渐进均匀化理论在复合材料力学性能中的应用

本文以渐进均匀化理论模型来分析碳纤维增强木质复合材料,利用插入小参数的方法把宏观和微观两尺度耦合起来,再把小参数渐进展开的力学变量代入单胞控制方程,推导研究材料的弹性模量来解方程,通过实验来验证渐进均匀化理论对复合材料力学性能的预测精度,以此来研究渐进均匀化理论的有效性。     

Multiscale computation on feedforward neural network and recurrent neural network

Homogenization methods can be used to predict the effective macroscopic properties of materials that are heterogenous at micro- or fine-scale. Among existing methods for homogenization, computational homogenization is widely used in multiscale analyses of structures and materials. Conventional computational homogenization suffers from long computing times, which substantially limits its application in analyzing engineering problems. The neural networks can be used to construct fully decoupled approaches in nonlinear multiscale methods by mapping macroscopic loading and microscopic response. Computational homogenization methods for nonlinear material and implementation of offline multiscale computation are studied to generate data set. This article intends to model the multiscale constitution using feedforward neural network (FNN) and recurrent neural network (RNN), and appropriate set of loading paths are selected to effectively predict the materials behavior along unknown paths. Applications to two-dimensional multiscale analysis are tested and discussed in detail.     

基于桩侧阻概化模式的基桩均化附加应力系数研究

基于群桩Mindlin应力解附加应力场和群桩基础变形分布特征,考虑承台和上部结构刚度对沉降变形的均化效应,在现有Mindlin解均化应力分层总和法计算群桩基础沉降基础上,提出任意布桩模式下基桩均化附加应力系数数值计算方法。针对特定侧阻分布概化模式给出不同长径比、不同桩距条件下的基桩均化附加应力系数表格,为手算群桩基础沉降所需的均化附加应力计算提供有效的简易方法。提供的均化附加应力计算方法计算群桩沉降通过工程实例验证,与Boussinesq实体深基础计算法和等效作用计算法比较,其沉降计算值与实测竣工沉降值较为接近。     

脆性岩石损伤与热传导特性的细观力学模型

 基于均匀化方法给出低孔隙率脆性岩石在热–力耦合荷载作用条件下的各向异性损伤模型和有效热传导特性模型。其中,损伤模型可考虑非等温条件下裂纹的法向压缩变形、刚度恢复以及裂纹的滑动剪胀特性,热传导特性模型可反映损伤过程中细观结构的演化以及裂纹形态、孔隙率和饱和度变化对岩石有效热传导特性的影响。讨论低孔隙率结晶岩裂纹形态和饱和度对其有效热传导特性的影响;采用瑞典Äspö闪长岩在三轴压缩条件下的应力–应变曲线验证损伤模型的有效性,并分析岩石在损伤演化过程中裂纹体积率、密度、形态、饱和度和有效热传导特性的演化规律。研究成果对于深部岩体的热–力耦合特性研究具有一定参考意义。     

层状岩体渗透特性多尺度演化模型研究

考虑层状岩体内部微裂纹、层面等不同尺度结构特征,采用两步均匀化方法,建立了层状岩体细观损伤模型与渗透特性多尺度演化模型。两步均匀化过程分别考虑了层状岩体内部细观结构与宏观结构对渗透特性的影响。层状岩体渗透特性演化模型可同时考虑微裂纹损伤扩展、滑移剪胀,层理面滑移磨损、剪胀演化特性以及微裂纹与层理面相互作用等特征,较好地反映了内部不同尺度微结构变化对其渗透特性演化的影响以及渗透特性的各向异性特征。基于该模型,通过数值模拟层状岩体中地下洞室开挖扰动过程,研究了层面倾角以及岩体强度各向异性特征对洞周围岩损伤与渗透特性演化规律的影响。研究成果对于深部层状岩体水–力耦合特性研究具有一定参考意义。     

Spatial homogenization algorithm for bridging disparities in scale between the fire and solid domains

The analysis of structures exposed to non-uniform heating from localized fires is a challenging task due to the spatially varying boundary conditions and the differences in scale between the fire simulation and solid heat transfer model. This paper presents a spatial homogenization algorithm for capturing non-uniform boundary conditions from a high-resolution fire simulation in a low-resolution finite element heat transfer model of a structure. The homogenization algorithm uses numerical integration by the trapezoid rule to calculate the equivalent thermal flux vector in the finite element heat transfer model for a spatially varying surface flux. The proposed method is compared to other approximating techniques, including averaging, sampling, and least squares methods, for a 2D heat transfer problem. The results demonstrate that the proposed homogenization algorithm converges rapidly due to the energy-equivalent representation of the thermal boundary condition. The homogenization algorithm is then implemented in a 3D heat transfer model that uses macro-level plate elements. For an application involving a horizontal plate exposed to a localized fire, the model is shown to converge to the results obtained by a solid finite element model. The homogenization algorithm combined with the plate heat transfer element proves to be an accurate and highly efficient means for analyzing structures with spatially varying thermal boundary conditions calculated by computational fluid dynamics.     

Mindlin解均化应力法计算桩基沉降及工程应用

基于群桩Mindlin应力解附加应力场和群桩基础变形分布特征,考虑承台和上部结构刚度对沉降变形的均化效应,总结了Mindlin解均化应力分层总和法计算群桩基础沉降的具体步骤细则。针对计算中具体问题,诸如压缩层计算厚度、上部结构刚度贡献、变刚度调平设计中桩类型的多样性,结合特定侧阻分布概化模式不同长径比、不同桩距条件给出基桩均化附加应力计算简易方法。应用所提供的均化附加应力计算方法计算群桩沉降,通过工程实例验证,与Boussinesq实体深基础计算法和等效作用计算法比较,其沉降计算值与实测竣工沉降值较为接近。     

考虑多尺度结构的贯通节理岩体损伤摩擦耦合模型

基于贯通节理岩体结构的多尺度特征,采用两步均匀化方法,给出了节理岩体在复杂荷载作用下的自由焓表达式,建立了节理岩体损伤摩擦耦合本构模型。模型可同时考虑岩块损伤扩展、微裂纹滑移剪胀、法向刚度恢复,节理面多阶凸起体滑移磨损、剪胀演化以及节理与岩块相互作用等特征,较好地反映岩体内部微裂纹、节理等不同尺度微结构变化对其力学特性的影响。采用Lac du Bonnet花岗岩三轴压缩试验、花岗岩节理剪切试验以及不同节理倾角与不同围压下Martinsburg板岩三轴压缩强度试验等成果对模型进行了验证,模型预测值与实测值相当吻合,论证了模型的准确性。     

Static analysis of corrugated panels using homogenization models and a cell-based smoothed mindlin plate element (CS-MIN3)

Homogenization is a promising approach to capture the behavior of complex structures like corrugated panels. It enables us to replace high-cost shell models with stiffness-equivalent orthotropic plate alternatives. Many homogenization models for corrugated panels of different shapes have been proposed. However, there is a lack of investigations for verifying their accuracy and reliability. In addition, in the recent trend of development of smoothed finite element methods, the cell-based smoothed three-node Mindlin plate element (CS-MIN3) based on the first-order shear deformation theory (FSDT) has been proposed and successfully applied to many analyses of plate and shell structures. Thus, this paper further extends the CS-MIN3 by integrating itself with homogenization models to give homogenization methods. In these methods, the equivalent extensional, bending, and transverse shear stiffness components which constitute the equivalent orthotropic plate models are represented in explicit analytical expressions. Using the results of ANSYS and ABAQUS shell simulations as references, some numerical examples are conducted to verify the accuracy and reliability of the homogenization methods for static analyses of trapezoidally and sinusoidally corrugated panels.     

A simplified two-phase macroscopic model for reinforced soils

This paper presents the formulation of a macroscopic model for reinforced soil structures in which the interface is taken into consideration as a rigid-plastic contact. The model is formulated in the framework of a so-called multiphase model recently introduced for reinforced soil masses. The proposed simplified two-phase model can be considered as an optimal solution between extremely simplified perfect bonding model on one hand, and using a third phase for the interface on the other hand, which results in a more complicated and time-consuming model. The introduced platform is implemented in a numerical code. The proposed model is evaluated by simulating (a) the failure of laboratorial plane strain compression tests; (b) the behavior of a 1-g reinforced soil retaining wall model under external loading, and (c) the deformation of a reinforced soil structure under its own weight, which has been analyzed by another homogenization approach including elastoplastic interface model. The results indicate that the deformation of reinforced soil structures can be satisfactorily predicted by the proposed model.     

Mixed mode crack propagation of homogenized cracks by the two-dimensional DDM analysis

The crack propagation process in rock mass is numerically estimated by two-dimensional stress analysis. Rock mass typically contains numerous cracks within, with varying extent and orientation. In order to analyze the mechanical interaction of cracks, the homogenization method is introduced too in this study. In the analysis, SC-DDM (stress compensation-displacement discontinuity method) and DDCM (displacement discontinuity comparison method) are applied to the crack homogenization model, and the stress intensity factors are calculated. Then the crack propagation of the model is analyzed, using the maximum circumferential stress criterion. The influences of the mechanical interaction between cracks to the crack propagation is discussed.     

Analysis of long-term deformations of MSE walls based on various corrosion scenarios

This paper deals with the long-term deformation of Mechanically Stabilized Earth (MSE) walls induced by the corrosion of the steel strips that ensure their internal stability. The analysis consists of defining assumptions regarding the spatial variations of the corrosion process throughout the wall, called corrosion scenarios, that define the evolution of the stiffness and strength of the steel strips. This evolution is introduced into finite element simulations of the behavior of a typical wall, in which interactions between the backfill and the strips are considered using a generalized homogenization procedure (called a multiphase model). The results of the simulations are used to discuss the influence of the heterogeneity of the corrosion process on the overall time evolution of the wall.     

Prediction of elastic and acoustic behaviors of calcarenite used for construction of historical monuments of Rabat,Morocco

Natural materials (e.g. rocks and soils) are porous media, whose microstructures present a wide diversity. They generally consist of a heterogeneous solid phase and a porous phase which may be fully or partially saturated with one or more fluids. The prediction of elastic and acoustic properties of porous materials is very important in many fields, such as physics of rocks, reservoir geophysics, civil engineering, construction field and study of the behavior of historical monuments. The aim of this work is to predict the elastic and acoustic behaviors of isotropic porous materials of a solid matrix containing dry, saturated and partially saturated spherical pores. For this, a homogenization technique based on the Mori–Tanaka model is presented to connect the elastic and acoustic properties to porosity and degree of water saturation. Non-destructive ultrasonic technique is used to determine the elastic properties from measurements of P-wave velocities. The results obtained show the influence of porosity and degree of water saturation on the effective properties. The various predictions of Mori–Tanaka model are then compared with experimental results for the elastic and acoustic properties of calcarenite.     

Three-scale stochastic homogenization of elastic recycled aggregate concrete based on nano-indentation digital images

In this paper, three-scale stochastic elastic finite element analyses are made for recycled aggregate concrete (RAC) based on nano-indentation digital images. The elastic property of RAC contains uncertainties across scales. It has both theoretical and practical values to model and predict its mechanical performance. Based on homogenization theory, effective stochastic elastic moduli of RAC at three different scales are obtained using moving window technique, nano-indentation digital images, and Monte-Carlo method. It involves the generation of a large number of random realizations of microstructure geometry based on different volume fraction of the inclusions and other parameters. The mean value, coefficient of variation and probability distribution of the effective elastic moduli are computed considering the material multiscale structure. The microscopic randomness is taken into account, and correlations of RAC among five phases are investigated. The effective elastic properties are used to obtain the global behavior of a composite structure. It is indicated that the response variability can be considerably affected by replacement percentage of recycled aggregates.     

On the modelling of stress-dilatancy behavior in weakly cemented sands

A comprehensive study on the stress-dilatancy behavior of cemented sand and its modeling is presented. The effect of confining pressure, relative density, and cement content on stress-dilatancy behavior are studied from the published experimental results and an additional series of experiments performed in this study. To facilitate a contrast and comparison of stress-dilatancy behavior between these datasets, a normalized stress ratio is proposed which removes the effect of mineralogy and morphology of parent sand. A set of key insights were obtained from this comparative study which aided in improving the stress-dilatancy relation; for example, the effect of initial conditions on stress-dilatancy behavior was found to be captured by the ratio of cohesion intercept (or tensile strength) and mean effective stress before shearing. The limitations of stress transformation, often used in modelling of cemented sand, were also systematically studied by a set of carefully designed experiments; it was found to be only applicable before gross yielding of cementation. After gross yielding, it is necessary to take in account of the breakage of bonds/cementation. The gross yield locus was identified from 70 experimental datasets and a cohesion/bond degradation model was formulated to model the stress-dilatancy behavior of cemented sand. The efficacy of stress-dilatancy relations (after including the gross yield locus and bond degradation behavior) is evaluated from the experimental results; the Rowe's stress-dilatancy relation was found to be most suitable with the proposed bond/cohesion degradation model.     

Multi-scale modeling of the thermal decomposition of fire retardant plywood

Due to the complexity and costs of full scale fire-test experiments, numerical simulations provide a useful alternative when investigating the fire behavior of new materials. The mass loss rate of the solid is one of the most important parameters in assessing fire behavior as it is directly linked with the pyrolysis gas flow rate and represents the initial factor of the combustion process. In this paper, fire retardant plywood is investigated with a focus on the solid mass loss rate modeling. A multi-scale approach is followed in order to establish the kinetic mechanism of thermal degradation. A combination of small scale and large scale tests were completed to fully develop and validate the proposed kinetic mechanism. For small scale testing, experiments are conducted by using thermo-gravimetric analysis coupled to gas analysis with FTIR technique under nitrogen and air atmospheres. These experiments were completed at several heating rates. Thermo-gravimetric results are used to propose a kinetic mechanism for the thermal decomposition of the solid and the kinetic parameters are calculated by using the genetic algorithms method. For larger-scale testing, experiments were carried out in a cone calorimeter coupled to a FTIR gas analyzer. The experiments were completed in air atmosphere in order to validate the kinetic mechanism developed from small-scale testing. The kinetic model developed is implemented into the general Gpyro model which takes into account both thermal and mass transfer phenomena inside the solid. The results showed good agreement between the model calculations and the experimental data.     

Circular footings resting on geotextile-reinforced sand bed

The note pertains to an experimental study made on circular footings resting on semi-infinite layer of sand reinforced with geotextiles. Using the concept of homogenization of such soils, both analytical and numerical analyses have also been conducted to predict the load-settlement behavior and compared with experimental observations. The study highlights the effect of the footing size, number of reinforcing layers, reinforcement placement pattern and bond length and the relative density of the soil on the load-settlement characteristics of the footings.     

Numerical Simulation of Model Tests of Pier-Shallow Foundation Systems Subjected to Earthquake Loads Using an Elasto-Uplift-Plastic Macro Element

A dynamic analysis model for the nonlinear behavior of a shallow foundation subjected to seismic loads is developed. A macro-element approach is revised assuming elasto-uplift-plastic behavior, in which uplifting and coupling effects of vertical, horizontal, and moment loads are taken into account. Large-scale shake table experiments of model pier footings are also conducted and simulated using the revised macro-element model. The numerical result reveals that the shape of the hysteresis loops for coupled load-displacement relationships is predicted very well, including the effects of uplift. In addition, the revised model can account for settlement with some inclination that has accumulated during the excitation.     

A model of multi-purpose shopping trip behavior

Existing utility-based models of complex choice behavior do not adequately deal with the interdependencies of chained choices. In this paper, we introduce a model of multi-purpose shopping which is aimed at overcoming this shortcoming. In the proposed model, dependencies between choices within as well as between trips are covered by a recursive definition of trip utility. The standard log-likelihood estimation procedure is used to calibrate the model. Simulation experiments show that estimation results are satisfactorily accurate and robust. Comparison of the model to a conventional choice model using simulated data indicates that even low tendencies to make multi-purpose trips have a significant influence on predicted destination choice. Furthermore, it is shown that conventional models do not satisfactorily predict simulated multi-purpose behavior.