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The twoscale asymptotic error analysis for piezoelectric problems in the quasi-periodic structure

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Science China(Physics,Mechanics & Astronomy) 2013年第10期56卷 1844-1853页

作者： FENG YongPing DENG MingXiang guan xiaofei School of Mathematics and Information Sciences Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes Guangzhou University Guangzhou 510006 China Department of Mathematics University of California San Diego 92093 USA Department of Mathematics Tongji University Shanghai 200092 China

Applications for piezoelectric effect have grown rapidly, and piezoelectric materials play important roles in countless areas of modem life. By means of twoscale method and coupled boundary layer, some new kinds of twoscale asymptotic expansions for solutions to the electrical potential and the displacement in quasi-periodic structure under coupled piezoelectric effect are derived, and the homogenization constants of piezoelectric materials are presented. The coupled twoscale relation between the electrical potential and the displacement is set up, and some improved asymptotic error estimates are analyzed.

关键词： twoscale method piezoelectricity quasi-periodic structure homogenization constants

CONVERGENCE AND SUPERCONVERGENCE ANALYSIS OF LAGRANGE RECTANGULAR ELEMENTS WITH ANY ORDER ON ARBITRARY RECTANGULAR MESHES

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Journal of Computational Mathematics 2014年第2期32卷 169-182页

作者： Mingxia Li xiaofei guan Shipeng Mao School of Science China University of Geosciences (Beijing) Beijing 100083 China Department of Mathematics Tongji University Shanghai 200092 China LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

This paper is to study the convergence and superconvergence of rectangular finite elements under anisotropic meshes. By using of the orthogonal expansion method, an anisotropic Lagrange interpolation is presented. The family of Lagrange rectangular elements with all the possible shape function spaces are considered, which cover the Intermediate families, Tensor-product families and Serendipity families. It is shown that the anisotropic interpolation error estimates hold for any order Sobolev norm. We extend the convergence and superconvergence result of rectangular finite elements to arbitrary rectangular meshes in a unified way.

关键词： Lagrange interpolation Anisotropic error bounds Arbitrary rectangular meshes,Orthogonal expansion Superconvergence.

Design of optimum solid oxide membrane electrolysis cells for metals production

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Progress in Natural Science:Materials International 2015年第6期25卷 591-594页

作者： xiaofei guan Uday B.Pal Division of Materials Science and Engineering Boston University Department of Mechanical Engineering Boston University John A.Paulson School of Engineering and Applied Sciences Harvard University

Oxide to metal conversion is one of the most energy-intensive steps in the value chain for metals *** oxide membrane(SOM)electrolysis process provides a general route for directly reducing various metal oxides to their respective metals,alloys,or *** of its lower energy use and ability to use inert anode resulting in zero carbon emission,SOM electrolysis process emerges as a promising technology that can replace the state-of-the-art metals production *** this paper,a careful study of the SOM electrolysis process using equivalent DC circuit modeling is performed and correlated to the experimental results.A discussion on relative importance of each resistive element in the circuit and on possible ways of lowering the rate-limiting resistive elements provides a generic guideline for designing optimum SOM electrolysis cells.

关键词： Electrolysis Solid oxide Membranes Metals production Environmentally benign

Multi-Modes Multiscale Approach of Heat Transfer Problems in Heterogeneous Solids with Uncertain Thermal Conductivity

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Advances in Applied Mathematics and Mechanics 2023年第1期15卷 69-93页

作者： Shan Zhang Zihao Yang xiaofei guan College of Mathematics and Physics Shanghai University of Electric PowerShanghai 200090China School of Mathematics and Statistics Northwestern Polytechnical UniversityXi’anShanxi 710072China School of Mathematical Sciences Tongji UniversityShanghai 200092China

Stochastic temperature distribution should be carefully inspected in the thermal-failure design of heterogeneous solids with unexpected random energy *** multiscale modeling for these problems involve multiscale and highdimensional uncertain thermal parameters,which remains limitation of prohibitive *** this paper,we propose a multi-modes based constrained energy minimization generalized multiscale finite element method(MCEM-GMsFEM),which can transform the original stochastic multiscale model into a series of recursive multiscale models sharing the same deterministic material parameters by multiscale ***,MCEM-GMsFEM reveals an inherent low-dimensional representation in random space,and is designed to effectively reduce the complexity of repeated computation of discretized multiscale *** addition,the convergence analysis is established,and the optimal error estimates are ***,several typical random fluctuations on multiscale thermal conductivity are considered to validate the theoretical results in the numerical *** numerical results indicate that the multi-modes multiscale approach is a robust integrated method with the excellent performance.

关键词： Stochastic multiscale heat transfer problems uncertainty quantification MCEMGMsFEM multimodes expansion

A Normalizing Field Flow Induced Two-Stage Stochastic Homogenization Method for Random Composite Materials

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Communications in Computational Physics 2023年第8期34卷 787-812页

作者： Zihao Yang Xintong Wang xiaofei guan Jizu Huang Xixin Wu School of Mathematics and Statistics Northwestern Polytechnical UniversityXi’an 710072China Institute of Mathematics Henan Academy of SciencesZhengzhou 450046China MOE Key Laboratory for Complexity Science in Aerospace Northwestern Polytechnical UniversityXi’an 710072China School of Mathematical Sciences Tongji UniversityShanghai 200092China LSEC Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

The traditional stochastic homogenization method can obtain homogenized solutions of elliptic problems with stationary random ***,many random composite materials in scientific and engineering computing do not satisfy the stationary *** overcome the difficulty,we propose a normalizing field flow induced two-stage stochastic homogenization method to efficiently solve the random elliptic problem with non-stationary *** applying the two-stage stochastic homogenization method,the original elliptic equation with random and fast oscillatory coefficients is approximated as an equivalent elliptic equation,where the equivalent coefficients are obtained by solving a set of cell *** the stationary assumption,the number of cell problems is large and the corresponding computational cost is *** improve the efficiency,we apply the normalizing field flow model to learn a reference Gaussian field for the random equivalent coefficients based on a small amount of data,which is obtained by solving the cell problems with the finite element *** results demonstrate that the newly proposed method is efficient and accurate in tackling high dimensional partial differential equations in composite materials with complex random microstructures.

关键词： Two-stage stochastic homogenization normalizing field flows multi-modes Monte Carlo method random composite materials non-stationary random

An Improved Peridynamic Model with Energy-Based Micromodulus Correction Method for Fracture in Particle Reinforced Composites

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Communications in Computational Physics 2022年第7期32卷 424-449页

作者： Zihao Yang Shaoqi Zheng Fei Han Shangkun Shen xiaofei guan School of Mathematics and Statistics Northwestern Polytechnical UniversityXi’an 710072China Department of Engineering Mechanics Dalian University of TechnologyDalian 116023China School of Mathematical Sciences Tongji UniversityShanghai 200092China

We introduce an improved bond-based peridynamic(BPD)model for simulating brittle fracture in particle reinforced composites based on a micromodulus correction *** the peridynamic(PD)constitutive model of particle reinforced composites,three kinds of interactive bond forces are considered,and precise definition of mechanical properties for PD bonds is essential for the fracture analysis in particle reinforced composites.A new micromodulus model of PD bonds for particle reinforced composites is proposed based on the equivalence between the elastic strain energy density of classical continuum mechanics and peridynamic model and the harmonic average *** damage of particle reinforced composites is defined locally at the level of pairwise bond,and the critical stretch criterion is described as a function of fracture energy based on the composite failure *** algorithm procedure for the improved BPD model based on the finite element/discontinuous Galerkin finite element method is brought forward in *** numerical examples are performed to test the feasibility and effectiveness of the proposed model and algorithm in analysis of elastic deformation,crack nucleation and propagation in particle reinforced ***,the impact of distribution,shape and size of particles on the fractures of composite materials are also *** results demonstrate that the improved BPD model can effectively be used to analyze the fracture in particle reinforced composites.

关键词： Particle reinforced composite peridynamics bonds micromodulus correction fracture crack growth path

Learning Invariant Representation of Multiscale Hyperelastic Constitutive Law from Sparse Experimental Data

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Communications in Computational Physics 2023年第7期34卷 392-417页

作者： Rui He Junzhi Cui Zihao Yang Jieqiong Zhang xiaofei guan School of Mathematics and Statistics Northwestern Polytechnical UniversityXi’an 710072China LSEC ICMSECAcademy of Mathematics and Systems ScienceCASBeijing 100190China Innovation Center NPU Chongqing Northwestern Polytechnical UniversityChongqing 400000China School of Mathematics Northwest UniversityXi’an 710127China School of Mathematical Sciences Tongji UniversityShanghai 200092China

Constitutive modeling of heterogeneous hyperelastic materials is still a challenge due to their complex and variable *** propose a multiscale datadriven approach with a hierarchical learning strategy for the discovery of a generic physics-constrained anisotropic constitutive model for the heterogeneous hyperelastic *** on the sparse multiscale experimental data,the constitutive artificial neural networks for hyperelastic component phases containing composite interfaces are established by the particle swarm optimization algorithm.A microscopic finite element coupled constitutive artificial neural networks solver is introduced to obtain the homogenized stress-stretch relation of heterogeneous materials with different *** a dense stress-stretch relation dataset is generated by training a neural network through the FE ***,a generic invariant representation of strain energy function(SEF)is proposed with a parameter set being implicitly expressed by artificial neural networks(SANN),which describes the hyperelastic properties of heterogeneous materials with different microstructures.A convexity constraint is imposed on the SEF to ensure that the multiscale constitutive model is physically relevant,and the ℓ_(1) regularization combined with thresholding is introduced to the loss function of SANN to improve the interpretability of this ***,the multiscale model is hierarchically trained,cross-validated and tested using the experimental data of cord-rubber composite materials with different *** proposed multiscale model provides a convenient and general methodology for constitutive modeling of heterogeneous hyperelastic materials.

关键词： Heterogeneous hyperelastic materials data-driven approach multiscale generic constitutive model physics-constrained

Statistical Multiscale Analysis of Transient Conduction and Radiation Heat Transfer Problem in Random Inhomogeneous Porous Materials

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Computer Modeling in Engineering & Sciences 2018年第4期115卷 1-24页

作者： Yiqiang Li Liang Ma Zhiqiang Yang xiaofei guan Yufeng Nie Zihao Yang Department of Applied Mathematics Northwestern Polytechnical UniversityXi’an 710072China State Key Laboratory of Solidification Processing Northwestern Polytechnical UniversityXi’an 710072China School of Astronautics Harbin Institute of TechnologyHarbin 150001China School of Mathematics Sciences Tongji UniversityShanghai 200092China

This paper is devoted to the homogenization and statistical multiscale analysis of a transient heat conduction problem in random porous materials with a nonlinear radiation boundary condition.A novel statistical multiscale analysis method based on the two-scale asymptotic expansion is *** the statistical multiscale formulations,a unified linear homogenization procedure is established and the second-order correctors are introduced for modeling the nonlinear radiative heat transfer in random perforations,which are our main ***,a numerical algorithm based on the statistical multiscale method is given in *** results prove the accuracy and efficiency of our method for multiscale simulation of transient nonlinear conduction and radiation heat transfer problem in random porous materials.

关键词： Statistical multiscale analysis method transient heat conduction problem nonlinear radiation boundary condition random porous materials

Stochastic Second-Order Two-Scale Method for Predicting the Mechanical Properties of Composite Materials with Random Interpenetrating Phase

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Communications in Mathematical Research 2020年第2期36卷 193-210页

作者： Hao Dong Zihao Yang xiaofei guan Zhiqiang Yang School of Mathematics and Statistics Xidian UniversityXi’an710071China Department of Applied Mathematics Northwestern Polytechnical UniversityXi’an710129China School of Mathematical Sciences Tongji UniversityShanghai200092China Department of Astronautic Science and Mechanics Harbin Institute of TechnologyHarbin150001China

In this paper,a stochastic second-order two-scale(SSOTS)method is proposed for predicting the non-deterministic mechanical properties of composites with random interpenetrating ***,based on random morphology description functions(RMDF),the randomness of the material properties of the constituents as well as the correlation among these random properties are fully characterized through the topologies of the ***,by virtue of multiscale asymptotic analysis,the random effective quantities such as stiffness parameters and strength parameters along with their numerical computation formulae are derived by a SSOTS strategy combined with the Monte-Carlo ***,the SSOTS method developed in this paper shows an excellent computational accuracy,and therefore present an important advance towards computationally efficient multiscale modeling frameworks considering microstructure uncertainties.

关键词： Mechanical properties stochastic second-order two-scale method random interpenetrating phase composites strength properties