Multiscale Nonlinear Thermo-Mechanical Coupling Analysis of Composite Structures with Quasi-Periodic Properties

This paper reports a multiscale analysis method to predict the thermomechanical coupling performance of composite structures with quasi-periodic properties.In these material structures,the configurations are periodic,and the material coefficients are quasi-periodic,i.e.,they depend not only on the microscale information but also on the macro location.Also,a mutual interaction between displacement and temperature fields is considered in the problem,which is our particular interest in this study.The multiscale asymptotic expansions of the temperature and displacement fields are constructed and associated error estimation in nearly pointwise sense is presented.Then,a finite element-difference algorithm based on the multiscale analysis method is brought forward in detail.Finally,some numerical examples are given.And the numerical results show that the multiscale method presented in this paper is effective and reliable to study the nonlinear thermo-mechanical coupling problem of composite structures with quasiperiodic properties.

Global Top Ten Engineering Achievements 2022

Engineering is an integrated activity in which humans create or change the characters of things by using science and technology and employing resources in an organized manner in order to survive,develop,and achieve specific purposes[1].From the pyramids in ancient Egypt to the Eiffel Tower in modern Paris,and from the Apollo Manned Lunar Landing Project in the United States to the Three Gorges Key Water Conservancy Project in China,human engineering practices profoundly change the planet we live on and are constantly enriching and expanding our world.

Global Top Ten Engineering Achievements 2021

Engineering is a direct productive force for mankind to change the world.Throughout the ages,mankind has created countless amazing engineering achievements,promoting profound changes in the whole society and pushing human civilization to a new higher stage[1].To motivate engineering progress and innovation and draw global attention to engineering science and technology.

Macroscopic damping model for structural dynamics with random polycrystalline configurations

In this paper the macroscopic damping model for dynamical behavior of the structures with random polycrystalline configurations at micro-nano scales is established. First, the global motion equation of a crystal is decomposed into a set of motion equations with independent single degree of freedom （SDOF） along normal discrete modes, and then damping behavior is introduced into each SDOF motion. Through the interpolation of discrete modes, the continuous representation of damping effects for the crystal is obtained. Second, from energy conservation law the expression of the damping coefficient is derived, and the approximate formula of damping coefficient is given. Next, the continuous damping coefficient for polycrystalline cluster is expressed, the continuous dynamical equation with damping term is obtained, and then the concrete damping coefficients for a polycrystalline Cu sample are shown. Finally, by using statistical two-scale homogenization method, the macroscopic homogenized dynamical equation containing damping term for the structures with random polycrystalline configurations at micro-nano scales is set up.

2023全球十大工程成就发布

Engineering benefits humanity,and technology creates the future.Linking scientific discoveries,technological inventions,and industrial innovation,engineering technology is an important driving force for economic and social development and a key support for addressing global risks and challenges.Today,in the early 21st century,a new round of technological revolution and industrial transformation is continuing to evolve,and engineering technology innovation has entered a dense and active cycle,especially in fields such as information technology,energy technology,biotechnology,advanced manufacturing,and space exploration.Groundbreaking achievements in engineering innovation are constantly emerging.

Second-order two-scale computational method for ageing linear viscoelastic problem in composite materials with periodic structure

The correspondence principle is an important mathematical technique to compute the non-ageing linear viscoelastic problem as it allows to take advantage of the computational methods originally developed for the elastic case. However, the correspon- dence principle becomes invalid when the materials exhibit ageing. To deal with this problem, a second-order two-scale （SOTS） computational method in the time domain is presented to predict the ageing linear viscoelastic performance of composite materials with a periodic structure. First, in the time domain, the SOTS formulation for calcu- lating the effective relaxation modulus and displacement approximate solutions of the ageing viscoelastic problem is formally derived. Error estimates of the displacement ap- proximate solutions for SOTS method are then given. Numerical results obtained by the SOTS method are shown and compared with those by the finite element method in a very fine mesh. Both the analytical and numerical results show that the SOTS computational method is feasible and efficient to predict the ageing linear viscoelastic performance of composite materials with a periodic structure.

Dynamic thermo-mechanical coupled simulation of statistically inhomogeneous materials by statistical second-order two-scale method

In this paper,a statistical second-order twoscale（SSOTS） method is developed to simulate the dynamic thcrmo-mechanical performances of the statistically inhomogeneous materials.For this kind of composite material,the random distribution characteristics of particles,including the shape,size,orientation,spatial location,and volume fractions,are all considered.Firstly,the repre.sentation for the microscopic configuration of the statistically inhomogeneous materials is described.Secondly,the SSOTS formulation for the dynamic thermo-mechanical coupled problem is proposed in a constructive way,including the cell problems,effective thermal and mechanical parameters,homogenized problems,and the SSOTS formulas of the temperatures,displacements,heat flux densities and stresses.And then the algorithm procedure corresponding to the SSOTS method is brought forward.The numerical results obtained by using the SSOTS algorithm are compared with those by classical methods.In addition,the thermo-mechanical coupling effect is studied by comparing the results of coupled case with those of uncoupled case.It demonstrates that the coupling effect on the temperatures,heat flux densities,displacements,and stresses is very distinct.The results show that the SSOTS method is valid to predict the dynamic thermo-mechanical coupled performances of statistically inhomogeneous materials.

Multiscale analysis-based peridynamic simulation of fracture in porous media

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.

Multiscale method for identifying and marking the multiform fractures from visible-light rock-mass images

Multiform fractures have a direct impact on the mechanical performance of rock masses.To accurately identify multiform fractures,the distribution patterns of grayscale and the differential features of fractures in their neighborhoods are summarized.Based on this,a multiscale processing algorithm is proposed.The multiscale process is as follows.On the neighborhood of pixels,a grayscale continuous function is constructed using bilinear interpolation,the smoothing of the grayscale function is realized by Gaussian local filtering,and the grayscale gradient and Hessian matrix are calculated with high accuracy.On small-scale blocks,the pixels are classified by adaptively setting the grayscale threshold to identify potential line segments and mini-fillings.On the global image,potential line segments and mini-fillings are spliced together by progressing the block frontier layer-by-layer to identify and mark multiform fractures.The accuracy of identifying multiform fractures is improved by constructing a grayscale continuous function and adaptively setting the grayscale thresholds on small-scale blocks.And the layer-by-layer splicing algorithm is performed only on the domain of the 2-layer small-scale blocks,reducing the complexity.By using rock mass images with different fracture types as examples,the identification results show that the proposed algorithm can accurately identify the multiform fractures,which lays the foundation for calculating the mechanical parameters of rock masses.

Prediction on nonlinear mechanical performance of random particulate composites by a statistical second-order reduced multiscale approach

A novel statistical second-order reduced multiscale(SSRM)approach is established for nonlinear composite materials with random distribution of grains.For these composites considered in this work,the complex microstructure of grains,including their shape,orientation,size,spatial distribution,volume fraction and so on,results in changing of the macroscopic mechanical properties.The first-and second-order unit cell functions based on two-scale asymptotic expressions are constructed at first.Then,the expected homogenized parameters are defined,and the nonlinear homogenization equation on global structure is established,successively.Further,an effective reduced model format for analyzing second-order nonlinear unit cell problem with less computation cost is introduced in detail.Finally,some numerical examples for the materials with varying distribution models are evaluated and compared with the data by theoretical models and experimental results.These examples illustrate that the proposed SSRM approaches are effective for predicting the macroscopic properties of the random composite materials and supply a potential application in actual engineering computation.

A Multiscale Algorithm for Heat Conduction-Radiation Problems in Porous Materials with Quasi-Periodic Structures

This paper develops a second-order multiscale asymptotic analysis and numerical algorithms for predicting heat transfer performance of porous materials with quasi-periodic structures.In these porousmaterials,they have periodic configurations and associated coefficients are dependent on the macro-location.Also,radiation effect at microscale has an important influence on the macroscopic temperature fields,which is our particular interest in this study.The characteristic of the coupled multiscale model between macroscopic scale and microscopic scale owing to quasi-periodic structures is given at first.Then,the second-ordermultiscale formulas for solving temperature fields of the nonlinear problems are constructed,and associated explicit convergence rates are obtained on some regularity hypothesis.Finally,the corresponding finite element algorithms based on multiscale methods are brought forward and some numerical results are given in detail.Numerical examples including different coefficients are given to illustrate the efficiency and stability of the computational strategy.They show that the expansions to the second terms are necessary to obtain the thermal behavior precisely,and the local and global oscillations of the temperature fields are dependent on the microscopic and macroscopic part of the coefficients respectively.

Second-Order Two-Scale Analysis Method for the Heat Conductive Problem with Radiation Boundary Condition in Periodical Porous Domain

In this paper a second-order two-scale(SOTS)analysismethod is developed for a static heat conductive problem in a periodical porous domain with radiation boundary condition on the surfaces of cavities.By using asymptotic expansion for the temperature field and a proper regularity assumption on the macroscopic scale,the cell problem,effective material coefficients,homogenization problem,first-order correctors and second-order correctors are obtained successively.The characteristics of the asymptotic model is the coupling of the cell problems with the homogenization temperature field due to the nonlinearity and nonlocality of the radiation boundary condition.The error estimation is also obtained for the original solution and the SOTS’s approximation solution.Finally the corresponding finite element algorithms are developed and a simple numerical example is presented.

A Mixed Wavelet-Learning Method of Predicting Macroscopic Effective Heat Transfer Conductivities of Braided Composite Materials

In this paper,a novel mixed wavelet-learning method is developed for predicting macroscopic effective heat transfer conductivities of braided composite materials with heterogeneous thermal conductivity.This innovative methodology integrates respective superiorities of multi-scale modeling,wavelet transform and neural networks together.By the aid of asymptotic homogenization method(AHM),off-line multi-scalemodeling is accomplished for establishing thematerial databasewith highdimensional and highly-complexmappings.Themulti-scalematerial database and the wavelet-learning strategy ease the on-line training of neural networks,and enable us to efficiently build relatively simple networks that have an essentially increasing capacity and resisting noise for approximating the high-complexity mappings.Moreover,it should be emphasized that the wavelet-learning strategy can not only extract essential data characteristics from the material database,but also achieve a tremendous reduction in input data of neural networks.The numerical experiments performed using multiple 3D braided composite models verify the excellent performance of the presentedmixed approach.The numerical results demonstrate that themixedwaveletlearningmethodology is a robustmethod for computing themacroscopic effective heat transfer conductivities with distinct heterogeneity patterns.The presentedmethod can enormously decrease the computational time,and can be further expanded into estimating macroscopic effective mechanical properties of braided composites.

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

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.