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Statistical Multiscale Analysis of Transient Conduction and Radiation Heat Transfer Problem in Random Inhomogeneous Porous Materials
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作者 Yiqiang Li Liang Ma +3 位作者 Zhiqiang Yang xiaofei guan Yufeng Nie Zihao Yang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2018年第4期1-24,共24页
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 multi... 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 proposed.In 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 contributions.Besides,a numerical algorithm based on the statistical multiscale method is given in details.Numerical 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. 展开更多
关键词 STATISTICAL multiscale analysis method transient heat conduction PROBLEM nonlinear radiation BOUNDARY condition RANDOM porous materials
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Stochastic Second-Order Two-Scale Method for Predicting the Mechanical Properties of Composite Materials with Random Interpenetrating Phase
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作者 Hao Dong Zihao Yang +1 位作者 xiaofei guan Zhiqiang Yang 《Communications in Mathematical Research》 CSCD 2020年第2期193-210,共18页
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 phase.Firstly,based on random morphology... 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 phase.Firstly,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 constituents.Then,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 method.Finally,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. 展开更多
关键词 Mechanical properties stochastic second-order two-scale method random interpenetrating phase composites strength properties
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Multiscale analysis-based peridynamic simulation of fracture in porous media
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作者 Zihao YANG Shangkun SHEN +2 位作者 xiaofei guan Xindang HE Junzhi CUI 《Frontiers of Structural and Civil Engineering》 SCIE EI CSCD 2024年第1期1-13,共13页
The simulation of fracture in large-scale structures made of porous media remains a challenging task.Current techniques either assume a homogeneous model,disregarding the microstructure characteristics,or adopt a micr... The simulation of fracture in large-scale structures made of porous media remains a challenging task.Current techniques either assume a homogeneous model,disregarding the microstructure characteristics,or adopt a micro-mechanical model,which incurs an intractable computational cost due to its complex stochastic geometry and physical properties,as well as its nonlinear and multiscale features.In this study,we propose a multiscale analysis-based dual-variable-horizon peridynamics(PD)model to efficiently simulate macroscopic structural fracture.The influence of microstructures in porous media on macroscopic structural failure is represented by two PD parameters:the equivalent critical stretch and micro-modulus.The equivalent critical stretch is calculated using the microscale PD model,while the equivalent micro-modulus is obtained through the homogenization method and energy density equivalence between classical continuum mechanics and PD models.Numerical examples of porous media with various microstructures demonstrate the validity,accuracy,and efficiency of the proposed method. 展开更多
关键词 porous media multiscale variable-horizon peridynamic equivalent critical stretch equivalent micro-modulus
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Learning Invariant Representation of Multiscale Hyperelastic Constitutive Law from Sparse Experimental Data
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作者 Rui He Junzhi Cui +2 位作者 Zihao Yang Jieqiong Zhang xiaofei guan 《Communications in Computational Physics》 SCIE 2023年第7期392-417,共26页
Constitutive modeling of heterogeneous hyperelastic materials is still a challenge due to their complex and variable microstructures.We propose a multiscale datadriven approach with a hierarchical learning strategy fo... Constitutive modeling of heterogeneous hyperelastic materials is still a challenge due to their complex and variable microstructures.We 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 materials.Based 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 microstructures.And a dense stress-stretch relation dataset is generated by training a neural network through the FE results.Further,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 model.Finally,the multiscale model is hierarchically trained,cross-validated and tested using the experimental data of cord-rubber composite materials with different microstructures.The proposed multiscale model provides a convenient and general methodology for constitutive modeling of heterogeneous hyperelastic materials. 展开更多
关键词 Heterogeneous hyperelastic materials data-driven approach multiscale generic constitutive model physics-constrained
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A Normalizing Field Flow Induced Two-Stage Stochastic Homogenization Method for Random Composite Materials
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作者 Zihao Yang Xintong Wang +2 位作者 xiaofei guan Jizu Huang Xixin Wu 《Communications in Computational Physics》 SCIE 2023年第8期787-812,共26页
The traditional stochastic homogenization method can obtain homogenized solutions of elliptic problems with stationary random coefficients.However,many random composite materials in scientific and engineering computin... The traditional stochastic homogenization method can obtain homogenized solutions of elliptic problems with stationary random coefficients.However,many random composite materials in scientific and engineering computing do not satisfy the stationary assumption.To 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 coefficients.By 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 problems.Without the stationary assumption,the number of cell problems is large and the corresponding computational cost is high.To 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 method.Numerical 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. 展开更多
关键词 Two-stage stochastic homogenization normalizing field flows multi-modes Monte Carlo method random composite materials non-stationary random
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Multi-Modes Multiscale Approach of Heat Transfer Problems in Heterogeneous Solids with Uncertain Thermal Conductivity
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作者 Shan Zhang Zihao Yang xiaofei guan 《Advances in Applied Mathematics and Mechanics》 SCIE 2023年第1期69-93,共25页
Stochastic temperature distribution should be carefully inspected in the thermal-failure design of heterogeneous solids with unexpected random energy excitations.Stochastic multiscale modeling for these problems invol... Stochastic temperature distribution should be carefully inspected in the thermal-failure design of heterogeneous solids with unexpected random energy excitations.Stochastic multiscale modeling for these problems involve multiscale and highdimensional uncertain thermal parameters,which remains limitation of prohibitive computation.In 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 analysis.Thus,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 systems.In addition,the convergence analysis is established,and the optimal error estimates are derived.Finally,several typical random fluctuations on multiscale thermal conductivity are considered to validate the theoretical results in the numerical examples.The numerical results indicate that the multi-modes multiscale approach is a robust integrated method with the excellent performance. 展开更多
关键词 Stochastic multiscale heat transfer problems uncertainty quantification MCEMGMsFEM multimodes expansion
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CONVERGENCE AND SUPERCONVERGENCE ANALYSIS OF LAGRANGE RECTANGULAR ELEMENTS WITH ANY ORDER ON ARBITRARY RECTANGULAR MESHES 被引量:1
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作者 Mingxia Li xiaofei guan Shipeng Mao 《Journal of Computational Mathematics》 SCIE CSCD 2014年第2期169-182,共14页
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... 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. 展开更多
关键词 Lagrange interpolation Anisotropic error bounds Arbitrary rectangular meshes Orthogonal expansion Superconvergence.
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An Improved Peridynamic Model with Energy-Based Micromodulus Correction Method for Fracture in Particle Reinforced Composites 被引量:1
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作者 Zihao Yang Shaoqi Zheng +2 位作者 Fei Han Shangkun Shen xiaofei guan 《Communications in Computational Physics》 SCIE 2022年第7期424-449,共26页
We introduce an improved bond-based peridynamic(BPD)model for simulating brittle fracture in particle reinforced composites based on a micromodulus correction approach.In the peridynamic(PD)constitutive model of parti... We introduce an improved bond-based peridynamic(BPD)model for simulating brittle fracture in particle reinforced composites based on a micromodulus correction approach.In 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 approach.The 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 theory.The algorithm procedure for the improved BPD model based on the finite element/discontinuous Galerkin finite element method is brought forward in detail.Several 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 composites.Additionally,the impact of distribution,shape and size of particles on the fractures of composite materials are also investigated.Numerical results demonstrate that the improved BPD model can effectively be used to analyze the fracture in particle reinforced composites. 展开更多
关键词 Particle reinforced composite peridynamics bonds micromodulus correction FRACTURE crack growth path
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