in modeling uncertainties and evaluating reliabilities; the longer the correlation length, the greater the dispersion range of the structure response and the higher the failure probability.

关键词: uncertainty     spectral stochastic finite element method     correlation length     reliability assessment     reinforced concrete beam/slab    

Multiscale stochastic finite element method on random field modeling of geotechnical problems – a fast

Xi F. XU

《结构与土木工程前沿(英文)》 2015年 第9卷 第2期   页码 107-113 doi: 10.1007/s11709-014-0268-4

摘要: The Green-function-based multiscale stochastic finite element method (MSFEM) has been formulated based on the stochastic variational principle. In this study a fast computing procedure based on the MSFEM is developed to solve random field geotechnical problems with a typical coefficient of variance less than 1. A unique fast computing advantage of the procedure enables computation performed only on those locations of interest, therefore saving a lot of computation. The numerical example on soil settlement shows that the procedure achieves significant computing efficiency compared with Monte Carlo method.

关键词: multiscale     finite element     settlement     perturbation     random field     geotechnical    

广域电磁法和拟流场法精细探测技术——以井工一矿水害探测为例 Article

何继善

《工程(英文)》 2018年 第4卷 第5期   页码 667-675 doi: 10.1016/j.eng.2018.09.006

摘要:

井工一矿存在严重的老空区和水害。以往的单一勘探方法,如地震法、直流电法、音频大地电磁法、可控源音频大地电磁法、瞬变电磁法等,均未能探明老采空区范围和水害赋存情况。为了解决这个难题,联合采用广域电磁法和井- 地拟流场法的三位一体立体式探测技术,并利用三维反演电阻率资料精准获取富水区域和采空区的位置,确定了不同层位水的连通性,为井工一矿的安全生产提供了可靠的技术保障。结果合理、成效显著,释放了近4 km2 的可采面积。

关键词: 广域电磁法     拟流场法     采空区     富水性     精细探测    

A review on different theoretical models of electrocaloric effect for refrigeration

《能源前沿(英文)》 2023年 第17卷 第4期   页码 478-503 doi: 10.1007/s11708-023-0884-6

摘要: The performance parameters for characterizing the electrocaloric effect are isothermal entropy change and the adiabatic temperature change, respectively. This paper reviews the electrocaloric effect of ferroelectric materials based on different theoretical models. First, it provides four different calculation scales (the first-principle-based effective Hamiltonian, the Landau-Devonshire thermodynamic theory, phase-field simulation, and finite element analysis) to explain the basic theory of calculating the electrocaloric effect. Then, it comprehensively reviews the recent progress of these methods in regulating the electrocaloric effect and the generation mechanism of the electrocaloric effect. Finally, it summarizes and anticipates the exploration of more novel electrocaloric materials based on the framework constructed by the different computational methods.

关键词: electrocaloric effect     effective Hamiltonian     phase-field modeling     different theoretical models    

Scaled boundary finite element method with exact defining curves for two-dimensional linear multi-field

Jaroon RUNGAMORNRAT, Chung Nguyen VAN

《结构与土木工程前沿(英文)》 2019年 第13卷 第1期   页码 201-214 doi: 10.1007/s11709-018-0488-0

摘要: This paper presents an efficient and accurate numerical technique based upon the scaled boundary finite element method for the analysis of two-dimensional, linear, second-order, boundary value problems with a domain completely described by a circular defining curve. The scaled boundary finite element formulation is established in a general framework allowing single-field and multi-field problems, bounded and unbounded bodies, distributed body source, and general boundary conditions to be treated in a unified fashion. The conventional polar coordinates together with a properly selected scaling center are utilized to achieve the exact description of the circular defining curve, exact geometry of the domain, and exact spatial differential operators. Standard finite element shape functions are employed in the discretization of both trial and test functions in the circumferential direction and the resulting eigenproblem is solved by a selected efficient algorithm. The computational performance of the implemented procedure is then fully investigated for various scenarios to demonstrate the accuracy in comparison with standard linear elements.

关键词: multi-field problems     defining curve     exact geometry     general boundary conditions     SBFEM    

Two-phase early prediction method for remaining useful life of lithium-ion batteries based on a neural

《能源前沿(英文)》 doi: 10.1007/s11708-023-0906-4

摘要: Lithium-ion batteries (LIBs) are widely used in transportation, energy storage, and other fields. The prediction of the remaining useful life (RUL) of lithium batteries not only provides a reference for health management but also serves as a basis for assessing the residual value of the battery. In order to improve the prediction accuracy of the RUL of LIBs, a two-phase RUL early prediction method combining neural network and Gaussian process regression (GPR) is proposed. In the initial phase, the features related to the capacity degradation of LIBs are utilized to train the neural network model, which is used to predict the initial cycle lifetime of 124 LIBs. The Pearson coefficient’s two most significant characteristic factors and the predicted normalized lifetime form a 3D space. The Euclidean distance between the test dataset and each cell in the training dataset and validation dataset is calculated, and the shortest distance is considered to have a similar degradation pattern, which is used to determine the initial Dual Exponential Model (DEM). In the second phase, GPR uses the DEM as the initial parameter to predict each test set’s early RUL (ERUL). By testing four batteries under different working conditions, the RMSE of all capacity estimation is less than 1.2%, and the accuracy percentage (AP) of remaining life prediction is more than 98%. Experiments show that the method does not need human intervention and has high prediction accuracy.

关键词: lithium-ion batteries     RUL prediction     double exponential model     neural network     Gaussian process regression (GPR)    

Influence of advanced engineering measures on displacement and stress field of surrounding rock in tunnels

《结构与土木工程前沿(英文)》 doi: 10.1007/s11709-023-0966-x

摘要: Based on significant improvements in engineering materials, three advanced engineering measures have been proposed—super anchor cables, high-strength concrete anti-fault caverns, and grouting modification using high-strength concrete-to resist fault dislocation in the surrounding rock near tunnels crossing active strike-slip faults. Moreover, single- or multiple-joint advanced engineering measures form the local rock mass-anti-fault (LRAF) method. A numerical method was used to investigate the influence of LRAF methods on the stress and displacement fields of the surrounding rock, and the anti-fault effect was evaluated. Finally, the mechanism of action of the anchor cable was verified using a three-dimensional numerical model. The numerical results indicated that the anchor cable and grouting modification reduced the displacement gradient of the local surrounding rock near the tunnels crossing fault. Furthermore, anchor cable and grouting modifications changed the stress field of the rock mass in the modified area. The tensile stress field of the rock mass in the modified anchor cable area was converted into a compressive stress field. The stress field in the modified grouting area changed from shear stress in the fault slip direction to tensile stress in the axial tunnel direction. The anti-fault cavern resisted the dislocation displacement and reduced the maximum dislocation magnitude, displacement gradient, and shear stress. Among the three advanced engineering measures, the anchor cable was the core of the three advanced engineering measures. An anchor cable, combined with other LRAF measures, can form an artificial safety island at the cross-fault position of the rock mass to protect the tunnel. The research results provide a new supporting idea for the surrounding rock of tunnels crossing active strike-slip faults.

关键词: anti-fault effect     engineering measures     LRAF method     stress and displacement field     tunnel-crossing active faults    

Design and optimization of reactive distillation: a review

《化学科学与工程前沿(英文)》 2022年 第16卷 第6期   页码 799-818 doi: 10.1007/s11705-021-2128-9

摘要: Reactive distillation process, a representative process intensification technology, has been widely applied in the chemical industry. However, due to the strong interaction between reaction and separation, the extension of reactive distillation technology is restricted by the difficulties in process analysis and design. To overcome this problem, the design and optimization of reactive distillation have been widely studied and illustrated for plenty of reactive mixtures over the past three decades. These design and optimization methods of the reactive distillation process are classified into three categories: graphical, optimization-based, and evolutionary/heuristic methods. The primary objective of this article is to provide an up-to-date review of the existing design and optimization methods. Desired and output information, advantages and limitations of each method are stated, the modification and development for original methodologies are also reviewed. Perspectives on future research on the design and optimization of reactive distillation method are proposed for further research.

关键词: reactive distillation     process intensification     design method     reactive phase diagram     optimization algorithm    

Design method and magnetic field analysis of axial-magnetized permanent magnet micromotor

YANG Jiewei, WU Yihui, JIA Hongguang, ZHANG Ping, WANG Shurong

《机械工程前沿(英文)》 2007年 第2卷 第3期   页码 318-322 doi: 10.1007/s11465-007-0056-0

摘要: To investigate the impact of size on its performance in designing an axial-magnetized permanent magnet micro motor, the finite element method is adopted to simulate the magnetic field of the dual rotor motor, and the flux density wave form distributed in the airgap is obtained. The influence of the external dimensions, pole numbers and magnet thicknesses of the rotor, and the airgap distances on the flux density, are analyzed and analytical results are given. With the increase of the airgap distance, the flux density under more poles reduces more quickly than under fewer poles. With the increase of the magnet thickness, the flux density is a rising curve, and after the magnet thickness attains a certain point, the flux density is almost a constant. While reducing the diameter of the rotor, the decrease of the flux density slows down as magnet thickness is reduced. To avoid having a seriously distorted waveform, the distance between inner and outer radii of the rotor must be larger than 1.5 millimeter. Results of the magnetic field analysis can guide a microminiaturization of the motor. Moreover, the results are analyzed theoretically and the simulated values are almost consistent with the experimental values.

关键词: axial-magnetized permanent     diameter     constant     certain     magnetic    

membranes with micro-nano composite structure using a facile atomization-assisted nonsolvent induced phaseseparation method

《化学科学与工程前沿(英文)》 2022年 第16卷 第8期   页码 1268-1280 doi: 10.1007/s11705-022-2143-5

摘要: The micro-nano composite structure can endow separation membranes with special surface properties, but it often has the problems of inefficient preparation process and poor structural stability. In this work, a novel atomization-assisted nonsolvent induced phase separation method, which is also highly efficient and very simple, has been developed. By using this method, a bicontinuous porous microfiltration membrane with robust micro-nano composite structure was obtained via commercially available polymers of polyacrylonitrile and polyvinylpyrrolidone. The formation mechanism of the micro-nano composite structure was proposed. The microphase separation of polyacrylonitrile and polyvinylpyrrolidone components during the atomization pretreatment process and the hydrogen bonding between polyacrylonitrile and polyvinylpyrrolidone molecules should have resulted in the nano-protrusions on the membrane skeleton. The membrane exhibits superhydrophilicity in air and superoleophobicity underwater. The membrane can separate both surfactant-free and surfactant-stabilized oil-in-water emulsions with high separation efficiency and permeation flux. With excellent antifouling property and robust microstructure, the membrane can easily be recycled for long-term separation. Furthermore, the scale-up verification from laboratory preparation to continuous production has been achieved. The simple, efficient, cost-effective preparation method and excellent membrane properties indicate the great potential of the developed membranes in practical applications.

关键词: atomization     nonsolvent induced phase separation     bicontinuous porous structure     micro-nano composite structure     oil-water separation    

一种用于抑制相移误差和零级串扰的相移算法通用设计方法 None

Chao FANG, Yang XIANG, Ke-qi QI

《信息与电子工程前沿(英文)》 2018年 第19卷 第6期   页码 809-814 doi: 10.1631/FITEE.1601692

摘要: 为降低零级串扰和相移误差对光栅横向剪切干涉仪波前复原精度的影响,进一步提升光栅横向剪切干涉仪检测光刻镜头系统波像差精度,推导出一种设计光栅剪切干涉相移算法的一般表达式,给出相移算法的具体设计方法。根据该表达式和设计方法,可以针对不同的零级串扰和相移误差建立相应的4种相移算法,实现高精度系统波像差检测。同时设计和评价了一种新的13步相移算法,结果证明所推导的一般表达式的有效性和先进性。

关键词: 测量;横向剪切干涉仪;相移算法;相位复原    

标题 作者 时间 类型 操作

A FEniCS implementation of the phase field method for quasi-static brittle fracture

HIRSHIKESH, Sundararajan NATARAJAN, Ratna Kumar ANNABATTULA

期刊论文

Implementation aspects of a phase-field approach for brittle fracture

G. D. HUYNH, X. ZHUANG, H. NGUYEN-XUAN

期刊论文

High-order phase-field model with the local and second-order max-entropy approximants

Fatemeh AMIRI

期刊论文

A MATLAB code for the material-field series-expansion topology optimization method

期刊论文

Applying the spectral stochastic finite element method in multiple-random field RC structures

Abbas YAZDANI

期刊论文

Multiscale stochastic finite element method on random field modeling of geotechnical problems – a fast

Xi F. XU

期刊论文

广域电磁法和拟流场法精细探测技术——以井工一矿水害探测为例

何继善

期刊论文

A review on different theoretical models of electrocaloric effect for refrigeration

期刊论文

Scaled boundary finite element method with exact defining curves for two-dimensional linear multi-field

Jaroon RUNGAMORNRAT, Chung Nguyen VAN

期刊论文

Two-phase early prediction method for remaining useful life of lithium-ion batteries based on a neural

期刊论文

Influence of advanced engineering measures on displacement and stress field of surrounding rock in tunnels

期刊论文

Design and optimization of reactive distillation: a review

期刊论文

Design method and magnetic field analysis of axial-magnetized permanent magnet micromotor

YANG Jiewei, WU Yihui, JIA Hongguang, ZHANG Ping, WANG Shurong

期刊论文

membranes with micro-nano composite structure using a facile atomization-assisted nonsolvent induced phaseseparation method

期刊论文

一种用于抑制相移误差和零级串扰的相移算法通用设计方法

Chao FANG, Yang XIANG, Ke-qi QI

期刊论文